University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Multi-Objective Hybrid Metaheuristic Search Algorithm for Distributed Reentrant Permutation Flow Shop Scheduling Via Considering Preventive Maintenance under Uncertainty Multi-Objective Hybrid Metaheuristic Search Algorithm for Distributed Reentrant Permutation Flow Shop Scheduling Via Considering Preventive Maintenance under Uncertainty 1 22 23067 10.22108/jpom.2018.92504.0 FA Ali Akbar Hasani Assistant professor, Department of Industrial Engieering and Management, Shahrood University of Technology, Shahrood, Iran Journal Article 2016 06 20 Abstract: Distributing the production activities among the supply chain facilities with regard to the considered criteria can have a significant impact on the productive management. In this paper, a comprehensive mathematical model for reentrant permutation flow shop scheduling via considering a preventive maintenance and distributed jobs on different facilities is proposed. The uncertainty of the time of preventive maintenance operation is handled using robust optimization technique based on the uncertainty budget approach. Job assignment to production facilities and job scheduling are determined in the proposed model by considering multiple objectives include Cmax minimization, production cost minimization, and average tardiness. Due to the NP-hard nature of the proposed flow shop scheduling problem, a new hybrid meta-heuristic based on the novel adaptive large neighborhood search and the simulated annealing is adopted. The obtained results from an extensive numerical experimentation indicate the efficiency of the proposed model and solution algorithm to tackle the proposed problem. Introduction: In certain manufacturing industries, it has been observed that the classical assumption of flow shop scheduling, stating that each job visits each machine exactly once, is occasionally violated. The prime example can be noticed in the high-tech industries, i.e. semiconductor wafer fabrication in which the operation processes of the jobs are performed by re-visiting some workstations (Gupta & Sivakumar, 2006). The scheduling problem of this nature of processing is categorized as a distinct flow shop with reentrant line configuration, called reentrant flow shop scheduling (RFS) (Katragjini et. al., 2015). The significance of RFS is the processing layers l. Each layer begins from the first workstation and completes on the last workstation. It means that once a job finished a layer of a set of operations, it will repeat its process to the next layer starting on the first workstation until all operations are completed. The RFS scheduling has been an active research area and attracted a considerable attention since the past decade due to the development and improvement of high-tech industry. The complexity of RFS cannot be circumvented since it involves more operations than the classical flow shop. Moreover, the cyclic operations where the jobs with higher layers may overlap other jobs in the same work station are essential to be considered. As a result, these complexities have triggered the development of the efficient scheduling approaches to improve the system performance. Various researchers surveyed the scheduling techniques in semiconductor manufacturing and providing the global view on reentrant scheduling problems. Another form of RFS is reentrant permutation flow shop (RPFS) where at each level no passing is permitted, that is, not only the machine sequence the same for all jobs, but also the job sequence is the same for each machine (Rifai et al., 2016). Despite the enormous literature on the RFS, most studies -if not all- base their research on the assumption that the process only involves a single production line. Some studies exploredthe problem on hybrid RFS where the production stages have more than one machines available to process the jobs. Nevertheless, hybrid RFS is based on the single production line. Nowadays, single factory firms are less common, with multi-plant companies and supply chains taking a more important role in practice. Several literatures mentioned that multiple production lines with more than one production center, named as distributed manufacturing system, enables companies to achieve higher product quality, lower production costs and lower management risks. However, existing studies focused more on the economic field anddistributed finite capacity scheduling is seldom tackled. Materials and Methods:In this section, a novel hybrid meta-heuristic via considering the specific assumptions of the flow shop problem as a NP-hard problem is proposed. The proposed solution algorithm incorporates adaptive large neighborhood search and the simulated annealing algorithms. Various new construction and deconstruction neighborhood structures are applied in the proposed adaptive large neighborhood search algorithm. Details of the proposed algorithm is presented in Fig.1. Results and Discussion: The results of the proposed solution algorithm assessment are presented based on the two common performance assessment criteria which are proposed in the literature after 10 times runs of the applied solution algorithms. These criteria are the average number of obtained Pareto solution at each iteration of the algorithm and average number of Pareto solutions which are not dominated by solutions from other compared algorithms. In addition, computational time is considered as a third criteria for performance assessment of the proposed solution algorithm (See Table 1). Obtained results indicate the superiority of the proposed solution algorithm. Fig. 1- Peseudo code of the proposed solution algorithm Table 1- Performance assessment of the proposed solution algorithm Compared Alg. Proposed Alg. Pro. Compared Alg. Proposed Alg. Pro. 1 2 3 1 2 3 1 2 3 1 2 3 0.7270 39.30 72.01 0.4129 25.95 57.12 15 0.6120 18.71 3392.26 0.5114 13.80 3019.18 75 0.6991 34.43 180.23 0.5972 28.80 152.11 30 0.6523 18.01 5900.74 0.5304 11.20 5631.07 90 0.9009 48.23 479.19 0.6543 38.10 398.06 45 0.6914 15.23 6801.69 0.5713 11.83 6594.29 105 0.9207 47.3 1308.21 0.7810 36.30 1200.47 60 Conclusion: In this study, a comprehensive optimization model for an extended reentrant permutation flow shop scheduling via considering a preventive maintenance and distributed jobs on different facilities is proposed. To enhance the applicability of the proposed model, uncertainty of the time of preventive maintenance operation is handled using robust optimization technique based on the uncertainty budget approach. In the proposed mathematical model, multiple objectives include Cmax minimization, production cost minimization, and average tardiness are considered. The aim of the proposed model is to determine the job assignment to production facilities and job scheduling. A new hybrid meta-heuristic based on the novel adaptive large neighborhood search and the simulated annealing is applied as a consequence of the NP-hard nature of the proposed flow shop scheduling problem,. The obtained results from an extensive numerical experimentation indicate the efficiency of the proposed model and solution algorithm to tackle the proposed problem. References Gupta, A. K., & Sivakumar, A. I. (2006). “Job Shop Scheduling Techniques In Semiconductor Manufacturing”. Int. J. Adv. Manuf. Technol, 27(11), 1163-1169. Katragjini, K., Vallada, E., & Ruiz, R. (2015). “Rescheduling Flowshops Under Simultaneous Disruptions”. Paper presented at the 6th IESM Conference, Seville, Spain. Rifai, A. P., Nguyen, H. T., & Dawal, S. Z. M. (2016). “Multi-Objective Adaptive Large Neighborhood Search For Distributed Reentrant Permutation Flow Shop Scheduling”. Applied Soft Computing, 40(1), 42–57. Abstract: Distributing the production activities among the supply chain facilities with regard to the considered criteria can have a significant impact on the productive management. In this paper, a comprehensive mathematical model for reentrant permutation flow shop scheduling via considering a preventive maintenance and distributed jobs on different facilities is proposed. The uncertainty of the time of preventive maintenance operation is handled using robust optimization technique based on the uncertainty budget approach. Job assignment to production facilities and job scheduling are determined in the proposed model by considering multiple objectives include Cmax minimization, production cost minimization, and average tardiness. Due to the NP-hard nature of the proposed flow shop scheduling problem, a new hybrid meta-heuristic based on the novel adaptive large neighborhood search and the simulated annealing is adopted. The obtained results from an extensive numerical experimentation indicate the efficiency of the proposed model and solution algorithm to tackle the proposed problem. Introduction: In certain manufacturing industries, it has been observed that the classical assumption of flow shop scheduling, stating that each job visits each machine exactly once, is occasionally violated. The prime example can be noticed in the high-tech industries, i.e. semiconductor wafer fabrication in which the operation processes of the jobs are performed by re-visiting some workstations (Gupta & Sivakumar, 2006). The scheduling problem of this nature of processing is categorized as a distinct flow shop with reentrant line configuration, called reentrant flow shop scheduling (RFS) (Katragjini et. al., 2015). The significance of RFS is the processing layers l. Each layer begins from the first workstation and completes on the last workstation. It means that once a job finished a layer of a set of operations, it will repeat its process to the next layer starting on the first workstation until all operations are completed. The RFS scheduling has been an active research area and attracted a considerable attention since the past decade due to the development and improvement of high-tech industry. The complexity of RFS cannot be circumvented since it involves more operations than the classical flow shop. Moreover, the cyclic operations where the jobs with higher layers may overlap other jobs in the same work station are essential to be considered. As a result, these complexities have triggered the development of the efficient scheduling approaches to improve the system performance. Various researchers surveyed the scheduling techniques in semiconductor manufacturing and providing the global view on reentrant scheduling problems. Another form of RFS is reentrant permutation flow shop (RPFS) where at each level no passing is permitted, that is, not only the machine sequence the same for all jobs, but also the job sequence is the same for each machine (Rifai et al., 2016). Despite the enormous literature on the RFS, most studies -if not all- base their research on the assumption that the process only involves a single production line. Some studies exploredthe problem on hybrid RFS where the production stages have more than one machines available to process the jobs. Nevertheless, hybrid RFS is based on the single production line. Nowadays, single factory firms are less common, with multi-plant companies and supply chains taking a more important role in practice. Several literatures mentioned that multiple production lines with more than one production center, named as distributed manufacturing system, enables companies to achieve higher product quality, lower production costs and lower management risks. However, existing studies focused more on the economic field anddistributed finite capacity scheduling is seldom tackled. Materials and Methods:In this section, a novel hybrid meta-heuristic via considering the specific assumptions of the flow shop problem as a NP-hard problem is proposed. The proposed solution algorithm incorporates adaptive large neighborhood search and the simulated annealing algorithms. Various new construction and deconstruction neighborhood structures are applied in the proposed adaptive large neighborhood search algorithm. Details of the proposed algorithm is presented in Fig.1. Results and Discussion: The results of the proposed solution algorithm assessment are presented based on the two common performance assessment criteria which are proposed in the literature after 10 times runs of the applied solution algorithms. These criteria are the average number of obtained Pareto solution at each iteration of the algorithm and average number of Pareto solutions which are not dominated by solutions from other compared algorithms. In addition, computational time is considered as a third criteria for performance assessment of the proposed solution algorithm (See Table 1). Obtained results indicate the superiority of the proposed solution algorithm. Fig. 1- Peseudo code of the proposed solution algorithm Table 1- Performance assessment of the proposed solution algorithm Compared Alg. Proposed Alg. Pro. Compared Alg. Proposed Alg. Pro. 1 2 3 1 2 3 1 2 3 1 2 3 0.7270 39.30 72.01 0.4129 25.95 57.12 15 0.6120 18.71 3392.26 0.5114 13.80 3019.18 75 0.6991 34.43 180.23 0.5972 28.80 152.11 30 0.6523 18.01 5900.74 0.5304 11.20 5631.07 90 0.9009 48.23 479.19 0.6543 38.10 398.06 45 0.6914 15.23 6801.69 0.5713 11.83 6594.29 105 0.9207 47.3 1308.21 0.7810 36.30 1200.47 60 Conclusion: In this study, a comprehensive optimization model for an extended reentrant permutation flow shop scheduling via considering a preventive maintenance and distributed jobs on different facilities is proposed. To enhance the applicability of the proposed model, uncertainty of the time of preventive maintenance operation is handled using robust optimization technique based on the uncertainty budget approach. In the proposed mathematical model, multiple objectives include Cmax minimization, production cost minimization, and average tardiness are considered. The aim of the proposed model is to determine the job assignment to production facilities and job scheduling. A new hybrid meta-heuristic based on the novel adaptive large neighborhood search and the simulated annealing is applied as a consequence of the NP-hard nature of the proposed flow shop scheduling problem,. The obtained results from an extensive numerical experimentation indicate the efficiency of the proposed model and solution algorithm to tackle the proposed problem. References Gupta, A. K., & Sivakumar, A. I. (2006). “Job Shop Scheduling Techniques In Semiconductor Manufacturing”. Int. J. Adv. Manuf. Technol, 27(11), 1163-1169. Katragjini, K., Vallada, E., & Ruiz, R. (2015). “Rescheduling Flowshops Under Simultaneous Disruptions”. Paper presented at the 6th IESM Conference, Seville, Spain. Rifai, A. P., Nguyen, H. T., & Dawal, S. Z. M. (2016). “Multi-Objective Adaptive Large Neighborhood Search For Distributed Reentrant Permutation Flow Shop Scheduling”. Applied Soft Computing, 40(1), 42–57.

https://jpom.ui.ac.ir/article_23067_20a797a907a8b32f4900351514729ca2.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Developing Dynamic Network DEA Approach and its Combination with Interval Type-2 Fuzzy Sets Theory Case of Passenger Airports’ Performance Based on Sustainability Principles Developing Dynamic Network DEA Approach and its Combination with Interval Type-2 Fuzzy Sets Theory Case of Passenger Airports’ Performance Based on Sustainability Principles 23 36 23060 10.22108/jpom.2018.92492.0 FA Laya Olfat Associate Professor, Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran Maghsoud Amiri Professor, Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran Jahanyar BamdadSoufi Assistant Professor, Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran Mahsa Pishdar Ph.D. Student, Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran Journal Article 2016 04 04 Abstract: Fuzzy DEA methods have been introduced to deal with the fuzziness of variables. Although, some of these variables are affected by uncertainty and also information granularity, the membership function of fuzzy set is certain and this contrasts with the fuzzy concept as a whole. Type-2 fuzzy sets are introduced because of this and their membership functions have the nature of fuzzy type-1. The calculations of type-2 fuzzy sets are very complicated. However, interval type-2 fuzzy sets which have the characteristics of type-2 fuzzy sets and do not add any complexity to the calculation process can be applied to deal with such a problem. That is why in this paper, it is explored that how an extension of interval type-2 fuzzy dynamic network DEA approach helps to measure airports’ sustainability. Sustainable airports play an irrefutable role in making transportation systems sustainable. Such an integrative approach in DEA models is unprecedented. So, this extension of DEA is valuable from both technical and conceptual aspects. Introduction: Airports are an essential component of aviation (Knudsen, 2004). The importance of airports becomes clearer when it comes to the fact that aviation traffic is more than before and, therefore, sustainability becomes difficult. While, various studies have suggested that the sustainability of airports is essential to improve the performance of these systems, improve the living conditions of the public and increase the airport's credit (Brian, 2005; ICAO, 2012; SAGA, 2015). Paying attention to the concept of sustainability in managing airports has various benefits, such as increased competitiveness by purifying activities, reducing operating costs, and reducing costs for life cycle of materials and equipment, better use of assets, utilization newer and better technologies, reducing asset development costs, getting more support from the community, improving working conditions and, as a result, improving employee productivity, reducing environmental risks, health, safety and promotion (SAGA, 2015; Bretzke, 2013; TRB, 2012; ACARE, 2011; Too, Earl, 2010). For the reasons mentioned, it can be said that it is necessary to pay attention to the sustainability of the passenger airports of the country. Certainly, before adopting any approach, the current situation must be assessed correctly. Various methods have been used to evaluate performance, but Data Envelopment Analysis (DEA) is one of the most widely used methods (Azizi et al., 2004). Data envelopment analysis is a functional and nonparametric method that allows consideration of various components as input and output or intermediate activities (Bray et al., 2015). However, no research has been found to determine the performance of airports in accordance with the principles of sustainability in Iran. Materials and Methods: Type-2 fuzzy Dynamic Data Envelopment Analysis (DEA) is used to assess the performance of Iran’s passenger airports based on sustainability development. By use of Dynamic Network Data Envelopment Analysis, one can see how the different parts of a decision unit can be linked. It also shows how the past performance of a decision-making unit can affect its current performance. In this type of data envelopment analysis, the function of the decision-making unit is transmitted through time-based intermediaries to the next period. Thus via using dynamic data envelopment analysis method, it is possible to consider the activities of different parts of a decision unit and also the efficiency with respect to time periods. However, the point is that in the real world, due to the increasing socioeconomic complexity and the inherent ambiguity of human thinking, there is no possibility of precise determination of many of the components. For this reason, type-2 fuzzy theory is employed that its membership function is the fuzzy of the first type. Since the complexity of calculations while using type-2 fuzzy set is high, interval type-2 fuzzy is applied. The 20 most popular passenger airports in Iran are selected to evaluate their performance in accordance with the principles of sustainability principles and via the help of the developed DEA model. Results and Discussion: Results of investigation show that Larestan Airport is the most efficient one among all and the last rank is allocated to the Isfahan airport considering fixed return to scale while in variable return to scale, Shiraz airport gets the last rank. The efficiency intervals of airports such as Larestan, Gorgan, Rasht and Yazd have little difference in two modes of return to scale. For this reason, we can say that there is no significant function inefficiency about these airports. But this difference is more evident in the efficiency of airports such as Mashhad. Airports, whose performance is generally low or are inefficient, are able to provide a groundbreaking improvement with appropriate benchmarking. Since airports operate in different conditions, difference in climatic conditions and the in workforce etc. should be considered while benchmarking. References ACARE (Advisory Council for Aeronautics Research in Europe) (2011). "Flight path 2050 Europe’s Vision for Aviation". Luxembourg: Publications Office of the European Union. Azizi, H., Kordrostami, S., & Amirteimoori, A. (2015). "Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers". Computers & Industrial Engineering, 79, 42-51. Azizi, H., Jafari Shaerlar, A., & Farzipoor Saen, R. (2014). "A new Approach for Considering a Dual-Role Factor in Supplier Selection Problem: DEA with efficient and inefficient frontiers". Journal of production and operation management. 6(2), 129-144. Bray, S., Caggiani, l., & Ottomanelli, M. (2015). "Measuring transport systems efficiency under uncertainty by fuzzy sets theory based Data Envelopment Analysis: theoretical and practical comparison with traditional DEA model". Transportation Research Procedia, 5, 186 – 200. Bretzke, W.R. (2013). "Service Quality Versus Sustainability: A New Conflict of Objectives". Information Technology in Environmental Engineering Part of the series Environmental Science and Engineering, Springer, 179-190. Brian, E. (2005). "The Modern Airport Terminal: New Approaches to Airport Architecture". 2nd Edition, Taylor & Francis. ICAO (International Civil Aviation Organization) (2012). "Sustainable Future for Aviation: ICAO Rio+20 Global Initiative". http://climate-l.iisd.org/news/icao-publishes-booklet-for-rio20-decision makers (accessed 14.09.2015). Knudsen, F.B. (2004). "Defining Sustainability in the Aviation Sector". Brussell: Eurocontrol Experimental Centre. SAGA (Sustainable Aviation Guidance Alliance) (2015). "Learn". http://www.airportsustainability.org/learn, (accessed 16.12.2015). Transport Research Board (TRB) (2011). "Critical Issues in Aviation and the Environment 2011". Washington, DC: TRB. Too, L., & Earl, L. (2010). "Public transport service quality and sustainable development: a community stakeholder perspective". Sustainable Development. 18(1), 51-61. Abstract: Fuzzy DEA methods have been introduced to deal with the fuzziness of variables. Although, some of these variables are affected by uncertainty and also information granularity, the membership function of fuzzy set is certain and this contrasts with the fuzzy concept as a whole. Type-2 fuzzy sets are introduced because of this and their membership functions have the nature of fuzzy type-1. The calculations of type-2 fuzzy sets are very complicated. However, interval type-2 fuzzy sets which have the characteristics of type-2 fuzzy sets and do not add any complexity to the calculation process can be applied to deal with such a problem. That is why in this paper, it is explored that how an extension of interval type-2 fuzzy dynamic network DEA approach helps to measure airports’ sustainability. Sustainable airports play an irrefutable role in making transportation systems sustainable. Such an integrative approach in DEA models is unprecedented. So, this extension of DEA is valuable from both technical and conceptual aspects. Introduction: Airports are an essential component of aviation (Knudsen, 2004). The importance of airports becomes clearer when it comes to the fact that aviation traffic is more than before and, therefore, sustainability becomes difficult. While, various studies have suggested that the sustainability of airports is essential to improve the performance of these systems, improve the living conditions of the public and increase the airport's credit (Brian, 2005; ICAO, 2012; SAGA, 2015). Paying attention to the concept of sustainability in managing airports has various benefits, such as increased competitiveness by purifying activities, reducing operating costs, and reducing costs for life cycle of materials and equipment, better use of assets, utilization newer and better technologies, reducing asset development costs, getting more support from the community, improving working conditions and, as a result, improving employee productivity, reducing environmental risks, health, safety and promotion (SAGA, 2015; Bretzke, 2013; TRB, 2012; ACARE, 2011; Too, Earl, 2010). For the reasons mentioned, it can be said that it is necessary to pay attention to the sustainability of the passenger airports of the country. Certainly, before adopting any approach, the current situation must be assessed correctly. Various methods have been used to evaluate performance, but Data Envelopment Analysis (DEA) is one of the most widely used methods (Azizi et al., 2004). Data envelopment analysis is a functional and nonparametric method that allows consideration of various components as input and output or intermediate activities (Bray et al., 2015). However, no research has been found to determine the performance of airports in accordance with the principles of sustainability in Iran. Materials and Methods: Type-2 fuzzy Dynamic Data Envelopment Analysis (DEA) is used to assess the performance of Iran’s passenger airports based on sustainability development. By use of Dynamic Network Data Envelopment Analysis, one can see how the different parts of a decision unit can be linked. It also shows how the past performance of a decision-making unit can affect its current performance. In this type of data envelopment analysis, the function of the decision-making unit is transmitted through time-based intermediaries to the next period. Thus via using dynamic data envelopment analysis method, it is possible to consider the activities of different parts of a decision unit and also the efficiency with respect to time periods. However, the point is that in the real world, due to the increasing socioeconomic complexity and the inherent ambiguity of human thinking, there is no possibility of precise determination of many of the components. For this reason, type-2 fuzzy theory is employed that its membership function is the fuzzy of the first type. Since the complexity of calculations while using type-2 fuzzy set is high, interval type-2 fuzzy is applied. The 20 most popular passenger airports in Iran are selected to evaluate their performance in accordance with the principles of sustainability principles and via the help of the developed DEA model. Results and Discussion: Results of investigation show that Larestan Airport is the most efficient one among all and the last rank is allocated to the Isfahan airport considering fixed return to scale while in variable return to scale, Shiraz airport gets the last rank. The efficiency intervals of airports such as Larestan, Gorgan, Rasht and Yazd have little difference in two modes of return to scale. For this reason, we can say that there is no significant function inefficiency about these airports. But this difference is more evident in the efficiency of airports such as Mashhad. Airports, whose performance is generally low or are inefficient, are able to provide a groundbreaking improvement with appropriate benchmarking. Since airports operate in different conditions, difference in climatic conditions and the in workforce etc. should be considered while benchmarking. References ACARE (Advisory Council for Aeronautics Research in Europe) (2011). "Flight path 2050 Europe’s Vision for Aviation". Luxembourg: Publications Office of the European Union. Azizi, H., Kordrostami, S., & Amirteimoori, A. (2015). "Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers". Computers & Industrial Engineering, 79, 42-51. Azizi, H., Jafari Shaerlar, A., & Farzipoor Saen, R. (2014). "A new Approach for Considering a Dual-Role Factor in Supplier Selection Problem: DEA with efficient and inefficient frontiers". Journal of production and operation management. 6(2), 129-144. Bray, S., Caggiani, l., & Ottomanelli, M. (2015). "Measuring transport systems efficiency under uncertainty by fuzzy sets theory based Data Envelopment Analysis: theoretical and practical comparison with traditional DEA model". Transportation Research Procedia, 5, 186 – 200. Bretzke, W.R. (2013). "Service Quality Versus Sustainability: A New Conflict of Objectives". Information Technology in Environmental Engineering Part of the series Environmental Science and Engineering, Springer, 179-190. Brian, E. (2005). "The Modern Airport Terminal: New Approaches to Airport Architecture". 2nd Edition, Taylor & Francis. ICAO (International Civil Aviation Organization) (2012). "Sustainable Future for Aviation: ICAO Rio+20 Global Initiative". http://climate-l.iisd.org/news/icao-publishes-booklet-for-rio20-decision makers (accessed 14.09.2015). Knudsen, F.B. (2004). "Defining Sustainability in the Aviation Sector". Brussell: Eurocontrol Experimental Centre. SAGA (Sustainable Aviation Guidance Alliance) (2015). "Learn". http://www.airportsustainability.org/learn, (accessed 16.12.2015). Transport Research Board (TRB) (2011). "Critical Issues in Aviation and the Environment 2011". Washington, DC: TRB. Too, L., & Earl, L. (2010). "Public transport service quality and sustainable development: a community stakeholder perspective". Sustainable Development. 18(1), 51-61.

https://jpom.ui.ac.ir/article_23060_e91a20ad155a80e164f240f06c0a84c9.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Warranty Policy Determination using Data-Mining Association Rules (Case study: Electronic Facilities Company) Warranty Policy Determination using Data-Mining Association Rules (Case study: Electronic Facilities Company) 37 56 23059 10.22108/jpom.2018.92487.0 FA Safar Fazli Associate Professor of Industrial Management, Imam Khomeini International University, Qazvin, Iran Reyhaneh Jamaati Tafti M.Sc. of Industrial Management, Imam Khomeini International University, Qazvin, Iran Journal Article 2016 03 12 Abstract: Nowadays, varieties of warranties are presented by manufacturers. Improving the warranty policy imposes some costs on the producers. As a result, one needs to rely on factual and reliable data as well as the data on defects and repair when it comes to making warranty policy. To this end, this study uses data mining method. That is, an electronic equipment company's warranty data including 3500 defects reports within a 5-year period sample were mined, using association rules. This yielded significant patterns based on the data. Out of total derived rules and patterns, some rules describe the associations between the products and their defects and repairs better than others. So, having these information, we could determine the warranty policy for 24 products. The findings of this study can reduce warranty costs via optimization of warranty policies decisions. Introduction: Buyers of products want assurance that the product will perform satisfactorily over its useful life when operated properly. This is achieved through post-sale support (also called product support) provided by the manufacturer. Warranty is one of post-sale supports that serves as a way to promote the competiveness capacity of the products. The complex competitive market and customers' demands have increased the competitions among the manufacturers in order to provide more customers with better warranties. Consequently, nowadays, varieties of warranties are presented by manufacturers. Effective management of product warranty requires proper evaluation of alternative warranty policies (Blischke & Murthy, 1992). Offering better warranty policies conveys greater assurance to buyers and can result in greater sales. However, this increases the cost of servicing the warranty. As a result, one needs to rely on factual and reliable data as well as the data on defects and repair rather than estimation and guess when it comes to making warranty policy. A producer can use the data gathered during the warranty period (generally called “warranty data”) for various purposes. Since warranty data features a variety of failure modes, it can activate an early warning for design errors, highlight faults in the manufacturing process, and help enhance a product by understanding customer usage proﬁle. This information can also help in estimating future expenses (Jeon & Sohn, 2015). Warranty data are strictly conﬁdential for most companies because they relate to product quality, reliability, and are therefore critical to consumers’ product goodwill (Buddhakulsomsiri & Zakarian, 2009). Materials and Methods:Product quality problems are monitored during the warranty period through the claims ﬁled against the products. This process generates large volumes of warranty data records, such as product problems in the form of repair related labor codes, problem descriptions, actions taken, repair dates, and repair costs (labor and parts). Analyses of these data records may provide signiﬁcant beneﬁts to product manufacturers (Buddhakulsomsiri & Zakarian, 2009). To this end, this study uses association rule method. The association rule (AR), which is a data-mining method, is used to determine the degree of relevance between variables (Jeon & Sohn, 2015). In this paper, an electronic equipment company's warranty database including 3500 defects reports and resulting warranties within a 5-year period sample were mined, using association rules. This yielded significant patterns and rules based on the data. Data processing is done using SPSS Modeler 14.2 software. Results and Discussion: The results were obtained from the implementation of the model by the software, including 475 association rules. Out of total derived rules, 72 rules which describe the associations between the products and their defects and repairs better than others, were selected. These rules clarify the relationship between various products and their types of defects, the intensity of the defect, the number of the defect, the repeatability of the defect, reparability and the repair costs. This information provides the knowledge needed to decide on all variables in a warranty policy. And having this information, we could determine the warranty policy for 24 different products, in 4 categories of ‘warranty period’, ‘warranty cost’, ‘Compensation method’ and ‘warranty dimensions’. Conclusion: The findings of this study can decrease warranty costs via optimization of warranty policies decisions. Because, implementing these warranty policies reduces the manufacturer's risk of warranted products and reduces the cost of warranty service. Consequently, companies not only use the huge amount of stored data that contains valuable information about the various product failure and product warranties, but also will be interested both in the promotional benefits of the warranties in attracting customers, and in the benefits of reduction of the warranty costs by providing a good warranty policy for their products. This finally leads to increased profitability of the organization while achieving competitive advantage. The producers are recommended to reduce the warranty costs and to increase the profitability of production industries, using the proposed method as well as numerous data to make warranty policies in different firms. References Blischke, W.R. & Murthy, D.N.P. (1992a) “Product warranty management – I: A taxonomy for warranty policies”, European Journal of Operational Research, 62, 127–148. Buddhakulsomsiri, J. & Zakarian, A. (2009) “Sequential pattern mining algorithm for automotive warranty data”, Computers and Industrial Engineering, 57)1), 137–147. Jeon, J. & Sohn, S.Y. (2015) “Product failure pattern analysis from warranty data using association rule and Weibull regression analysis: A case study”, Reliability Engineering and System Safety, 133, 176–183. Abstract: Nowadays, varieties of warranties are presented by manufacturers. Improving the warranty policy imposes some costs on the producers. As a result, one needs to rely on factual and reliable data as well as the data on defects and repair when it comes to making warranty policy. To this end, this study uses data mining method. That is, an electronic equipment company's warranty data including 3500 defects reports within a 5-year period sample were mined, using association rules. This yielded significant patterns based on the data. Out of total derived rules and patterns, some rules describe the associations between the products and their defects and repairs better than others. So, having these information, we could determine the warranty policy for 24 products. The findings of this study can reduce warranty costs via optimization of warranty policies decisions. Introduction: Buyers of products want assurance that the product will perform satisfactorily over its useful life when operated properly. This is achieved through post-sale support (also called product support) provided by the manufacturer. Warranty is one of post-sale supports that serves as a way to promote the competiveness capacity of the products. The complex competitive market and customers' demands have increased the competitions among the manufacturers in order to provide more customers with better warranties. Consequently, nowadays, varieties of warranties are presented by manufacturers. Effective management of product warranty requires proper evaluation of alternative warranty policies (Blischke & Murthy, 1992). Offering better warranty policies conveys greater assurance to buyers and can result in greater sales. However, this increases the cost of servicing the warranty. As a result, one needs to rely on factual and reliable data as well as the data on defects and repair rather than estimation and guess when it comes to making warranty policy. A producer can use the data gathered during the warranty period (generally called “warranty data”) for various purposes. Since warranty data features a variety of failure modes, it can activate an early warning for design errors, highlight faults in the manufacturing process, and help enhance a product by understanding customer usage proﬁle. This information can also help in estimating future expenses (Jeon & Sohn, 2015). Warranty data are strictly conﬁdential for most companies because they relate to product quality, reliability, and are therefore critical to consumers’ product goodwill (Buddhakulsomsiri & Zakarian, 2009). Materials and Methods:Product quality problems are monitored during the warranty period through the claims ﬁled against the products. This process generates large volumes of warranty data records, such as product problems in the form of repair related labor codes, problem descriptions, actions taken, repair dates, and repair costs (labor and parts). Analyses of these data records may provide signiﬁcant beneﬁts to product manufacturers (Buddhakulsomsiri & Zakarian, 2009). To this end, this study uses association rule method. The association rule (AR), which is a data-mining method, is used to determine the degree of relevance between variables (Jeon & Sohn, 2015). In this paper, an electronic equipment company's warranty database including 3500 defects reports and resulting warranties within a 5-year period sample were mined, using association rules. This yielded significant patterns and rules based on the data. Data processing is done using SPSS Modeler 14.2 software. Results and Discussion: The results were obtained from the implementation of the model by the software, including 475 association rules. Out of total derived rules, 72 rules which describe the associations between the products and their defects and repairs better than others, were selected. These rules clarify the relationship between various products and their types of defects, the intensity of the defect, the number of the defect, the repeatability of the defect, reparability and the repair costs. This information provides the knowledge needed to decide on all variables in a warranty policy. And having this information, we could determine the warranty policy for 24 different products, in 4 categories of ‘warranty period’, ‘warranty cost’, ‘Compensation method’ and ‘warranty dimensions’. Conclusion: The findings of this study can decrease warranty costs via optimization of warranty policies decisions. Because, implementing these warranty policies reduces the manufacturer's risk of warranted products and reduces the cost of warranty service. Consequently, companies not only use the huge amount of stored data that contains valuable information about the various product failure and product warranties, but also will be interested both in the promotional benefits of the warranties in attracting customers, and in the benefits of reduction of the warranty costs by providing a good warranty policy for their products. This finally leads to increased profitability of the organization while achieving competitive advantage. The producers are recommended to reduce the warranty costs and to increase the profitability of production industries, using the proposed method as well as numerous data to make warranty policies in different firms. References Blischke, W.R. & Murthy, D.N.P. (1992a) “Product warranty management – I: A taxonomy for warranty policies”, European Journal of Operational Research, 62, 127–148. Buddhakulsomsiri, J. & Zakarian, A. (2009) “Sequential pattern mining algorithm for automotive warranty data”, Computers and Industrial Engineering, 57)1), 137–147. Jeon, J. & Sohn, S.Y. (2015) “Product failure pattern analysis from warranty data using association rule and Weibull regression analysis: A case study”, Reliability Engineering and System Safety, 133, 176–183.

https://jpom.ui.ac.ir/article_23059_53df78140d00f82072224d6999f07829.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Integrated production-distribution planning in a reverse supply chain via multi-objective mathematical modeling; case study in a high-tech industry Integrated production-distribution planning in a reverse supply chain via multi-objective mathematical modeling; case study in a high-tech industry 57 76 23061 10.22108/jpom.2018.101750.1011 FA Saeed Rezaie Moghadam PhD student in Industrial Engineering, Department of Industrial Engineering, Malek-e-Ashtar University of Technology, Isfahan, Iran Ommolbanin Yousefi Assistant Professor, Department of Industrial Engineering, Malek-e-Ashtar University of Technology, Isfahan, Iran Mehdi Karbasian Associate Professor, Department of Industrial Engineering, Malek-e-Ashtar University of Technology, Isfahan, Iran Bijan Khayambashi Assistant Professor, Department of Industrial Engineering, Malek-e-Ashtar University of Technology, Isfahan, Iran Journal Article 2017 01 14 Abstract: This article presents an integrated production-distribution plan in a reverse supply chain via multi objective mathematical modeling in a high-tech environment. The objectives of the proposed model include 1) minimizing total costs including production, maintenance, inventory and manpower costs, 2) maximizing customer and supplier satisfaction, and 3) maximizing the quality of manufactured products. The supply chain consists of several suppliers, a producer, customers, a repair center to repair the customer's goods and a repair and maintenance center for repairing or disposing products that have passed their warranty period. Among the contributions of this research, we can consider such issues as considering the quality of products manufactured, returned or supplied from suppliers in order to realize the win-win relationship with suppliers, using the maximum capacity of suppliers and supply of parts by each reconstruction center. In order to validate the model, it is solved for some examples using Lingo software and LP metric method. Introduction: In reverse supply chain, what is addressed is recycling and reconstructing the products which are spending final stage of their life cycle. In this regard, after gathering and inspecting the returned products, they are partitioned in to recyclable and non-recyclable (scrap) products (Mirzapour et. al, 2013). Aggregate production planning is a process that determines the optimal level of production and stock inventory to meet the demands for the product in a long term period which considering the capacity limitation of the means and resources (Gholamian et al, 2015). In this research, investigation is regarding designing and solving a mathematics model for aggregate production planning in reverse supply chain in a high-tech industry. High-tech products are usually made up of chemical, mechanical, and electronic components. Inspection of the products in the supply chain of latter industry is of demolition type, that is, in case where the quality of the products is not confirmed by the customer, they are in masse retuned to the supplier. The returned products are either demolished in the re-construction units or delivered to the producer after re-construction. Also, in case of the non-usage of the products by the customer after technical warranty expiration, they are dispatched to the repair and maintenance unit and after undergoing correctional measures, they are re-dispatched to the customer or producer. The aim of the present research is to conduct an investigation into the performance manner of the producer in making decision regarding producing the afore-mentioned products. In order to achieve objectives, the producer can manufacture the required products on his/her own plant. Accordingly, he/she should decide on considering the capacity of available means and facilities, production expenditures, and the quality of the produced commodity, what measure of products to produce at regular working hours, and what amount to produce at non-regular (over-time) working hours. In his/her aggregate production planning, he/she might also decide on out-sourcing the production of a portion of his/her required products to outside suppliers. Such planning becomes of utmost importance since he/she should decide- while considering such requisite indices and criteria as expenditure, quality level, and priority- what percentage of the products to delegate to what supplier. Along this line in the proposed model, a win-win relation with the suppliers is deemed essential. Thus, in the model offered here, the optimization of the customer’s satisfaction is taken into account so that- by considering customer’s prioritization- the shortage rate of the unmet demands on the part of the supplier is kept at minimum. Materials and Methods: The supply chain of the proposed model contains three levels of suppliers, producer, consumers and a center for reconstruction, repair and maintenance. In this chain, a producer starts out by sending several merchandise to customers. The process is carried out in a way that part of customers’ needs are produced by the producer himself/herself at regular and overtime workhouse. Another portion of the producer’s needs are met by different suppliers, which are shipped to the producer who sends them to the customers. Eventually the goods delivered to the customers, in case they are defective, are returned by customers to the reconstruction center, where, after undergoing correctional actions, are sent again to the producer, so in later cycles, they are re-sent to the customers. Additionally, when the expiry data of the product’s warranty arrives, it is shipped to the reconstruction center by the customers, and if possible, after receiving necessary repairs and corrections, are re-sent to the customers; otherwise, the product is de-assembled and returned to the producer. Hence, in the design of the applied-extended model proposed in this research study, such cases as determining the contribution of the suppliers, reconstruction centers, repair and maintenance, production at regular hours, and overtime manufacture of each of the products as well as the amount of dispatched products to each of the customers are among decisions considered in the latter model. Moreover, such objectives as minimizing producer’s cost including production expenditures, cost of retaining and inventory deficit, costs related to supplying products through outsourcing, maximizing the quality of the manufactured products at regular time, overtime, and production by suppliers or procuring products from repair, maintenance and reconstruction centers, where each one has a distinct quality are among parameters considered in the propounded model. Also, special attention is paid to the assessment of suppliers and customers so that optimum satisfaction of the latter two groups is provided. Thus, the proposed model contains 4 objective functions and about 20 constraints. The objective functions are minimizing total costs including production, maintenance, inventory and manpower costs, maximizing customer and supplier satisfaction and maximizing the quality of manufactured products. The constraints are such as inventory balance, capacity for holding, firing and hiring of force work, over time and regular time limit and so on. Finally the proposed model has been solved for the case study and one numerical example using Lingo software and LP metric method. Results and Discussion: The developed model has been solved by L-P metric method for case study and numerical example from the literature (Mirzapour et al, 2011). In each case, by changing P and weight of objectives (wi), the Pareto optimal solutions (POS) have been delivered. In the case study for two values of P, some Pareto optimal solutions (Zi) have been shown in Table 1. In the article, for more value of P and wi the model has been solved and more POSs have been delivered. For each POS, the optimum value of decision variables from can be determined as the outputs of the model. Table1- some Pareto optimal solutions p w1 w2 w3 w4 Z1 Z2 Z3 Z4 1 0.1 0.2 0.4 0.3 0 157843.2 0 0 0.6 0.4 0 0 0 157843.2 0 0 2 0.2 0.4 0.3 0.1 1.396537 130326.1 8508.600 0 0.1 0.2 0.3 0.4 1.505717 13036.6 8508.600 0 Conclusion: In this article, a multi objective model for aggregate planning in a reverse supply chain for a high-tech industry has been developed. The proposed model contains four objective functions and 20 constraints. The model has been solved by L-P metric method via LINGO software for the case study and a numerical example from the literature. For future research, uncertainty conditions can be considered in the model. References Gholamian, N., Mahdavia, I., & Tavakkoli-Moghaddam, R. (2015). "Multi-objective multi-productmulti-site aggregate production planning in a supply chain under uncertainty: fuzzy multi-objective optimization". International Journal of Computer Integrated Manufacturing, 29(2), 149-165. Mirzapour Al-e-hashem, S.M.J., Malekly, H, & Aryanezhada, M.B. (2011). "Multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty", International Journal of Production Economics, 134(1), 28–42. Mirzapour Al-e-hashem, S.M.J., Babolib, A. , & Sazvarb, C. (2013). "A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions", European, Journal of Operational Research, 230(1), 26–41. Abstract: This article presents an integrated production-distribution plan in a reverse supply chain via multi objective mathematical modeling in a high-tech environment. The objectives of the proposed model include 1) minimizing total costs including production, maintenance, inventory and manpower costs, 2) maximizing customer and supplier satisfaction, and 3) maximizing the quality of manufactured products. The supply chain consists of several suppliers, a producer, customers, a repair center to repair the customer's goods and a repair and maintenance center for repairing or disposing products that have passed their warranty period. Among the contributions of this research, we can consider such issues as considering the quality of products manufactured, returned or supplied from suppliers in order to realize the win-win relationship with suppliers, using the maximum capacity of suppliers and supply of parts by each reconstruction center. In order to validate the model, it is solved for some examples using Lingo software and LP metric method. Introduction: In reverse supply chain, what is addressed is recycling and reconstructing the products which are spending final stage of their life cycle. In this regard, after gathering and inspecting the returned products, they are partitioned in to recyclable and non-recyclable (scrap) products (Mirzapour et. al, 2013). Aggregate production planning is a process that determines the optimal level of production and stock inventory to meet the demands for the product in a long term period which considering the capacity limitation of the means and resources (Gholamian et al, 2015). In this research, investigation is regarding designing and solving a mathematics model for aggregate production planning in reverse supply chain in a high-tech industry. High-tech products are usually made up of chemical, mechanical, and electronic components. Inspection of the products in the supply chain of latter industry is of demolition type, that is, in case where the quality of the products is not confirmed by the customer, they are in masse retuned to the supplier. The returned products are either demolished in the re-construction units or delivered to the producer after re-construction. Also, in case of the non-usage of the products by the customer after technical warranty expiration, they are dispatched to the repair and maintenance unit and after undergoing correctional measures, they are re-dispatched to the customer or producer. The aim of the present research is to conduct an investigation into the performance manner of the producer in making decision regarding producing the afore-mentioned products. In order to achieve objectives, the producer can manufacture the required products on his/her own plant. Accordingly, he/she should decide on considering the capacity of available means and facilities, production expenditures, and the quality of the produced commodity, what measure of products to produce at regular working hours, and what amount to produce at non-regular (over-time) working hours. In his/her aggregate production planning, he/she might also decide on out-sourcing the production of a portion of his/her required products to outside suppliers. Such planning becomes of utmost importance since he/she should decide- while considering such requisite indices and criteria as expenditure, quality level, and priority- what percentage of the products to delegate to what supplier. Along this line in the proposed model, a win-win relation with the suppliers is deemed essential. Thus, in the model offered here, the optimization of the customer’s satisfaction is taken into account so that- by considering customer’s prioritization- the shortage rate of the unmet demands on the part of the supplier is kept at minimum. Materials and Methods: The supply chain of the proposed model contains three levels of suppliers, producer, consumers and a center for reconstruction, repair and maintenance. In this chain, a producer starts out by sending several merchandise to customers. The process is carried out in a way that part of customers’ needs are produced by the producer himself/herself at regular and overtime workhouse. Another portion of the producer’s needs are met by different suppliers, which are shipped to the producer who sends them to the customers. Eventually the goods delivered to the customers, in case they are defective, are returned by customers to the reconstruction center, where, after undergoing correctional actions, are sent again to the producer, so in later cycles, they are re-sent to the customers. Additionally, when the expiry data of the product’s warranty arrives, it is shipped to the reconstruction center by the customers, and if possible, after receiving necessary repairs and corrections, are re-sent to the customers; otherwise, the product is de-assembled and returned to the producer. Hence, in the design of the applied-extended model proposed in this research study, such cases as determining the contribution of the suppliers, reconstruction centers, repair and maintenance, production at regular hours, and overtime manufacture of each of the products as well as the amount of dispatched products to each of the customers are among decisions considered in the latter model. Moreover, such objectives as minimizing producer’s cost including production expenditures, cost of retaining and inventory deficit, costs related to supplying products through outsourcing, maximizing the quality of the manufactured products at regular time, overtime, and production by suppliers or procuring products from repair, maintenance and reconstruction centers, where each one has a distinct quality are among parameters considered in the propounded model. Also, special attention is paid to the assessment of suppliers and customers so that optimum satisfaction of the latter two groups is provided. Thus, the proposed model contains 4 objective functions and about 20 constraints. The objective functions are minimizing total costs including production, maintenance, inventory and manpower costs, maximizing customer and supplier satisfaction and maximizing the quality of manufactured products. The constraints are such as inventory balance, capacity for holding, firing and hiring of force work, over time and regular time limit and so on. Finally the proposed model has been solved for the case study and one numerical example using Lingo software and LP metric method. Results and Discussion: The developed model has been solved by L-P metric method for case study and numerical example from the literature (Mirzapour et al, 2011). In each case, by changing P and weight of objectives (wi), the Pareto optimal solutions (POS) have been delivered. In the case study for two values of P, some Pareto optimal solutions (Zi) have been shown in Table 1. In the article, for more value of P and wi the model has been solved and more POSs have been delivered. For each POS, the optimum value of decision variables from can be determined as the outputs of the model. Table1- some Pareto optimal solutions p w1 w2 w3 w4 Z1 Z2 Z3 Z4 1 0.1 0.2 0.4 0.3 0 157843.2 0 0 0.6 0.4 0 0 0 157843.2 0 0 2 0.2 0.4 0.3 0.1 1.396537 130326.1 8508.600 0 0.1 0.2 0.3 0.4 1.505717 13036.6 8508.600 0 Conclusion: In this article, a multi objective model for aggregate planning in a reverse supply chain for a high-tech industry has been developed. The proposed model contains four objective functions and 20 constraints. The model has been solved by L-P metric method via LINGO software for the case study and a numerical example from the literature. For future research, uncertainty conditions can be considered in the model. References Gholamian, N., Mahdavia, I., & Tavakkoli-Moghaddam, R. (2015). "Multi-objective multi-productmulti-site aggregate production planning in a supply chain under uncertainty: fuzzy multi-objective optimization". International Journal of Computer Integrated Manufacturing, 29(2), 149-165. Mirzapour Al-e-hashem, S.M.J., Malekly, H, & Aryanezhada, M.B. (2011). "Multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty", International Journal of Production Economics, 134(1), 28–42. Mirzapour Al-e-hashem, S.M.J., Babolib, A. , & Sazvarb, C. (2013). "A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions", European, Journal of Operational Research, 230(1), 26–41.

https://jpom.ui.ac.ir/article_23061_f644df7b036acb9f79161a4bf31f0ed3.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Two-Stage and Robust Stochastic Optimization of Closed-Loop Supply Chain Network under Uncertainty Two-Stage and Robust Stochastic Optimization of Closed-Loop Supply Chain Network under Uncertainty 77 97 23076 10.22108/jpom.2017.92475 FA Mona Behzadi M.Sc. student, Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran, Iran Mehdi Seifabrghy Associate Professor, Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran, Iran Journal Article 2015 12 27 Abstract: In this paper, a network of closed-loop supply chain is considered, including external supplier, production/recovery facilities, hybrid distribution/collection centers, disposal centers and customers. Generally, in the closed-loop chains production is done by the returned products, we can’t achieve a correct analysis by considering one period. In many situations in the real world, we need to consider more than one period, therefore the studied model is assumed in the form of some multi-period and suppliers are used to supply the shortage of parts. In this paper, it is assumed that parameters of demand, quantity and quality of returns and variable costs are uncertain. To evaluate the uncertainty, two approaches of two-stage and robust stochastic optimization have been used. The results show that performance of robust optimization is better than the two-stage stochastic optimization under uncertainty. Introduction: In recent years, closed-loop supply chain networks and reverse logistics have been highly regarded as being used to minimize waste and recycling of products. Since the process of collecting, retrieving, and re-manufacturing requires time, it does not provide a real result in a model in a single period. Therefore, in this paper, a multi-period closed-loop supply network model is developed. Also, in the first period, raw materials are supplied from foreign suppliers, but in subsequent periods, the recycled materials are also used in production, thus saving raw materials purchase costs. Materials and Methods:A Mixed-Integer Linear Programming (MILP) model is proposed. Its objectives are to minimize the costs of establishing centers, shipping costs, purchasing, producing, maintaining, refining, and disposal, as well as costs associated with unused capacity penalties centers. The mathematical model of this paper is as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) Constraint (2) shows the flow of customer demand. Constraints (3) ensures that returned products are collected from customers. Constraints (4) to (7) establish the flow equilibrium. Equations (8) to (12) are the capacity constraints of the production centers, the link centers are in forward and reverse, and disposal centers. Constraint (13) represents the flow of the number of pieces purchased from the supplier in the first period. Constraint (14) states that after the second period, the recycled parts will be produced and purchased from the supplier as needed. Constraints (15) and (16) represent the status of the decision variables. Results and Discussion: In order to have an efficient logistics network, the uncertainty in demand, the quantity and quality of returning products and variable costs are considered in the model, which are solved by two methods of two-stage random planning. The EVPI and VSS indices have been used to compare the solutions used. Conclusion: In this paper, a multi-cycle model of closed loop supply chain network including foreign suppliers, production / rehabilitation centers, distribution / collection centers, disposal centers and customers are presented. To evaluate the model under uncertainty, two-stage randomization and robust optimization methods presented by Mulvey et al (1995) have been used. The more scenarios are scattered, the responsiveness of the model is better than the two-stage model response, and it shows a better performance of the steady model. References Mulvey, J., Vanderberi, R., & zenios, S. (1995). Robust Optimization of Large-Scale Systems. Operations research. Operations Research, 43, 264-281. Abstract: In this paper, a network of closed-loop supply chain is considered, including external supplier, production/recovery facilities, hybrid distribution/collection centers, disposal centers and customers. Generally, in the closed-loop chains production is done by the returned products, we can’t achieve a correct analysis by considering one period. In many situations in the real world, we need to consider more than one period, therefore the studied model is assumed in the form of some multi-period and suppliers are used to supply the shortage of parts. In this paper, it is assumed that parameters of demand, quantity and quality of returns and variable costs are uncertain. To evaluate the uncertainty, two approaches of two-stage and robust stochastic optimization have been used. The results show that performance of robust optimization is better than the two-stage stochastic optimization under uncertainty. Introduction: In recent years, closed-loop supply chain networks and reverse logistics have been highly regarded as being used to minimize waste and recycling of products. Since the process of collecting, retrieving, and re-manufacturing requires time, it does not provide a real result in a model in a single period. Therefore, in this paper, a multi-period closed-loop supply network model is developed. Also, in the first period, raw materials are supplied from foreign suppliers, but in subsequent periods, the recycled materials are also used in production, thus saving raw materials purchase costs. Materials and Methods:A Mixed-Integer Linear Programming (MILP) model is proposed. Its objectives are to minimize the costs of establishing centers, shipping costs, purchasing, producing, maintaining, refining, and disposal, as well as costs associated with unused capacity penalties centers. The mathematical model of this paper is as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) Constraint (2) shows the flow of customer demand. Constraints (3) ensures that returned products are collected from customers. Constraints (4) to (7) establish the flow equilibrium. Equations (8) to (12) are the capacity constraints of the production centers, the link centers are in forward and reverse, and disposal centers. Constraint (13) represents the flow of the number of pieces purchased from the supplier in the first period. Constraint (14) states that after the second period, the recycled parts will be produced and purchased from the supplier as needed. Constraints (15) and (16) represent the status of the decision variables. Results and Discussion: In order to have an efficient logistics network, the uncertainty in demand, the quantity and quality of returning products and variable costs are considered in the model, which are solved by two methods of two-stage random planning. The EVPI and VSS indices have been used to compare the solutions used. Conclusion: In this paper, a multi-cycle model of closed loop supply chain network including foreign suppliers, production / rehabilitation centers, distribution / collection centers, disposal centers and customers are presented. To evaluate the model under uncertainty, two-stage randomization and robust optimization methods presented by Mulvey et al (1995) have been used. The more scenarios are scattered, the responsiveness of the model is better than the two-stage model response, and it shows a better performance of the steady model. References Mulvey, J., Vanderberi, R., & zenios, S. (1995). Robust Optimization of Large-Scale Systems. Operations research. Operations Research, 43, 264-281.

https://jpom.ui.ac.ir/article_23076_579d8673cdcd92192c0123061032b94e.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Multi-objective modeling for Member Selection of Cross-functional Teams Multi-objective modeling for Member Selection of Cross-functional Teams 99 113 23070 10.22108/jpom.2018.92501.0 FA Elham Mahmudinejad MSc. of Industrial Management, Faculty of Management and Economic, Tarbiat Modares University, Tehran, Iran Adel Azar Professor, Faculty of Management and Economic, Tarbiat Modares University, Tehran, Iran Ali Rajabzadeh Associate professor, Faculty of Management and Economic, Tarbiat Modares University, Tehran, Iran Abbas Rezaei Pandari Ph.D. of Industrial Management, Faculty of Management and Economic, Tarbiat Modares University, Tehran, Iran Journal Article 2016 05 25 Using cross-functional team (CFT) is a suitable strategy for improving the performance of organizations. The member selection problem is an important aspect of the CFT formation. Several evidences showed the important criteria for choosing true members are: cooperation and coordination, functional expertise, individual abilities, cost, and communication. In this paper, effective features for member selection are identified and a multi-objective 0–1 nonlinear programming model is developed. This model is developed by using individual and collaborative performance. Afterward, it is converted into the linear form by changing variables to solve it more easily. The proposed model is used in the real example in Census cross-functional team in the statistical center of Iran and required data were collected by surveys and interviews. The results indicate that this proposed model has better performance compared to recommendation of experts and can be used in other fields. Introduction: Nowadays using teams is increased; it helps companies and organizations to survive in product markets’ competition, business pressure, and customers’ expectations (Proehl, 1996; Santa, Ferrer, Bretherton et al. 2010; Fan, Feng, Jiang et al, 2009). Among various teams, cross-functional team is one of the most effective strategy which is used in NPD (Wang, Yan, and Ma, 2003), lean production, TQM and continuous improvement (Love and Roper, 2009). CFT is defined by a group of members who come from different functional areas (Feng, Jiang, Fan et al, 2010) in the same hierarchy as level within an organization, or even between organizations for a limited time )Saarani and Bakri, 2012). CFT has several advantages such as positive impact on cycle time and project performance )Barczak and Wilemon, 2003(, increasing learning, processing optimization, knowledge sharing (Love and Roper, 2009), creativity, problem solving (Santa, Ferrer, Bretherton et al. 2010; Saarani and Bakri, 2012), increasing competition in organization, responding to market changes (Santa, Ferrer, Bretherton et al. 2010), spanning organizational boundaries (Love and Roper, 2009; Feng, Jiang, Fan et al, 2010), and responding quickly to environmental changes (Zhang and Zhang, 2013) The first stage of team development is forming, therefore organizations must select candidates carefully to ensure CFT’s effects and success (Feng, Jiang, Fan et al, 2010). Correct selection prevents wasting time (Feng, Jiang, Fan et al, 2010), financial losses and productivity shortcoming )Saarani and Bakri, 2012(. Recently, some researchers have attended to CFT’s formation and discuss suitable characteristics to assemble members. In Chen and Lin (2004) study, functional expertise, teamwork experience, communication skill, flexibility in job assignment, and personality traits indicated as five important characteristics of team members that build successful multifunctional team. Fitzpatrick and Askin (2005) regarded innate tendencies, interpersonal skills, and technical skills as important criteria for member selection. Wang, Yan and Ma (2003) listed the selection attributes for the creation ability, management ability, utilization rates, cooperation levels, and so forth. Jiang et al. (2010) reported the criteria for selecting members for cross-functional teams: individual performance (such as work experience, ability to solve work problems, and technical knowledge), exterior organizational collaborative performance (such as the extent of external cooperation), and interior organizational collaborative performance (for instance mutual communication among members and collaboration in solving problems). Zhang and Zhang (2013) stated that the effective NPD team should have four capabilities: expertise and experience consistent, learning and knowledge sharing, communication, and problem-solving. Kargar and Zihayat (2012) discussed requirements such as communication, cost, and skills for desired members. Several evidences showed important criteria for choosing appropriate members. These are cooperation, coordination, functional expertise, individual abilities, cost, and communication. Existing researches focus on main skills of candidates while to the best of our knowledge there is no study that notices subskills of candidates. Furthermore, there is no study which considers all the criteria simultaneously. In addition, utilizing quantitative methods for the formation of CFTs has been the topic of recent researches. Chen and Lin (2004) used chain wise AHP to evaluate sharing knowledge and selecting members who have high knowledge rating in each department. Following that, they have proposed the nonlinear quantitative model to select the appropriate candidates based on teamwork capabilities and working relationships for teams in industrial environments. The working relationships and teamwork capabilities respectively are calculated by using MBTI and AHP. Fitzpatrick and Askin (2005) formulated mathematical model based on Kolbe Conative Index (synergy, inertia, and stability) that measures interpersonal structure for multi-functional teams and then solves it by heuristic solution. Zhang and Zhang (2013) presented nonlinear multi-objective optimization for NPD and employed Multi-objective Particle Swarm Optimization to resolve it. They improved fuzzy AHP based on Fuzzy Lin PreRa. In addition, they used the model to evaluate capability and employed MBTI to measure interpersonal relationships among members of interior and exterior departments of the organization. Jiang et al (2010) offered a multi-objective 0–1 programming model for formation cross-functional teams and developed an improved non dominated sorting genetic algorithm II (INSGA-II) to solve it. However, most of the existing methods for the formation of CFTs are nonlinear and there is no simple model for developing CFTs. Therefore the multi-objective nonlinear 0–1 programming model is built based on all of the criteria. Then to solve it more easily, it is converted into a linear form by changing variables. Materials and Methods: Five main measures are considered to form cross-functional teams: cooperation and coordination, functional expertise, individual abilities, cost, and communication. The Meyers-Briggs Type Indicator (MBTI) test is used to evaluate “cooperation and coordination”. MBTI is a self-help assessment test which indicates different psychological preferences in how people perceive the world and how they make decisions. The professional interview is conducted to assess “functional expertise”. In addition, the members answered self-report skill measures which rated in the Likert scale. In order to calculate “individual abilities” two methods are used: personal assessment (the participants are asked by questionnaire) and professional assessment (using the analytical hierarchy process (AHP) method). With the aim of realizing the “cost”, the paychecks of candidates are considered. Sociometry test is used to asses “communication”. The collected data, based on the mentioned methods, are analyzed and the model is developed. The proposed model minimizes the cost and maximizes the other objective measures. Global Criteria method is used to convert the multi-objective proposed model to the one-objective model. Furthermore, this non-linear model is transformed to linear by using the Glover and Woolsey’s method. Results and Discussion: In order to examine the proposed method, the Census cross-functional team in the statistical center of Iran as the real case is considered. Four departments were selected for this test. 10 people were nominated from chosen departments (3, 3, 2, and 2 members from each department, respectively). The proposed model was applied and the results were compared to the chosen team by the head of the office. Themembers selected by the proposed model are 1, 2, 4, 5 and 9. However, 1, 2, 4, 5, and 7 members are chosen by the expert. In fact, these two results are 80% in common. Conclusion: Forming cross-functional teams improves the performance of organizations. Selecting appropriate members for the team formation is a critical decision. Therefore, in this paper, significant features to form the CFT is found and a new model to solve the CFTs formation problem is developed. The findings show the vital criteria in CFTs are: cooperation and coordination, functional expertise, individual abilities, cost, and communication. We have developed simple, linear, multi-objective model which solve forming CFTs more easily and effectively. The outcome of the proposed model is better than the expert’s decision in all goals except the “individual abilities”, this exception may happen because of considering constraints. References Barczak, G., & Wilemon, D. (2003). Team member experiences in new product development: views from the trenches. R&D Management, 33(5), 463-479. Chen, S. J., & Lin, L. (2004). Modeling team member characteristics for the formation of a multifunctional team in concurrent engineering. IEEE Transactions on Engineering Management, 51(2), 111-124. Fan, Z. P., Feng, B., Jiang, Z. Z., & Fu, N. (2009). A method for member selection of R&D teams using the individual and collaborative information. Expert Systems with Applications, 36(4), 8313-8323. Feng, B., Jiang, Z. Z., Fan, Z. P., & Fu, N. (2010). A method for member selection of cross-functional teams using the individual and collaborative performances. European Journal of Operational Research, 203(3), 652-661. Fitzpatrick, E. L., & Askin, R. G. (2005). Forming effective worker teams with multi-functional skill requirements. Computers & Industrial Engineering, 48(3), 593-608. Kargar, M., An, A., & Zihayat, M. (2012, September). Efficient bi-objective team formation in social networks. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 483-498). Springer, Berlin, Heidelberg. Love, J. H., & Roper, S. (2009). Organizing innovation: complementarities between cross-functional teams. Technovation, 29(3), 192-203. Otero, L. D., Centeno, G., Otero, C. E., & Ruiz-Torres, A. J. (2012). A fuzzy goal programming model for skill-based personnel assignments. International Journal of Multicriteria Decision Making, 2(4), 313-337. Proehl, R. A. (1996). Enhancing the effectiveness of cross-functional teams. Leadership & Organization Development Journal, 17(5), 3-10. Saarani, C. R. B., & Bakri, N. (2012). Examining The Technical and Non Technical Member’s Participation in Cross-Functional Teams: A Case Study. Procedia-Social and Behavioral Sciences, 40, 187-196. Santa, R., Ferrer, M., Bretherton, P., & Hyland, P. (2010). Contribution of cross-functional teams to the improvement in operational performance. Team Performance Management: An international Journal, 16(3/4), 148-168. Wang, Z., Yan, H. S., & Ma, X. D. (2003). A quantitative approach to the rganization of cross-functional teams in concurrent engineering. The International Journal of Advanced Manufacturing Technology, 21(10-11), 879-888. Zhang, L., & Zhang, X. (2013). Multi-objective team formation optimization for new product development. Computers & Industrial Engineering, 64(3), 804-811. Using cross-functional team (CFT) is a suitable strategy for improving the performance of organizations. The member selection problem is an important aspect of the CFT formation. Several evidences showed the important criteria for choosing true members are: cooperation and coordination, functional expertise, individual abilities, cost, and communication. In this paper, effective features for member selection are identified and a multi-objective 0–1 nonlinear programming model is developed. This model is developed by using individual and collaborative performance. Afterward, it is converted into the linear form by changing variables to solve it more easily. The proposed model is used in the real example in Census cross-functional team in the statistical center of Iran and required data were collected by surveys and interviews. The results indicate that this proposed model has better performance compared to recommendation of experts and can be used in other fields. Introduction: Nowadays using teams is increased; it helps companies and organizations to survive in product markets’ competition, business pressure, and customers’ expectations (Proehl, 1996; Santa, Ferrer, Bretherton et al. 2010; Fan, Feng, Jiang et al, 2009). Among various teams, cross-functional team is one of the most effective strategy which is used in NPD (Wang, Yan, and Ma, 2003), lean production, TQM and continuous improvement (Love and Roper, 2009). CFT is defined by a group of members who come from different functional areas (Feng, Jiang, Fan et al, 2010) in the same hierarchy as level within an organization, or even between organizations for a limited time )Saarani and Bakri, 2012). CFT has several advantages such as positive impact on cycle time and project performance )Barczak and Wilemon, 2003(, increasing learning, processing optimization, knowledge sharing (Love and Roper, 2009), creativity, problem solving (Santa, Ferrer, Bretherton et al. 2010; Saarani and Bakri, 2012), increasing competition in organization, responding to market changes (Santa, Ferrer, Bretherton et al. 2010), spanning organizational boundaries (Love and Roper, 2009; Feng, Jiang, Fan et al, 2010), and responding quickly to environmental changes (Zhang and Zhang, 2013) The first stage of team development is forming, therefore organizations must select candidates carefully to ensure CFT’s effects and success (Feng, Jiang, Fan et al, 2010). Correct selection prevents wasting time (Feng, Jiang, Fan et al, 2010), financial losses and productivity shortcoming )Saarani and Bakri, 2012(. Recently, some researchers have attended to CFT’s formation and discuss suitable characteristics to assemble members. In Chen and Lin (2004) study, functional expertise, teamwork experience, communication skill, flexibility in job assignment, and personality traits indicated as five important characteristics of team members that build successful multifunctional team. Fitzpatrick and Askin (2005) regarded innate tendencies, interpersonal skills, and technical skills as important criteria for member selection. Wang, Yan and Ma (2003) listed the selection attributes for the creation ability, management ability, utilization rates, cooperation levels, and so forth. Jiang et al. (2010) reported the criteria for selecting members for cross-functional teams: individual performance (such as work experience, ability to solve work problems, and technical knowledge), exterior organizational collaborative performance (such as the extent of external cooperation), and interior organizational collaborative performance (for instance mutual communication among members and collaboration in solving problems). Zhang and Zhang (2013) stated that the effective NPD team should have four capabilities: expertise and experience consistent, learning and knowledge sharing, communication, and problem-solving. Kargar and Zihayat (2012) discussed requirements such as communication, cost, and skills for desired members. Several evidences showed important criteria for choosing appropriate members. These are cooperation, coordination, functional expertise, individual abilities, cost, and communication. Existing researches focus on main skills of candidates while to the best of our knowledge there is no study that notices subskills of candidates. Furthermore, there is no study which considers all the criteria simultaneously. In addition, utilizing quantitative methods for the formation of CFTs has been the topic of recent researches. Chen and Lin (2004) used chain wise AHP to evaluate sharing knowledge and selecting members who have high knowledge rating in each department. Following that, they have proposed the nonlinear quantitative model to select the appropriate candidates based on teamwork capabilities and working relationships for teams in industrial environments. The working relationships and teamwork capabilities respectively are calculated by using MBTI and AHP. Fitzpatrick and Askin (2005) formulated mathematical model based on Kolbe Conative Index (synergy, inertia, and stability) that measures interpersonal structure for multi-functional teams and then solves it by heuristic solution. Zhang and Zhang (2013) presented nonlinear multi-objective optimization for NPD and employed Multi-objective Particle Swarm Optimization to resolve it. They improved fuzzy AHP based on Fuzzy Lin PreRa. In addition, they used the model to evaluate capability and employed MBTI to measure interpersonal relationships among members of interior and exterior departments of the organization. Jiang et al (2010) offered a multi-objective 0–1 programming model for formation cross-functional teams and developed an improved non dominated sorting genetic algorithm II (INSGA-II) to solve it. However, most of the existing methods for the formation of CFTs are nonlinear and there is no simple model for developing CFTs. Therefore the multi-objective nonlinear 0–1 programming model is built based on all of the criteria. Then to solve it more easily, it is converted into a linear form by changing variables. Materials and Methods: Five main measures are considered to form cross-functional teams: cooperation and coordination, functional expertise, individual abilities, cost, and communication. The Meyers-Briggs Type Indicator (MBTI) test is used to evaluate “cooperation and coordination”. MBTI is a self-help assessment test which indicates different psychological preferences in how people perceive the world and how they make decisions. The professional interview is conducted to assess “functional expertise”. In addition, the members answered self-report skill measures which rated in the Likert scale. In order to calculate “individual abilities” two methods are used: personal assessment (the participants are asked by questionnaire) and professional assessment (using the analytical hierarchy process (AHP) method). With the aim of realizing the “cost”, the paychecks of candidates are considered. Sociometry test is used to asses “communication”. The collected data, based on the mentioned methods, are analyzed and the model is developed. The proposed model minimizes the cost and maximizes the other objective measures. Global Criteria method is used to convert the multi-objective proposed model to the one-objective model. Furthermore, this non-linear model is transformed to linear by using the Glover and Woolsey’s method. Results and Discussion: In order to examine the proposed method, the Census cross-functional team in the statistical center of Iran as the real case is considered. Four departments were selected for this test. 10 people were nominated from chosen departments (3, 3, 2, and 2 members from each department, respectively). The proposed model was applied and the results were compared to the chosen team by the head of the office. Themembers selected by the proposed model are 1, 2, 4, 5 and 9. However, 1, 2, 4, 5, and 7 members are chosen by the expert. In fact, these two results are 80% in common. Conclusion: Forming cross-functional teams improves the performance of organizations. Selecting appropriate members for the team formation is a critical decision. Therefore, in this paper, significant features to form the CFT is found and a new model to solve the CFTs formation problem is developed. The findings show the vital criteria in CFTs are: cooperation and coordination, functional expertise, individual abilities, cost, and communication. We have developed simple, linear, multi-objective model which solve forming CFTs more easily and effectively. The outcome of the proposed model is better than the expert’s decision in all goals except the “individual abilities”, this exception may happen because of considering constraints. References Barczak, G., & Wilemon, D. (2003). Team member experiences in new product development: views from the trenches. R&D Management, 33(5), 463-479. Chen, S. J., & Lin, L. (2004). Modeling team member characteristics for the formation of a multifunctional team in concurrent engineering. IEEE Transactions on Engineering Management, 51(2), 111-124. Fan, Z. P., Feng, B., Jiang, Z. Z., & Fu, N. (2009). A method for member selection of R&D teams using the individual and collaborative information. Expert Systems with Applications, 36(4), 8313-8323. Feng, B., Jiang, Z. Z., Fan, Z. P., & Fu, N. (2010). A method for member selection of cross-functional teams using the individual and collaborative performances. European Journal of Operational Research, 203(3), 652-661. Fitzpatrick, E. L., & Askin, R. G. (2005). Forming effective worker teams with multi-functional skill requirements. Computers & Industrial Engineering, 48(3), 593-608. Kargar, M., An, A., & Zihayat, M. (2012, September). Efficient bi-objective team formation in social networks. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 483-498). Springer, Berlin, Heidelberg. Love, J. H., & Roper, S. (2009). Organizing innovation: complementarities between cross-functional teams. Technovation, 29(3), 192-203. Otero, L. D., Centeno, G., Otero, C. E., & Ruiz-Torres, A. J. (2012). A fuzzy goal programming model for skill-based personnel assignments. International Journal of Multicriteria Decision Making, 2(4), 313-337. Proehl, R. A. (1996). Enhancing the effectiveness of cross-functional teams. Leadership & Organization Development Journal, 17(5), 3-10. Saarani, C. R. B., & Bakri, N. (2012). Examining The Technical and Non Technical Member’s Participation in Cross-Functional Teams: A Case Study. Procedia-Social and Behavioral Sciences, 40, 187-196. Santa, R., Ferrer, M., Bretherton, P., & Hyland, P. (2010). Contribution of cross-functional teams to the improvement in operational performance. Team Performance Management: An international Journal, 16(3/4), 148-168. Wang, Z., Yan, H. S., & Ma, X. D. (2003). A quantitative approach to the rganization of cross-functional teams in concurrent engineering. The International Journal of Advanced Manufacturing Technology, 21(10-11), 879-888. Zhang, L., & Zhang, X. (2013). Multi-objective team formation optimization for new product development. Computers & Industrial Engineering, 64(3), 804-811.

https://jpom.ui.ac.ir/article_23070_83863e505e07f553d402febd53b51690.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Inverse of Backup 2-Median Problems with Variable Edge Lengths and Vertex Weight on Trees and Variable Coordinates on the Plane Inverse of Backup 2-Median Problems with Variable Edge Lengths and Vertex Weight on Trees and Variable Coordinates on the Plane 115 137 23083 10.22108/jpom.2018.103725.1037 FA Morteza Nazari PhD student, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran Jafar Fathali Associate Professor, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran Mostafa Nazari Assistant Professor, Dept. of Mech. Eng., Shahrood University of Technology, Shahrood, Iran Seyed Mojtaba Varedi Koulaei Assistant Professor, Dept. of Mech. Eng., Shahrood University of Technology, Shahrood, Iran Journal Article 2017 04 27 In this paper we consider the inverse of backup 2-median problem. In this problem, a set of weighted points are given and we should change some parameters of the problem such as weights of vertices and edges and coordinates of points such that the two given points be the backup 2-median. We present mathematical models for inverse backup 2-median problems on graphs. In the case that the underlying network is a tree, linear models are presented for the problem with variable edges and weight of vertices. We also consider the continuous case of the problem with variable coordinates of vertices on the plane. In this case, we solve the model by PSO and a hybrid improved PSO methods. Computational results are compared for the varying amounts of parameters. Introduction: The inverse and backup location facility problems are two important branches of location theory that have been interested by many researchers in the recent decades. Let n weighted points be given in the plane or on a graph. The inverse median models investigate to change some parameters of problem such as coordinates, edge lengths and vertex weights such that the given facilities be the median points. For more information about inverse location problems see Burkard et al. (2004). On the other hand, in the backup median problems supposed that some facilities may failed. Therefore the other facilities should serve the clients. The backup 2-median problem on trees has been considered by Wang et al. (2009). Fathali (2014) investigated the backup multi-facility location problem on the plane. In this paper we consider the combination of inverse location and backup facility location problems. We want to change coordinates, weight of vertices or length of edges with minimum cost such that the given facilities be backup median facilities. Materials and Methods: 2. inverse Backup 2-Median On Trees: Let T=(V,E) be a tree with n vertices. Each vertex has a nonnegative weight . Let be the distance between two points and , and be the two given vertices in T which are assumed the location of facilities. Each facility may fail with a probability . For any vertex , suppose that the cost of increasing and decreasing per unit of is and , respectively. Let and be the amounts by which the weight is increased and decreased, respectively. Then, the model of inverse backup 2-median problem can be written as follows. Using some properties of backup 2-median problem on trees, this model can be converted to a linear programming model. 3. Inverse Backup 2-Median on The Plane: In this section we consider the inverse backup 2-median on the plane. Let n points be given in the plane. Let we have a limited budget B, to change the parameters. Then we want to modify the coordinate of given points such that the two points and be close to backup 2-median. With the same notation of inverse backup 2-median on trees, the model of inverse backup 2-median problem on the plane can be written as follow. Results and Discussion: Two Particle Swarm Optimization (PSO) methods have been applied to solve the inverse backup 2-median problem on the plane. Table 1, shows the results with varying norms , which obtained by running the two PSO methods on a problem with 80 points. Table 1. The results of two PSO models for BR2MP with n=80, B=700 and 1 5.81E+03 5.64E+03 676.09 481.06 2 4.71E+03 4.65E+03 353.89 378.37 5 4.19E+03 3.75E+03 526.14 462.06 10 3.83E+03 3.39E+03 362.328 657.44 Conclusion: In this paper we investigated the backup 2-median problem with variable edge lengths and vertices weights on trees. The problem with variable coordinates on the plane is also considered. The models of mentioned problems and computational results which obtained by two PSO methods are presented. References Burkard, R. E., Pleschiutsching, C., & Zhang, J. (2004). "Inverse median problems". Discrete Optimization, 1(1), 23-39. Fathali, J. (2014). "Backup multifacility location problem with norm". OPSEARCH, 52(2), 382-391. Wang, H. L., Wu, B. Y., & Chao, K. M. (2009). "The backup 2-center and backup 2-median problems on trees". Networks, 53(1), 39-49. In this paper we consider the inverse of backup 2-median problem. In this problem, a set of weighted points are given and we should change some parameters of the problem such as weights of vertices and edges and coordinates of points such that the two given points be the backup 2-median. We present mathematical models for inverse backup 2-median problems on graphs. In the case that the underlying network is a tree, linear models are presented for the problem with variable edges and weight of vertices. We also consider the continuous case of the problem with variable coordinates of vertices on the plane. In this case, we solve the model by PSO and a hybrid improved PSO methods. Computational results are compared for the varying amounts of parameters. Introduction: The inverse and backup location facility problems are two important branches of location theory that have been interested by many researchers in the recent decades. Let n weighted points be given in the plane or on a graph. The inverse median models investigate to change some parameters of problem such as coordinates, edge lengths and vertex weights such that the given facilities be the median points. For more information about inverse location problems see Burkard et al. (2004). On the other hand, in the backup median problems supposed that some facilities may failed. Therefore the other facilities should serve the clients. The backup 2-median problem on trees has been considered by Wang et al. (2009). Fathali (2014) investigated the backup multi-facility location problem on the plane. In this paper we consider the combination of inverse location and backup facility location problems. We want to change coordinates, weight of vertices or length of edges with minimum cost such that the given facilities be backup median facilities. Materials and Methods: 2. inverse Backup 2-Median On Trees: Let T=(V,E) be a tree with n vertices. Each vertex has a nonnegative weight . Let be the distance between two points and , and be the two given vertices in T which are assumed the location of facilities. Each facility may fail with a probability . For any vertex , suppose that the cost of increasing and decreasing per unit of is and , respectively. Let and be the amounts by which the weight is increased and decreased, respectively. Then, the model of inverse backup 2-median problem can be written as follows. Using some properties of backup 2-median problem on trees, this model can be converted to a linear programming model. 3. Inverse Backup 2-Median on The Plane: In this section we consider the inverse backup 2-median on the plane. Let n points be given in the plane. Let we have a limited budget B, to change the parameters. Then we want to modify the coordinate of given points such that the two points and be close to backup 2-median. With the same notation of inverse backup 2-median on trees, the model of inverse backup 2-median problem on the plane can be written as follow. Results and Discussion: Two Particle Swarm Optimization (PSO) methods have been applied to solve the inverse backup 2-median problem on the plane. Table 1, shows the results with varying norms , which obtained by running the two PSO methods on a problem with 80 points. Table 1. The results of two PSO models for BR2MP with n=80, B=700 and 1 5.81E+03 5.64E+03 676.09 481.06 2 4.71E+03 4.65E+03 353.89 378.37 5 4.19E+03 3.75E+03 526.14 462.06 10 3.83E+03 3.39E+03 362.328 657.44 Conclusion: In this paper we investigated the backup 2-median problem with variable edge lengths and vertices weights on trees. The problem with variable coordinates on the plane is also considered. The models of mentioned problems and computational results which obtained by two PSO methods are presented. References Burkard, R. E., Pleschiutsching, C., & Zhang, J. (2004). "Inverse median problems". Discrete Optimization, 1(1), 23-39. Fathali, J. (2014). "Backup multifacility location problem with norm". OPSEARCH, 52(2), 382-391. Wang, H. L., Wu, B. Y., & Chao, K. M. (2009). "The backup 2-center and backup 2-median problems on trees". Networks, 53(1), 39-49.

https://jpom.ui.ac.ir/article_23083_74c6c36166319ccee5fcea44c7be705c.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 A New Multi-objective Model for Projects Portfolio Optimization considering Integrated Efficiency-risk Approach using NSGA-ΙΙ A New Multi-objective Model for Projects Portfolio Optimization considering Integrated Efficiency-risk Approach using NSGA-ΙΙ 139 157 23074 10.22108/jpom.2018.109207.1107 FA Mohammadreza Sharifi Ghazvini PHD Student of Industrial Engineering, Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran Vahidreza Ghezavati Associate Professor of Industrial Engineering, Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran Ahmad Makui Professor of Industrial Engineering, Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran Sadigh Raissi Associate Professor of Industrial Engineering, Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran Journal Article 2018 01 27 Abstract: A project portfolio is a crucial decision-making process used to prepare an optimum collection of vast alternative projects. In most of the previous modeling methods, the focus is directed towards maximizing project efficiency and so, the role of risky aspects in selecting appropriate projects has been neglected. This paper presents an integrated multi-objective mathematical programming (MOMP) based on efficiency-risk for selecting a project portfolio using various techniques including data envelopment analysis (DEA), risk priority number (RPN) and non-dominated sorting genetic algorithm (NSGA-ΙΙ). The proposed model can support both the capability to nominate mutually exclusive projects (conflicting projects that only one of them can be done) or any type of predecessor projects (doing a project depends on another project) and concurrent projects (need to be done at the same time) selection. Another advantage of the model is that the hyper heuristic solutions can be found in the form of several non-dominated cases and it is possible for organization’s experts to choose the best and the most suitable solutions. Introduction: In the competitive world, intelligent optimum decision making is a vital task in the success of large systems. Due to lack of resources, it is not always possible to fully evaluate all proposed developmental projects. In this context, it is important to make an optimal portfolio of desired projects. The present article aimed to identify an applied methodology for the selection of project portfolios with regard to efficiency and risk assessment and the alignment of the projects’ purposes with the organization’s goals, while also considering the existing resource limitations and regarding risk as a main indicator. The efficiency of the projects is examined with regard to the resources used. The present paper seeks to respond to the following main questions: ü How can an optimal project portfolio be selected for an organization with maximum efficiency and minimum risk? ü Does project risk assessment in view of the two criteria of impact and probability sufficiently address the economic conditions and the complexity of the projects in the majority of research and development projects? ü What is the drawback of current risk assessment methods for project portfolios? Responding to these questions can help organization managers select optimal project portfolios and achieve their strategic organizational objectives. Many studies have been conducted on the selection of project portfolios and most of them follow a qualitative and quantitative approach and use combination classification. One of the applied studies conducted on project selection is by Eilat et al., (2008), in which projects were selected within the combinational framework of DEA and a balance score card was used to select proper research and development projects (Tahri, 2015) presented two numerical methods for mathematical optimization problems for both single and multiple objectives using two values (0 and 1) as the decision variable. (Huang et al., 2016) discussed the joint problem of optimal project selection and scheduling in situations when the projects’ initial outlays and net cash inflows are determined by experts’ estimates due to the lack of historical data. A literature review reveals that there are a lot of optimization models available to prepare project portfolios. Most of them have one objective function to maximize project benefits or to minimize operating costs subject to operational constraints. In most modeling methods, the role of risk aspects in selecting appropriate projects has been neglected. A few of them have explored the aspect of model constraints. In other words, in the past, the main focus is directed towards economic projects while the sustainable factors (e.g., environmental and social risks) have been neglected. For this purpose, this study presents an integrated MOMP based on efficiency-risk for selecting a project portfolio using various techniques including DEA, RPN and non-dominated sorting genetic algorithm (NSGA-ΙΙ). Materials and Methods: Step1) Preparing a list of candidate & feasible projects Step2) Calculating efficiency of each project by using the DEA method Step3) Calculating the risk priority number for each project Step4) Developing a MOMP model to select the best projects Step5) Solving the model using a Non-dominated Sorting Genetic Algorithm ΙΙ (NSGAΙΙ) method Results and Discussion: One of the main advantages of NSGAII is that the at-hand solutions can be found in the form of several non-dominated cases and therefore, it is possible for organization’s experts to choose the best and the most suitable solutions. Stated differently, the expert’s knowledge and viewpoints can be considered due to flexibility and availability of different solutions. Besides, it is feasible to compute the adjusted efficiency and to select the solution(s) producing the maximum efficiency as the final optimal answer(s). Conclusion: This article used the concepts of DEA, RPN, MOMP and NSGAII modeling to propose an applied methodology for extracting an optimal portfolio of projects. In other words, we suggest the use of a Non-dominated Sorting Genetic Algorithm ΙΙ as a solution method for the presented multi-objective model in order to deduce the optimal projects portfolio. By comparing the results for the proposed algorithm and existing methods, it was concluded that the previous methods can give portfolio of projects with suitable profit but these solutions face high risk and low reliability. Thus, such solutions are not acceptable by managers in organizations. The lack of attention to risk aspects leads to the non-realization of the estimated profit due to high probability of risk. Therefore, the valuable resources will be wasted. Whereas, by adjusting profit with the risk numbers, it is indicated that the profit gained by our method is so better and higher than previous methods after risk. This can indicate novelty, applicability, and performance of our method. References Eilat, H., Golany, B. & Shtub, A. (2008). R&D project evaluation: An integrated DEA and balanced scorecard approach. Omega, 36, 895-912. Huang, X., Zhao, T. & Kudratova, S. (2016). Uncertain mean-variance and mean-semivariance models for optimal project selection and scheduling. Knowledge-Based Systems, 93, 1-11. Tahri, H. (2015). Mathematical Optimization Methods: Application in Project Portfolio Management. Procedia-Social and Behavioral Sciences, 210, 339-347. Abstract: A project portfolio is a crucial decision-making process used to prepare an optimum collection of vast alternative projects. In most of the previous modeling methods, the focus is directed towards maximizing project efficiency and so, the role of risky aspects in selecting appropriate projects has been neglected. This paper presents an integrated multi-objective mathematical programming (MOMP) based on efficiency-risk for selecting a project portfolio using various techniques including data envelopment analysis (DEA), risk priority number (RPN) and non-dominated sorting genetic algorithm (NSGA-ΙΙ). The proposed model can support both the capability to nominate mutually exclusive projects (conflicting projects that only one of them can be done) or any type of predecessor projects (doing a project depends on another project) and concurrent projects (need to be done at the same time) selection. Another advantage of the model is that the hyper heuristic solutions can be found in the form of several non-dominated cases and it is possible for organization’s experts to choose the best and the most suitable solutions. Introduction: In the competitive world, intelligent optimum decision making is a vital task in the success of large systems. Due to lack of resources, it is not always possible to fully evaluate all proposed developmental projects. In this context, it is important to make an optimal portfolio of desired projects. The present article aimed to identify an applied methodology for the selection of project portfolios with regard to efficiency and risk assessment and the alignment of the projects’ purposes with the organization’s goals, while also considering the existing resource limitations and regarding risk as a main indicator. The efficiency of the projects is examined with regard to the resources used. The present paper seeks to respond to the following main questions: ü How can an optimal project portfolio be selected for an organization with maximum efficiency and minimum risk? ü Does project risk assessment in view of the two criteria of impact and probability sufficiently address the economic conditions and the complexity of the projects in the majority of research and development projects? ü What is the drawback of current risk assessment methods for project portfolios? Responding to these questions can help organization managers select optimal project portfolios and achieve their strategic organizational objectives. Many studies have been conducted on the selection of project portfolios and most of them follow a qualitative and quantitative approach and use combination classification. One of the applied studies conducted on project selection is by Eilat et al., (2008), in which projects were selected within the combinational framework of DEA and a balance score card was used to select proper research and development projects (Tahri, 2015) presented two numerical methods for mathematical optimization problems for both single and multiple objectives using two values (0 and 1) as the decision variable. (Huang et al., 2016) discussed the joint problem of optimal project selection and scheduling in situations when the projects’ initial outlays and net cash inflows are determined by experts’ estimates due to the lack of historical data. A literature review reveals that there are a lot of optimization models available to prepare project portfolios. Most of them have one objective function to maximize project benefits or to minimize operating costs subject to operational constraints. In most modeling methods, the role of risk aspects in selecting appropriate projects has been neglected. A few of them have explored the aspect of model constraints. In other words, in the past, the main focus is directed towards economic projects while the sustainable factors (e.g., environmental and social risks) have been neglected. For this purpose, this study presents an integrated MOMP based on efficiency-risk for selecting a project portfolio using various techniques including DEA, RPN and non-dominated sorting genetic algorithm (NSGA-ΙΙ). Materials and Methods: Step1) Preparing a list of candidate & feasible projects Step2) Calculating efficiency of each project by using the DEA method Step3) Calculating the risk priority number for each project Step4) Developing a MOMP model to select the best projects Step5) Solving the model using a Non-dominated Sorting Genetic Algorithm ΙΙ (NSGAΙΙ) method Results and Discussion: One of the main advantages of NSGAII is that the at-hand solutions can be found in the form of several non-dominated cases and therefore, it is possible for organization’s experts to choose the best and the most suitable solutions. Stated differently, the expert’s knowledge and viewpoints can be considered due to flexibility and availability of different solutions. Besides, it is feasible to compute the adjusted efficiency and to select the solution(s) producing the maximum efficiency as the final optimal answer(s). Conclusion: This article used the concepts of DEA, RPN, MOMP and NSGAII modeling to propose an applied methodology for extracting an optimal portfolio of projects. In other words, we suggest the use of a Non-dominated Sorting Genetic Algorithm ΙΙ as a solution method for the presented multi-objective model in order to deduce the optimal projects portfolio. By comparing the results for the proposed algorithm and existing methods, it was concluded that the previous methods can give portfolio of projects with suitable profit but these solutions face high risk and low reliability. Thus, such solutions are not acceptable by managers in organizations. The lack of attention to risk aspects leads to the non-realization of the estimated profit due to high probability of risk. Therefore, the valuable resources will be wasted. Whereas, by adjusting profit with the risk numbers, it is indicated that the profit gained by our method is so better and higher than previous methods after risk. This can indicate novelty, applicability, and performance of our method. References Eilat, H., Golany, B. & Shtub, A. (2008). R&D project evaluation: An integrated DEA and balanced scorecard approach. Omega, 36, 895-912. Huang, X., Zhao, T. & Kudratova, S. (2016). Uncertain mean-variance and mean-semivariance models for optimal project selection and scheduling. Knowledge-Based Systems, 93, 1-11. Tahri, H. (2015). Mathematical Optimization Methods: Application in Project Portfolio Management. Procedia-Social and Behavioral Sciences, 210, 339-347.

https://jpom.ui.ac.ir/article_23074_4d2e62aa53e51f21a48a58ce6a7e2e5e.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Application of Geographical Information System in Evaluating Productivity Growth of Sale Centers Using The Malmquist Productivity Index Application of Geographical Information System in Evaluating Productivity Growth of Sale Centers Using The Malmquist Productivity Index 159 178 23090 10.22108/jpom.2018.92292.0 FA Ali Mansouri Assistant professor, Department of Management, University of Zanjan, Zanjan, Iran Journal Article 2013 09 08 Evaluating productivity and efficiency is an important measure for managerial performance. Appraising and taking advantages of valid mechanisms to evaluate managerial performance is highly important. Malmquist productivity index and Geographical Information System (GIS) are two tools which their integration can provide a pervasive approach for decision making units (DMUs) appraising depend on geographical position. This research uses these techniques to evaluate productivity improvement of an Iranian company’s sale centers. For this purpose, a mathematical model is designed and also, ordinary productivity variables and GIS data base variables are considered. The results reveal that the most productivity improvement belongs to Store 2 with 24.7 percent of improvement which is graded as inefficient centers by primary evaluation. The mean total productivity improvement for all sales centers in a given period is recognized as 15.2 percent by this approach. Introduction: Sales centers and dealerships are among the largest industries in the world. From the point of view of sales engineering, sales centers interact with two other main components of supply chain sales, namely, manufacturers and customers, in other words, there are the main interface between these two groups. Also, due to direct relationship between sales centers with customers, their performance will greatly affect the net profit and sales volume of both groups of producers and sellers (Warley, 2006). Therefore, continuous evaluation of the performance of each sales center is a central requirement for the center to recognize its strengths and weaknesses. Calculation of the efficiency of each sales center is one of the best practices for evaluating performance. Performance is often defined for a sales center in terms of outputs to the inputs ratio of that center. Therefore, making more output with less input, will result in more efficient sales center (Gilbert, 2003). The data envelopment analysis model (DEA) is one of the best presented models for calculating the relative efficiency of different decision making units. In this model, by finding the best weights for inputs and outputs, the maximum amount of possible efficiency per unit is calculated; while other models depend on the constant weight of outputs and inputs thus basically applying the judgment of the decision maker will be allocated (this will affect the accuracy of the results). However, it is necessary that the efficiency of each decision making unit must be computed for several periods to assess the improvement or decline of each decision making units to procure fundamental guideline to each decision making unit directors. The productivity index of Malmquist specifies total factor productivity changes and their components for each of the decision-making units. Thus in this paper, productivity changes were measured for some sales centers using new considerable important variables such as number of competitors and number existence population considering GIS based model. Materials and Methods:In this paper, Malmquist productivity index was used to assess the main important productivity index in its component in detail for each DMUs. This index strongly based on distance function developed by Shephard. Based on this, Shephard defines distance function as follows (Shephard, 2015). (1) The distance function or coefficient θ shows the possibility of reducing inputs to produce a certain value, and the vector x is the vector that represents the production factors used for the production value for a decision unit. Accordingly, the Malmquist index can be defined as follows (Malmquist,1953). (2) Results and Discussion: The findings of papers were considerably important. The results revealed that the mean technical efficiency based of constant return to scale (CRS) for all seller centers equals 0.814 and mean technical efficiency based of variable return to scale(VRS) for all seller centers equals 0.761. The following table shows all the measures in detail. Table 1- central criteria and efficiency dispersion Description 16 Number of units 0.814 Average of technical efficiency based CRS 0.218 Standard error of technical efficiency based VRS 0.716 Average of technical efficiency based VRS 0.295 Standard error of technical efficiency based VRS Conclusion: The results revealed that the combination of GIS and Malmquist index provides strongly dependable criteria to assess efficiency factors. Using these useful measures, we found that the biggest growth relates to the seller center number 2 which categorized as inefficient center and the lower growth of efficiency based on Malmquist index relates to efficient seller centers. References Banker, R. D., A. Charnes, and W. W. Cooper (1984), "Some Methods for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis", Management Science, 30, 1078-92. Mansoury, A., & Salehi, M. (2011). Efficiency analysis and classification of bank by using Data Envelopment Analysis (DEA) Model: Evidence of Iranian Bank. International Journal of the Physical Sciences, 6(13), 3205-3217. Shepherd, R. W. (2015). Theory of cost and production functions. Princeton University Press. Evaluating productivity and efficiency is an important measure for managerial performance. Appraising and taking advantages of valid mechanisms to evaluate managerial performance is highly important. Malmquist productivity index and Geographical Information System (GIS) are two tools which their integration can provide a pervasive approach for decision making units (DMUs) appraising depend on geographical position. This research uses these techniques to evaluate productivity improvement of an Iranian company’s sale centers. For this purpose, a mathematical model is designed and also, ordinary productivity variables and GIS data base variables are considered. The results reveal that the most productivity improvement belongs to Store 2 with 24.7 percent of improvement which is graded as inefficient centers by primary evaluation. The mean total productivity improvement for all sales centers in a given period is recognized as 15.2 percent by this approach. Introduction: Sales centers and dealerships are among the largest industries in the world. From the point of view of sales engineering, sales centers interact with two other main components of supply chain sales, namely, manufacturers and customers, in other words, there are the main interface between these two groups. Also, due to direct relationship between sales centers with customers, their performance will greatly affect the net profit and sales volume of both groups of producers and sellers (Warley, 2006). Therefore, continuous evaluation of the performance of each sales center is a central requirement for the center to recognize its strengths and weaknesses. Calculation of the efficiency of each sales center is one of the best practices for evaluating performance. Performance is often defined for a sales center in terms of outputs to the inputs ratio of that center. Therefore, making more output with less input, will result in more efficient sales center (Gilbert, 2003). The data envelopment analysis model (DEA) is one of the best presented models for calculating the relative efficiency of different decision making units. In this model, by finding the best weights for inputs and outputs, the maximum amount of possible efficiency per unit is calculated; while other models depend on the constant weight of outputs and inputs thus basically applying the judgment of the decision maker will be allocated (this will affect the accuracy of the results). However, it is necessary that the efficiency of each decision making unit must be computed for several periods to assess the improvement or decline of each decision making units to procure fundamental guideline to each decision making unit directors. The productivity index of Malmquist specifies total factor productivity changes and their components for each of the decision-making units. Thus in this paper, productivity changes were measured for some sales centers using new considerable important variables such as number of competitors and number existence population considering GIS based model. Materials and Methods:In this paper, Malmquist productivity index was used to assess the main important productivity index in its component in detail for each DMUs. This index strongly based on distance function developed by Shephard. Based on this, Shephard defines distance function as follows (Shephard, 2015). (1) The distance function or coefficient θ shows the possibility of reducing inputs to produce a certain value, and the vector x is the vector that represents the production factors used for the production value for a decision unit. Accordingly, the Malmquist index can be defined as follows (Malmquist,1953). (2) Results and Discussion: The findings of papers were considerably important. The results revealed that the mean technical efficiency based of constant return to scale (CRS) for all seller centers equals 0.814 and mean technical efficiency based of variable return to scale(VRS) for all seller centers equals 0.761. The following table shows all the measures in detail. Table 1- central criteria and efficiency dispersion Description 16 Number of units 0.814 Average of technical efficiency based CRS 0.218 Standard error of technical efficiency based VRS 0.716 Average of technical efficiency based VRS 0.295 Standard error of technical efficiency based VRS Conclusion: The results revealed that the combination of GIS and Malmquist index provides strongly dependable criteria to assess efficiency factors. Using these useful measures, we found that the biggest growth relates to the seller center number 2 which categorized as inefficient center and the lower growth of efficiency based on Malmquist index relates to efficient seller centers. References Banker, R. D., A. Charnes, and W. W. Cooper (1984), "Some Methods for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis", Management Science, 30, 1078-92. Mansoury, A., & Salehi, M. (2011). Efficiency analysis and classification of bank by using Data Envelopment Analysis (DEA) Model: Evidence of Iranian Bank. International Journal of the Physical Sciences, 6(13), 3205-3217. Shepherd, R. W. (2015). Theory of cost and production functions. Princeton University Press.

https://jpom.ui.ac.ir/article_23090_8be21fd0dc9295cc7a96a9150693cce8.pdf

University of Isfahan Research in Production and Operations Management 2981-0329 9 2 2018 10 23 Pricing and Determining the Optimal Discount of Perishable Goods to Speed up Demand Rate Pricing and Determining the Optimal Discount of Perishable Goods to Speed up Demand Rate 179 193 23082 10.22108/jpom.2017.92450.0 FA Morteza Khakzar Bafruei Asistant Professor of Industrial Engineering, Technology Development Institute, ACECR, Tehran, Iran Fatemeh Zabihi Ph.D. Student of Industrial Engineering, Technology Development Institute, ACECR, Tehran, Iran Journal Article 2015 05 25 In the competitive market of perishable cargoes, determining the price of the product and making opportunities for customers to accelerate the sale of goods through discounts is crucial. Over the life of perishable goods, generally its value reduced to the customer, in this situation, to encourage the purchase, policies such as a discount or reduced price sales policies can be effective. Literature has not provided a model for determining the optimal time to announce a price reduction. While early or late prices announcement could reduce profit, the aim of this paper is to analyze such a model at the level of an enterprise. In the modeling, we assumed that by announcing price discount, tangible changes occur in demand, and demand is a function of price and time. The demand rate in the discount time is decreasing in the beginning of the time and then declining over time. The purpose of the model is determining the optimal price, discount time and order size to maximize the total profit in a single period. After modeling, concavity of the profit function is considered and optimal pricing and discounts are exclusive. Then, a heuristic algorithm derived from the literature was used in order to determine the optimal price, the optimal discount time and the optimal order quantity. Introduction: In this article, the term "perishable" is used for goods that, due to rapid technological changes or the introduction of new products by competitors, should lose their value over a period of time. For example, fashion goods in the season will quickly fall in price, because otherwise the need for spare parts for military aircraft is one of fashion goods that would be unusable if a new aircraft model is being used (Khanlarzadeh et al., 2014). When non-perishable products approach their expiration date, they often use price discounts. Tajbakhsh et al (2011) developed an inventory model at a price of Random Discount, and numerical analysis that showed cost saving through discounts. The research conducted in the field of pricing and bidding for the aforementioned commodities, only several models have been developed that are either definitive or random models with known distributions (Wang, 2012). Rajan et al. (1992) have developed pricing policies and ordered for definitive applications. Also, if problem modeling occurs in the supply chain, competition between the members of the chain is formed to generate more profit. Zhang et al. (2015) considered a supply chain model with a producer and retailer for degraded items at a time-rate and price-dependent demand. They have designed an algorithm for obtaining price and investment protection technology strategies, and have examined both centralized and decentralized scenarios. In this article, the pricing of a perishable goods is considered under discounted conditions, and given the importance of selling these products over the life of the customer, it is essential to pursue a policy that can encourage customers to buy more. Also, the discount policy comes with the synchronization of the demand function during the discount period. In the absence of discounts, the demand rate is a function of the time and price, and in the discount period, the demand function is initially at an incremental time, and after the discount, the time is reduced. In the literature examined, the price for the final customer, which affects demand and does not change the demand for demand function, is not taken into account. For example, Meihami and Karimi (2014) show a change in demand after advertising with a coefficient in the demand function has given. While in the real world, with the announcement of a discount, the function of the rate of demand for perishable goods varies and is not mentioned in any of the previous investigations. In the following, we describe the assumptions and symbolization of problem modeling. Materials and Methods: It is assumed that the maximum inventory in the first period (I0) is the order quantity, and its decreasing is only affected by demand. As a price mark-down should always be applied before the expiration date of the product, the time horizon for product selling can be divided into two intervals: [0, t] and [t,T]. Notice that due to the discount after the price mark-down, the demand rate function during the time intervals [0, t] and [t, T] is different, in the interval [t, T], the product is sold out at the discount price p(1-a). Due to the discount, a moderate growth in the demand initially occurs; however, it reduces gradually (see Fig. 1.). There is no shortage, nor surplus in the end of the time horizon, i.e., period T, so the inventory level is the demand in that period. On the other hand, the demand in the time interval [0,t] can be expressed as follows, , and the profit can be expressed, (1) (. (2) The methodology must be clearly stated and described in sufficient detail or with sufficient references containing the research model and tools. Discount time (t) T Q=I0 Fig. 1. Inventory level in period T Results and Discussion: The proposed algorithm is used for solving the following numerical example to illustrate the solution process and results. Mathematica 9 was used in this regard. Example.The following parameters and functions are used. T=2, c=200, =0.3 Table 1 show, the convergence of the algorithm, where for the quasi-optimal tolerance e, it results in p*= , t*=1.008, TP*= , Q*= , and the numerical results are obtained for the price interval [400, 1000]. Table 1- Computational results of Example 1. k pk tk TPk 1 2 3 4 5 6 Conclusion: In this paper, the pricing model for non-perishable goods was presented under discounted sales terms. In modeling the hypothesis problem by declaring a decline in sales prices, the demand rate has a tangible change, and demand is a function of price and time. In this paper, it was proved that the goal of profit is optimal and unique in terms of optimal price and discount time. With using a simple algorithm, a numerical example of a model and results are analyzed using sensitivity analysis on model parameters. The model presented in this paper is a comprehensive and complete model, and compares to different values of the parameters of the flexible demand function. The model presented in this study can be expanded in several ways; the demand rate in this paper is definite. It is considered to be time-dependent, with its probability, it is possible to define a suitable topic for future research. We can also consider the discount percentage variable. On the other hand, advertising policies, delay in payments and coordination models in the supply chain system and reviewing the results can be considered. References Khanlarzade, N. et. al. (2014), Inventory Control with Deteriorating Items: A State-Of-The-Art Literature Review. International journal of industrial engineering computations, 5(2): 179-198. Maihami, R., and Karimi B., (2014), Optimizing The Pricing And Replenishment Policy For Non-Instantaneous Deteriorating Items With Stochastic Demand And Promotional Efforts. Computers & Operations Research, 51:302-312. Rajan A., Steinberg R., Richard S., (1992), Dynamic pricing and ordering decisions by monopolist. Management Science, 38(2): 240-262. Tajbakhsh, M., Lee, C., & Zolfaghari, S. (2011). An inventory model with random discount offerings. Omega, 39, 710–718. Wang X., Li D., (2012), A dynamic product quality evaluation based pricing model for perishable food supply chains. Omega, 40: 906-917. Zhang, Jianxiong et al., (2015), Coordinating A Supply Chain For Deteriorating Items With A Revenue Sharing And Cooperative Investment Contract. Omega 56: 37-49. In the competitive market of perishable cargoes, determining the price of the product and making opportunities for customers to accelerate the sale of goods through discounts is crucial. Over the life of perishable goods, generally its value reduced to the customer, in this situation, to encourage the purchase, policies such as a discount or reduced price sales policies can be effective. Literature has not provided a model for determining the optimal time to announce a price reduction. While early or late prices announcement could reduce profit, the aim of this paper is to analyze such a model at the level of an enterprise. In the modeling, we assumed that by announcing price discount, tangible changes occur in demand, and demand is a function of price and time. The demand rate in the discount time is decreasing in the beginning of the time and then declining over time. The purpose of the model is determining the optimal price, discount time and order size to maximize the total profit in a single period. After modeling, concavity of the profit function is considered and optimal pricing and discounts are exclusive. Then, a heuristic algorithm derived from the literature was used in order to determine the optimal price, the optimal discount time and the optimal order quantity. Introduction: In this article, the term "perishable" is used for goods that, due to rapid technological changes or the introduction of new products by competitors, should lose their value over a period of time. For example, fashion goods in the season will quickly fall in price, because otherwise the need for spare parts for military aircraft is one of fashion goods that would be unusable if a new aircraft model is being used (Khanlarzadeh et al., 2014). When non-perishable products approach their expiration date, they often use price discounts. Tajbakhsh et al (2011) developed an inventory model at a price of Random Discount, and numerical analysis that showed cost saving through discounts. The research conducted in the field of pricing and bidding for the aforementioned commodities, only several models have been developed that are either definitive or random models with known distributions (Wang, 2012). Rajan et al. (1992) have developed pricing policies and ordered for definitive applications. Also, if problem modeling occurs in the supply chain, competition between the members of the chain is formed to generate more profit. Zhang et al. (2015) considered a supply chain model with a producer and retailer for degraded items at a time-rate and price-dependent demand. They have designed an algorithm for obtaining price and investment protection technology strategies, and have examined both centralized and decentralized scenarios. In this article, the pricing of a perishable goods is considered under discounted conditions, and given the importance of selling these products over the life of the customer, it is essential to pursue a policy that can encourage customers to buy more. Also, the discount policy comes with the synchronization of the demand function during the discount period. In the absence of discounts, the demand rate is a function of the time and price, and in the discount period, the demand function is initially at an incremental time, and after the discount, the time is reduced. In the literature examined, the price for the final customer, which affects demand and does not change the demand for demand function, is not taken into account. For example, Meihami and Karimi (2014) show a change in demand after advertising with a coefficient in the demand function has given. While in the real world, with the announcement of a discount, the function of the rate of demand for perishable goods varies and is not mentioned in any of the previous investigations. In the following, we describe the assumptions and symbolization of problem modeling. Materials and Methods: It is assumed that the maximum inventory in the first period (I0) is the order quantity, and its decreasing is only affected by demand. As a price mark-down should always be applied before the expiration date of the product, the time horizon for product selling can be divided into two intervals: [0, t] and [t,T]. Notice that due to the discount after the price mark-down, the demand rate function during the time intervals [0, t] and [t, T] is different, in the interval [t, T], the product is sold out at the discount price p(1-a). Due to the discount, a moderate growth in the demand initially occurs; however, it reduces gradually (see Fig. 1.). There is no shortage, nor surplus in the end of the time horizon, i.e., period T, so the inventory level is the demand in that period. On the other hand, the demand in the time interval [0,t] can be expressed as follows, , and the profit can be expressed, (1) (. (2) The methodology must be clearly stated and described in sufficient detail or with sufficient references containing the research model and tools. Discount time (t) T Q=I0 Fig. 1. Inventory level in period T Results and Discussion: The proposed algorithm is used for solving the following numerical example to illustrate the solution process and results. Mathematica 9 was used in this regard. Example.The following parameters and functions are used. T=2, c=200, =0.3 Table 1 show, the convergence of the algorithm, where for the quasi-optimal tolerance e, it results in p*= , t*=1.008, TP*= , Q*= , and the numerical results are obtained for the price interval [400, 1000]. Table 1- Computational results of Example 1. k pk tk TPk 1 2 3 4 5 6 Conclusion: In this paper, the pricing model for non-perishable goods was presented under discounted sales terms. In modeling the hypothesis problem by declaring a decline in sales prices, the demand rate has a tangible change, and demand is a function of price and time. In this paper, it was proved that the goal of profit is optimal and unique in terms of optimal price and discount time. With using a simple algorithm, a numerical example of a model and results are analyzed using sensitivity analysis on model parameters. The model presented in this paper is a comprehensive and complete model, and compares to different values of the parameters of the flexible demand function. The model presented in this study can be expanded in several ways; the demand rate in this paper is definite. It is considered to be time-dependent, with its probability, it is possible to define a suitable topic for future research. We can also consider the discount percentage variable. On the other hand, advertising policies, delay in payments and coordination models in the supply chain system and reviewing the results can be considered. References Khanlarzade, N. et. al. (2014), Inventory Control with Deteriorating Items: A State-Of-The-Art Literature Review. International journal of industrial engineering computations, 5(2): 179-198. Maihami, R., and Karimi B., (2014), Optimizing The Pricing And Replenishment Policy For Non-Instantaneous Deteriorating Items With Stochastic Demand And Promotional Efforts. Computers & Operations Research, 51:302-312. Rajan A., Steinberg R., Richard S., (1992), Dynamic pricing and ordering decisions by monopolist. Management Science, 38(2): 240-262. Tajbakhsh, M., Lee, C., & Zolfaghari, S. (2011). An inventory model with random discount offerings. Omega, 39, 710–718. Wang X., Li D., (2012), A dynamic product quality evaluation based pricing model for perishable food supply chains. Omega, 40: 906-917. Zhang, Jianxiong et al., (2015), Coordinating A Supply Chain For Deteriorating Items With A Revenue Sharing And Cooperative Investment Contract. Omega 56: 37-49.

https://jpom.ui.ac.ir/article_23082_743c783d7c5de1ebb2ab719c25753def.pdf