Vol 9, Issue 1, No. 16, Spring & Summer 2018
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article
1397
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Journal of Production and Operations Management
University of Isfahan
2251-6409
9
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1
no.
1397
0
0
http://jpom.ui.ac.ir/article_23023_dc259b26ef2a5d4fa2bfc5749b3d9851.pdf
Vehicle Routing in a Multi-product Supply Chain using Populated Simulated Annealing Algorithm
Mohammad Ali
Beheshtinia
Assistant Professor, Industrial engineering department, Semnan University, Semnan, Iran
author
Ali
Borumand
MA of industrial engineering, Semnan University, Semnan, Iran
author
Mohammad Reza
Taheri
MA of industrial engineering, Semnan University, Semnan, Iran
author
Hesam
Babaei
MA of industrial engineering, Semnan University, Semnan, Iran
author
text
article
2018
per
This paper aims to examine the scheduling of vehicles in a multi-product supply chain regarding to the mutual relationship between the transportation and the manufacturing units. The integration level in the supply chain consists of a manufacturer and its first tier suppliers, which are linked by a transportation fleet. The problem is determining orders allocation to the suppliers, orders production sequence at the suppliers, orders allocation to the vehicles, and orders transportation priority, in order to minimize the sum of orders delivery time. This issue has not been discussed in the literature, so far. At first, the mathematical model of the problem is presented, then the NP-Hardness of the problem is demonstrated. For solving the problem, a new combination of genetic algorithm and simulated annealing algorithm, named as Populated Simulated Annealing algorithm (PSA) is proposed. For verifying the PSA, its results are compared to results of simulated annealing algorithm (SA) and developed version of DGA algorithm, proposed for the nearest problem in the literature to our problem. Furthermore, relaxing some hypothesis, the results of PSA are compared to DGA results. All of the comparisons show that PSA is more efficient than the other algorithms. Finally, comparison of PSA with exact solution for small size problems demonstrates its proper efficiency. Introduction: The vehicle routing problem (VRP) is one of the most important issues in the world's industry, which, today, is highly regarded because of its practical applications in industries. We examined the scheduling of production and transportation in a multi-product supply chain considering the interaction between the transportation and the manufacturing units. The supply chain consists of two parts.The first part is suppliers which are located in different geographical locations handling specific orders. The second part consists of several vehicles that collect the orders processed by suppliers and deliver them to the company. The considered transportation system is similar to vehicle routing problem (VRP). The difference between VRP and the problem in this research is that in VRP the amount of goods that should be transported, and is known. However, as it is assumed in this research, the allocation of orders and sequencing of their manufacturing are the decisive variables. Problem objectives are determining the allocation of orders to suppliers, orders production sequence, orders allocation to the vehicles, and transportation sequence, in order to minimize the summation of the orders completion time. Innovation of this paper is as follows: A combination of production scheduling problem in suppliers and VRP in a supply chain when the supplier can’t process all orders. Developing a new mathematical model for solving the problem. Three algorithms have been proposed to solve this problem, including: developed DGA, simulated annealing algorithm (SA), and a new combination of these two algorithms, which is named populated simulated annealing algorithm (PSA). A supply chain consists of a set of suppliers, producers and distributors that cooperate with each other in order to satisfy customers’ need. A supply chain determines all levels in which the value is added to a product. VRP has several versions. In this study, it is considered that a number of heterogeneous vehicles are collecting orders from suppliers located in different geographical locations. With considering the integration level of companies in the supply chain, researches can be divided into four categories: 1) Researches that examine the relationship between manufacturers and suppliers; 2) Researches that examine the relationship between manufacturers and distributors or customers; 3) Researches that focus on the relationship between some manufacturers together (Outsourcing); 4) Researches that consider combination of the above scenarios. 5) Considering the examination level of supply chain, researches have been divided in two categories: 1) Researches that have a macro planning and coordinating in the completion chain; 2) Researches that have an operational scheduling and coordinating in the supply chain. The literature shows that the combination of VRP with scheduling problem in supply chains possessing constraint on allocating the orders to suppliers has not been studied. Materials and Methods:Step 1) Developing a new mathematical model for this problem. Step 2) Developing the PSA algorithm to solve the problem. Step 3) Validating PSA algorithm as follows: Step 3-1) Producing random samples with different structures. Step 3-2) Comparing PSA with SA and developing DGA. Step 3-3) Comparing PSA with DGA after adding a relaxation assumption. Step 3-4) Solving small samples with PSA and comparing with exact solution. Step 4) Doing sensitivity analysis on the three main parameters. (Number of orders, Number of suppliers, and Number of vehicles) Results and Discussion: The results of the comparison demonstrate that the populated simulated annealing algorithm shows better results than the other two. This method shows that the combination of genetic algorithm and simulated annealing in this specific way can adapt advantages of both methods. The results show that the mean of answers is increased by increasing number of orders,. With increasing suppliers, the objective function is improved because the orders allocate to different suppliers and the delivery time is decreased. By increasing orders processing time, the objective function value gets worse because the waiting time for processing orders is increased. By increasing transport times, the average solution is increased. It’s because vehicles should spend more time along the way. Conclusion This issue has not been discussed in the literature. At first, the mathematical model is presented and then it is shown that the problem is NP-Hard. Three algorithms have been proposed to solve this problem: Developed DGA, Simulated Annealing Algorithm, and a new combination of these two algorithms, which is named Populated Simulated Annealing Algorithm. Random samples with different structures is created and solved by these three algorithms. Also, relaxation of distance assumption between suppliers that are in the same location has been discussed at Zegordi and Beheshti Nia (2009) and is compared with PSA which shows that PSA is more efficient than the other algorithms. Finally, the comparison of PSA with exact solution for small size problems demonstrates its proper efficiency. References Archetti, C., Jabali, O., & Speranza, M. G. (2015). Multi-period vehicle routing problem with due dates. Computers & Operations Research, 61, 122-134. Ray, S., Soeanu, A., Berger, J., & Debbabi, M. (2014). The multi-depot split-delivery vehicle routing problem: Model and solution algorithm. Knowledge-Based Systems, 71, 238-265. Zegordi, S., & Beheshti Nia, M. (2009). Integrating production and transportation scheduling in a two-stage supply chain considering order assignment. The International Journal of Advanced Manufacturing Technology, 44(9-10), 928-939. doi: 10.1007/s00170-008-1910-x
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
v.
1
no.
2018
1
27
http://jpom.ui.ac.ir/article_22947_b28bde948ad0cfaad417c86b51f6501a.pdf
dx.doi.org/10.22108/jpom.2018.92451.0
Evaluation of LARG Supply Chain Competitive Strategies based on Gap Analysis in Cement Industries
Gholamreza
Jamali
Assistant Professor, Department of Industrial Management, Persian Gulf University, Bushehr, Iran
author
Elham
Karimi Asl
MA of Industrial Management, Gulf University, Iran
author
text
article
2018
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Supply Chain Management (SCM) is considered a strategic factor for the better attainment of organizational goals such as enhanced competitiveness, improved product quality and increased profitability in cement industry. This research aims at competitive positioning of LARG supply chain in Iranian cement industry and its strategic requirements (Strenghts, Weaknesses, Oportunities and Threats) Importance-Performance Analysis (IPA). A survey-descriptive research method was applied and an available sample which includes 11 Iranian cement companies were selected. First, using literature review and Delphi Method (DM), strategic requirements of LARG supply chain in the cement industry were identified. In the next step, the importance of strategic requirements was determined using SWARA method. Then, the results of applying Internal/External Factors Evaluation (IFE/EFE) matrix showed that the suitable position for LARG supply chain in Iranian cement industry would be an aggressive strategy. In the final step, applying Importance-Performance Analysis (IPA) matrix showed all requirements for the aggressive strategy, except exporting opportunities and cooperation culture in supply chain, were evaluated in quadrant II (keep up the good work). Finally some suggestions are presented toward improving LARG supply chain performance in Iranian cement industry. Introductıon: Supply Chain Management (SCM) is considered a strategic factor for the better attainment of organizational goals such as enhanced competitiveness, improved product quality and increased profitability. SCM is a value chain management from the supplier of a supplier to the customer of a customer of a company with the aim of attaining an overall value. Lean, Agile, Resilient and Green are now at the forefront in management methods and SCM (Espadinha–Cruz et al., 2011). The trade-offs between these managerial paradigms (LARG) are actual issues and may help supply chains to become more efficient, streamlined and sustainable. The supply chain as a network is expected to provide the right products and services on time with the required specifications at the right place to the customer. The main purpose of this research is a competitive positioning of LARG supply chain in Iranian cement industry and its strategic requirements (Strenghts, Weaknesses, Oportunities and Threats) Importance-Performance Analysis (IPA). Materıals and Methods: A survey-descriptive research method was applied and an available sample which includes 11 Iranian cement companies were selected. First, using literature review and Delphi Method (DM), strategic requirements of LARG supply chain in the cement industry were identified. In the next step, the importance of strategic requirements was determined using SWARA method. Then we used the Strategic Position and Action Evaluation Matrix (SPACE MATRIX) to select an appropriate strategy for LARG supply chain in Iranian cement industry. In the SPACE matrix, we assessed Iranian cement industries across four dimensions including: Industry Attractiveness (IA), Environmental Stability (ES), Competitive Advantage (CA) and Financial Strength (FS). The SPACE diagram showed favourable positions in all four dimensions. In the final step, an Importance-Performance Analysis (IPA) matrix was applied. Results And Dıscussıon: The results (as shown in Fig. 1) of applying SPACE matrix revealed that the suitable position for LARG supply chain in Iranian cement industry would be an aggressive strategy as it leverages its strengths into the opportunities. In other words, Strengths-Opportunities (SO) strategies are based on using a firm’s internal strengths to take advantage of external opportunities and threats. Fig. 1- SPACE Matrix for positioning of LARG supply chain in Iranian cement industries In order to determine the performance level, mean values of strategic requirements were calculated via 1 to 5 lykert continum questionnaire completed by cement experts. Also, we used SWARA method to determine the importance of strategic requirements. Importance-Performance Analysis (IPA) matrix showed all requirements for the aggressive strategy, except exporting opportunities and cooperation culture in supply chain, were evaluated in quadrant II (keep up the good work). Conclusıons:This study proposes a competitive positioning for LARG supply chain in the Iranian cement industry and its strategic requirements importance-performance analysis. In the SPACE matrix we assessed Iranian cement industries across four dimensions including: industry attractiveness, environmental stability, competitive advantage and financial strength. The SPACE diagram showed that Iranian cement industries can pursue an aggressive strategy as it has a strong competitive position in the market with rapid growth. The two big concerns in this competitive positioning are: 1) Avoid complacency – it seems that business is too easy but threats may come from new markets or as technology makes different sectors to converge; and 2) Avoid running foul of anticompetition policies. A business that is too strong may be able to attract the attention of regulators and especially if it uses predatory pricing aimed at driving competitors out of business. Applying Importance-Performance Analysis (IPA) matrix clarified that all strenghts and opportunities were important. While there are gaps between performance level and strategic requirements importance, the improvement process will be continued. This study showed that integration of LARG supply chain competitive positioning in the Iranian cement industry and IPA model, can help Iranian decision makers in strategic planning for the SCM performance improvement. Iranian cement industries are also blessed because it has a good competitive advantage in an industry which is considered to be attractive. So, among the strategic choices, develop new local markets strategy has the first priority, followed by the; Increase production capacity, Export markets development and Product diversification. References Azevedo, S. G., Carvalho, H., & Cruz-Machado, V. (2016). LARG index: a benchmarking tool for improving the leanness, agility, resilience and greenness of the automotive supply chain. Benchmarking: An International Journal, 23(6), 1472-1499. Espadinha-Cruz, P., Grilo, A., Puga-Leal, R., & Cruz-Machado, V. (2011). A Model for Evaluating Lean, Agile, Resilient and Green Practices Interoperability in Supply Chains. Proceedings of the 2011 IEEE IEEM (978-1-4577-0739-1/11/$26.00 ©2011 IEEE). 1209-1231. Jamali, G., Karimi Asl, E., Zolfani, S. H., & Šaparauskas, J. (2017). Analysing LARG supply chain management competitive strategies in Iranian cement industries. Ekonomika a Management, XX(3),70-83.
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
v.
1
no.
2018
29
54
http://jpom.ui.ac.ir/article_22948_6e4713c7cf58057956fd228b865fbed6.pdf
dx.doi.org/10.22108/jpom.2018.92479.0
Optimization of Discrete Facility Layout with a Candidate Grouping Approach
Aliasghar
Miri
MA, Industrial Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
author
Hamideh
Razavi
Associate Professor, Industrial Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
author
text
article
2018
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Facility Layout Problem (FLP) is an important issue in plant design, which directly affects production costs as well as safety concerns. Hierarchical and integrated approaches are two main methods used for the formulation of FLP. In the hierarchical approach, FLP is solved after the completion of the process design and scheduling, while the integrated approach treats FLP simultaneously with other phases. This paper presents a new approach based on the candidate groups for interactive functions; incorporating the advantages of the previous approaches. In the new approach, the design phases prior to FLP results in a set of models introducing by the engineering team in advance. Next, the models are solved such that instead of individual designs, a set of suggested structures are generated. These structures are then fed into the FLP as input data and solved by mixed integer programming technique. Some characteristics of the models are: presence of the hub stations, different and variable dimensions for each station, possibility of rotation for the stations and incorporating safety distances. Finally, test problems are solved and results are discussed. It should be noted that if a candidate group entails a different production flow then a different optimum solution might be obtained. Introduction: Simultaneous optimization of facility layout with process design, automation and scheduling has been the subject of many research studies (Taghavi & Murat, 2011), (Realff et al., 1996), (Barbosa, 2007). The current research introduces a hybrid method for interactive phases of process and layout design. It starts with suggested cluster structures by process designers and attempts to decide among the choices while searching for optimum layout of facilities. In the rest of the paper, after a short description of group structures, a formulation of the MILP model is presented and the constraints, parameters and variables are briefly defined. Finally, 7 sample problems have been solved by exact methods. Then the developed model is solved such that instead of a single solution, a set of candidate groups are suggested. This set is later used as input to the layout problem. The innovation of this approach is a layout solution with the following characteristics: - Obtaining different flow process in terms of candidate groups from the initial phase. - The possibility of adding or removing the workstations in the candidate groups - The possibility of various dimensions in the group structures - MILP formulation for supporting the above characteristics In this approach, the solution space for layout problem only contains the process designs which are previously defined by in the plant design phase. This has many advantageous over the hierarchical layout methods such as less expenses and faster modelling and solution and less computational complexity. It has also the advantageous of an integrated approach in workstation layout considering different functions and interactions. Materials and Methods: Model description: For layout design in discrete production lines, an MILP model is developed. Facility layout in this research is confined to a two-dimensional (x,y) space and has the following characteristics: - One or more candidate groups can be defined, each consisting of at least two different connection structures, i.e. from-to charts with specified inner links and connecting structures (piping, conveyors or similar means of material flow). - Group centres are well defined if present. - Transportation costs and those costs related to cluster structures, e.g. extra equipment, semi-finished inventories, etc. are known in advance. - Facilities are rectangular with related fixed length and distances between facilities are rectilinear. - Facilities can rotate counter-clockwise by integer multiples of 90 degrees. - Total available area is limited and pre-specified. Objective function of the model is the sum of the investments on the physical connections, material flow costs and structural expenses of candidate groups. The constraints is related to the rotations status of the facilities, distances, available space, overlaps and safety concerns. Cost matrix is a cross product of flow matrix and transportation costs matrix. The final solution contains optimum plant layout, facilities orientations as well as optimum connections inside candidate groups. The model is solved by CPLEX which is mostly used for problem incorporating less than 15 workstations. Table 1 lists the solution time for 7 different problems. As can be seen in this table, the solution time for P7 is more than 40000 seconds with 6% gap. Therefore, the solution is used when limited number of workstations are aimed. For greater number of workstations, heuristic algorithms can be developed. Table 1. Test problems solved by CPLEX Time(sec) Opt Slution Candidate Group Quantity Station Quantity P. 461.5 451 2 11 P1 2.92 1165 1 6 P2 940.5 1217 2 9 P3 3943.8 1327.75 2 11 P4 25380.52 1641 2 13 P5 31803 1467.8 3 14 P6 40000 1850* 4 15 P7 References Barbosa-Povoa, A. P. (2007). A critical review on the design and retrofit of batch plants. Computers & Chemical Engineering, 31(7), 833–855. Realff, M. J., Shah, N., & Pantelides, C. C. (1996). Simultaneous design, layout and scheduling of pipeless batch plants. Computers & Chemical Engineering, 20(6), 869–883. Taghavi, A., & Murat, A. (2011). A heuristic procedure for the integrated facility layout design and flow assignment problem. Computers & Industrial Engineering, 61(1), 55–63.
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
v.
1
no.
2018
55
78
http://jpom.ui.ac.ir/article_22949_b574e0ae8611853b86e76315a83c3f1d.pdf
dx.doi.org/10.22108/jpom.2018.92448.0
A Decision Support System for evaluation and prioritization, the import risks to manage the effects of sanctions on Iran (Case Study: Farabi Pharmaceutical Company)
Bahram
Izadi
Assistant Professor, Department of Management, Sheikh Bahaei University, Isfahan, Ira
author
Mahbobeh
Shafie
MA, Department of Management, Sheikh Bahaei University, Isfahan, Iran
author
text
article
2018
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This paper proposes a decision support system for the evaluation and prioritization of imports in sanction atmosphere based on fuzzy quantitative models which are implemented in an Iranian pharmaceutical company. The most important risks are obtained include international payment restrictions and shipping risks. At the end, the strategies are presented to alleviate the spotted risks. Introduction: Today’s organizations are facing many different risks, especially the ones whose nature of work is mostly commercial and are engaged in importing goods. Therefore, in order to survive and to reduce the activity risks, these organizations should constantly be under review and monitoring. In addition to common risks in the process of importing goods, the tough sanctions against some countries like Iran, have caused the importing of goods to become one of the most risky work. For this reason, in order to prevent the expanding problems arising from sanctions, it is necessary to determine the importance and priorities of the risks along with recognizing their occurrences on time. Thus, by analyzing and prioritizing the risks, it is possible to distribute the rare resources of the organizations effectively. With the presence of the sanctions, many decisions related to the imports are vague and uncertain; while making decision in the shortest possible time in these cases is a vital matter. These facts indicate the importance and the necessity of having a system to support the decisions on evaluating and prioritizing of risks in importing goods. Therefore, in this paper, a decision support system has been designed and implemented to evaluate and prioritize the risks involved in importing goods in Isfahan Farabi Pharmacy Company as a case study. A few models in decision support system are able to manage the available data even if they are vague and uncertain. Materials and Methods: İn this research, with inspiration from Project Management Body of Knowledge (PMBOK) model which is one of the most comprehensive models in risk management, a new model is presented to analyze and prioritize the risks of importing goods at the time of imposing sanctions. This model consists of five stages: 1- planning for analysis and priority of the risks, 2- identifying these risks, 3- analyzing the risks which means to review and evaluate four criteria of ‘the possibility of the occurance of the risks’, ‘the degree of the effect of the risks’, ‘organizations’ ability in response to these risks’ (McDermott and colleagues, 2009), and ‘the uncertainty of decision makers in estimation’ (Klein & Cork, 1998). Thus, GFAHP and VIKOR methods by phase, group, and Grey Relationship Analysis for risk prioritizing will combine together; 4- planning in response to the risks; 5- controling and following up of risks. Implimentation of the suggested model for a case study (Farabi Pharmacy Company) is performed as follows: The system designed consists of three segments: 1- Data Base: the data based on this system is prepared by using Microsoft Excel software. 2- Original Model: this is the main section of the system which provides the possibility of performing calculations and MatLab software has been used for coding purposes. 3- User Interface: this will provide the communication between the user (decision makers) and the system. Results and Discussion: The presented model was used to manage the risk of importing goods by using a software system which is designed in Farabi Pharmacy Company and the most important risks related to importing pharmaceutical ingredients in this company are recognized to be as follows: 1- risks related to transportation of importing goods, 2- unsecured paths of transfering exchanges, 3- failure to timely payment of exchange to selling companies, 4- the purchase from available limited and invalid suppliers, 5- lack of training and previous commercial experiences in confrontation with sanction situations, 6- increase of the values of foreign exchanges as compared with Iranian Rial, 7- liquidity shortage at sanction situation, 8- putting the commercial performance related to supply chain under pressure, 9- the decrease in precise and correct information in supply chain, 10- to decrease product quality as a result of bottlenecks arising from sanctions. After performing stages of analysis of risks by decision support system, the risks of ‘failure to timely payment of exchange to selling companies’, ‘unsecured paths of transfering exchanges’, and risks related to ‘transportation of importing goods’ were found to have the highest priorities. Therefore, the organization resources should first be used to edit and execute the strategies for management of these risks. Conclusion: This paper has paid attention to quantifying the risks of importing goods for the first time and has presented a combined method of quantity models in decision making for offices. Using such a system in importing goods causes the recognition and control of related risks and the reduction of time and expences which are sometimes irreparable. The organization should spend most of its financial and human resources on executing a strategy for confrontation with risks of high priorities. At the end, some strategies for control and confrontation with each well known risks are presented. References McDermott, R. E., Mikulak, R. J., & Beauregard, M. R. (2009). The Basics of FMEA (2th ed.). Taylor & Francis Group, LLC: USA. Klein, J. H., & Cork, R. B. (1998)."An approach to technical risk assessment". International Journal of Project Management, 16(6), 345-351.
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
v.
1
no.
2018
79
106
http://jpom.ui.ac.ir/article_22950_7d348b8121b845b1042ef867a45964cc.pdf
dx.doi.org/10.22108/jpom.2018.92395.0
Robust Method for Logistic Profiles Monitoring in Phase I
Ahmad
Hakimi
MA, Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
author
Amirhossein
Amiri
Assistant professor, Department of Industrial Engineering, Shahed University, Tehran, Iran
author
Reza
Kamranrad
PhD student, Department of Industrial Engineering, Shahed University, Tehran, Iran
author
text
article
2018
per
In this paper, a new robust method based on weighted maximum likelihood estimation (WMLE) is proposed to estimate the regression parameters in logistic profiles in Phase I. This approach reduces the outlier’s effects on the statistical performance of T2 control chart in terms of probability of Type I error. A numerical example is used to evaluate the performance of the proposed method. The results show the better performance of the proposed estimator compared to the maximum likelihood estimation method in terms of power in T2 control chart. Introduction: Yeh et al. (2009) proposed five based T2 statistics to monitor the binary logistic regression profile in Phase I. Different approaches are proposed to monitor logistic regression profiles in Phase II. So far, few researches have been done on monitoring the profile with the presence of contaminated data. In this area, Ebadi and Shahriari (2014) proposed robust estimation approach to monitor the simple linear profile based on two classic and robust methods (M-estimator) with two functions including Huber weighted and double square functions. The aim of this paper is to monitor the logistic regression profiles with the presence of outliers in Phase I based on weighted maximum likelihood robust estimator and T2 control chart. The main questions of this papers are as follows: a) Evaluating the effect of outliers on the mean and standard deviation of the proposed and classic estimators of the logistic regression profile parameters and probability of Type I error in common T2 control chart, b) Comparing performance of the proposed and classic estimators on the T2 control chart power for different shifts in logistic regression profile parameters under outliers in Phase I. Materials and Methods: Sometimes, there are outliers in the gathered data which lead to incorrect estimation of the profile parameters. Hence, to decrease or remove the effect of outlier(s), robust estimation methods are applied. In this paper, a robust approach called weighted maximum likelihood estimator (WMLE) is applied to estimate the parameters of the logistic regression profiles as follows (Maronna et al., 2006): (1) where, is the probability of response variable in each level of logistic regression profile using the estimated parameters. A robust estimate for obtaining parameters is achieved by minimizing the above function. However, in order to give less weight to outliers, we can consider the following relationship and minimize it. (2) where is the weight of the ith observation which is calculated as Equation (3) (3) in which W is a non-ascending function and computed based on Carroll and Pederson (1993) as follows: (4) Results and Discussion The Type I error probability of T2 control chart considering the outlier using MLE and WMLE methods is summarized in Table 1. Table 1- Type I error probability of T2 control chart considering MLE and WMLE methods WMLE MLE Estimation Method 0.0718 0.1242 Type I error probability In this section, r percentage of the total data is contaminated with an increase in the variance of the errors. For r equal to 0.07 and 0.15, the variance error is changed from 1 to 4 and Type I error probability of the T2 control chart with both classic and proposed estimators are calculated and reported in Table 2. Table 2- Type I error probability of the T2 control chart with both classic and proposed estimators under different r Type I error probability Estimation methods r=0.07 Type I error probability Estimation methods r=0.15 0.1801 MLE 0.2779 MLE 0.1021 WMLE 0.1541 WMLE Based on Table 2, Type I error probability of the T2 control chart under the classic method is more than the robust one and this result shows the better performance of the proposed method rather than the classic one. Conclusion In this paper, a robust approach was developed to estimate the logistic regression profiles with the presence of outliers in Phase I. The performance of the proposed robust estimator was compared with the classic method (MLE) based on Type I error probability and power of T2 control chart in Phase I. Results showed that the WMLE method outperforms the MLE in estimating the logistic regression profile parameter under outliers. References Ebadi, M., & Shahriari, H., (2014), "Robust Estimation of Parameters in Simple Linear Profiles Using M-Estimators", Communications in Statistics - Theory and Methods, 43(20), 4308-4323. Maronna, AR., Martin, R.D., & Yohai, V.J., (2006), Robust Statistics Theory and Methods, John Wiley, New York. Yeh A.B., Huwang L., & Li Y.M., (2009), "Profile Monitoring for a Binary Response", IIE Transactions, 41(13), 931-941.
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
v.
1
no.
2018
107
118
http://jpom.ui.ac.ir/article_22953_7e5d58be2c0e8e708648787788649183.pdf
dx.doi.org/10.22108/jpom.2018.92335.0
Risk Analysis for it Projects Using System Dynamics
Nastaran
Hajiheidari
Assistant Professor, Managemet faculty, University of Tehran, Iran
author
Fatemeh
Rahmati
MA of IT management, Alzahra University, Iran
author
text
article
2018
per
In today's complex world when we talk about IT projects, risk appears such as an inseparable part. The purpose of this study is to identify risks in IT project management and their effect on the overall risk of the project. In order to achieve this objective, we study a wide range of researches in the field of IT project risk analysis. We classify risk factors and the factors are simulated in a dynamic model. Then, some equations are extracted using examining relationship between structures and factors, and the risks are studied in a period of 12 month. The results of this study show that human resource risk is the most important risk that is repeated, after that project management risk is the second risk. Strategic risk is a risk that is appeared in some periods. So, we suggest IT project managers to pay more attention to these risks in the politics and strategies. Introduction: This research can be classified as applied researches because the researchers attempt to provide a solution for recognition and management of IT projects, considering the need for the current community to pay particular attention to risk and analyzing it in active organizations in the field of information technology, and by conducting fundamental research in this field. The achievement of this endeavor is to provide a dynamic simulation model for risk analysis of IT projects, which can be used to determine the priority of significant risks over a given time period. Since this study is based on existing projects in IT organizations, the scope of research can be defined by all projects that are carried out in companies and organizations with background in the field of information technology. The general purpose of this research is to provide a dynamic model of risk analysis in IT projects. Dedicated objectives are included: • Identification of risk factors in IT projects • Identification of Structures (Major Groups) Risk of IT Projects • Prioritizing the risk structures of IT projects • Examining the extent of explaining each of the risk structures by the relevant components in IT projects • Investigating the relationship among risk factors in IT projects • Investigating the impact of changes in the overall risks of IT projects for changes in each of the risk structures Row Researcher's name Year of research The topic of the research 1 Ssemaluulu, Paul and Williams Ddembe 2007 Complexity and Risk in IS Projects: A System Dynamics Approach 2 Trček, Denis 2008 Using System Dynamics for Managing Risks in Information Systems 3 Trček, Denis 2009 System Dynamics Based Risk Management for Distributed Information Systems 4 Sen, Wang Gui and yang, Li Xiang 2010 The Risk Analysis on IT Service Outsourcing of Enterprise with System Dynamics 5 Dash Wu, Desheng, et al. 2010 Modeling technological innovation risks of an entrepreneurial team using system dynamics: An agent-based perspective Materials and Methods: This study, first of all, reviews the background of the subject and identifies the factors involved in the risk of IT projects. The current study, investigates the researches that are done in this field and after extracting them and performing a survey by experts and managers for determining the importance of risks, they are categorized into 9 main factors. The PLS method is used to obtain confirmatory factor analysis. In order to identify the relationships among the main structures, the analysis of regression between them has been used. In the next step, the relationships among the variables are defined, their equations are tuned, and their dynamic simulation model is depicted. Finally, by analyzing the susceptibility to the model, the sensitivity of each risk and its impact on overall company's risk is assessed, and significant risks that require more attention in IT projects have been identified. Results and Discussion: Linear regression technique is used to analyze the relationship among research structures (risk indicators). The significance level for relationships to be meaningful is less than 0.05 (Sig <0.05). Additionally, the Beta Indicator indicates the effect (positive or negative). Finally, ARS specifies the modified coefficient of determination of the model. The purpose of presenting this coefficient is to show the percentage of dependent variable variations that occur for one unit change in an independent variable. The conceptual model of research can be presented as Fig1 for the study of causal relationships based on the dynamics of the system. Based on the relationships studied in the previous stages of the research, the dynamic diagram of the model, which is designed in VENSIM PLE software, can be presented as Fig. 2. Fig 1: Conceptual model of research structures Fig 2: Dynamic Simulation Model Conclusion: In this study, the risk factors in IT projects were identified and a wide range of studies conducted in previous years were reviewed. Risk factors were classified into 9 main groups according to the literature review. In the next step, by designing a questionnaire, the importance of these risks was determined by experts and the priority of each of them was determined. The explanation of each of the risk structures by the relevant components was also determined by using PLS and their relationship was determined. The conceptual model was drawn and finally, the model was implemented in Vensim via extracting the equations of the model by the obtained analyzes. After designing and simulating the model, we analyzed the susceptibility analysis of the model. At this stage, the results indicated that the most important risk that occurs during repeated periods of time is the risk of human resources. Risks that fall into the top priority include strategic risk, project management risk, and organizational structure risk. References Abdel-Hamid, T. K. (1989). The dynamics of software project staffing: a system dynamics based simulation approach. IEEE Transactions on Software Engineering, 15(2), 109- 119. Agarwal, N., & Rathod, U. (2006). Defining ‘success’ for software projects: An exploratory revelation. International journal of project management, 24(4), 358- 370. Akkermans, H., & van Helden, K. (2002). Vicious and virtuous cycles in ERP implementation: a case study of interrelations between critical success factors. European journal of information systems, 11(1), 35- 46.
Journal of Production and Operations Management
University of Isfahan
2251-6409
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1
no.
2018
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137
http://jpom.ui.ac.ir/article_22952_578bdfe9024e9eb6af1cdf16e8277283.pdf
dx.doi.org/10.22108/jpom.2018.92394.0
Assessing Dynamic Efficiency of Machine-made Carpet Industry by Network DEA Technique
Azadeh
Omid
MA, Industrial Engineering Department, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
author
Hessameddin
Zegordi
Associate Professor, Industrial Engineering Department, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
author
Nasim
Nahavandi
Associate Professor, Industrial Engineering Department, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
author
text
article
2018
per
The results of dynamic efficiency evaluation not only help managers to realize their business' position in competitive market, but also enable them to compare current company’s performance with previous periods and do strategic planning properly. For doing so, network data envelopment analysis is a logical approach. Hence, the main objective of this illustration is to measure dynamic efficiency by means of network data envelopment analysis technique. Although different approaches in network DEA are introduced recently, the need for a comprehensive methodology in this area is remained because of the defects of previous methodologies. Consequently, a novel approach based on multi-objective optimization is introduced in this paper in order to measure the efficiency of a network structure. Finally, the case of Machine Made Carpet Industry (MMCI) is used and the dynamic performance of MMCI's companies in the period of four years is measured. Efficiency results of case data showed that the methodology proposed in this paper is able to eliminate defects of previous approaches and evaluate both total and annual efficiency simultaneously Introduction: Dynamic efficiency assessment is so crucial for managers to watch out their business performance by passing the time. In a competitive market, understanding whether the company is performing in an efficient manner or not, in comparison to their rivals, is so important for managers. In this regard, assessing dynamic efficiency is the objective of this research and Machine-made Carpet Industry (MMCI) is taken into account as the case study. So, the companies producing machine made carpets are considered as the Decision Making Units (DMUs). Therefore, the main purpose of this research is to assess the dynamic efficiency of MMCI’s companies during a four-year period. The methodology used for assessing dynamic efficiency is network data envelopment analysis. Materials and Methods: The main purpose of this research is to assess the dynamic efficiency of MMCI’s companies during a four-year period by means of network data envelopment analysis technique. For doing so, five different approaches are used; while, four of this approaches include ‘Standard DEA approach, Separation approach, Average approach and Relational analysis approach’ are in the literature and the last approach, named as ‘Max-min approach’ is developed for the first time in this paper. All the first four approaches are used for assessing the efficiency of this research’s network structure and the disadvantages of all four approaches were highlighted by details. Finally, this paper introduces a multi-objective optimization method named as max-min approach for assessing total and partial efficiency of the network structure simultaneously. This new approach is able to eliminate the defeats of the previous ones and bring a comprehensive methodology for assessing the dynamic efficiency of DMUs. Results and Discussion: In this article, firstly, the weaknesses of the available methodologies in the literature for assessing the dynamic efficiency of a network structure by means of network data envelopment analysis are illustrated. Then, a new approach based on multi-objective optimization technique is proposed in order to assess dynamic efficiency of a four-stage network structure with extra inputs and outputs. In more details, this new approach has the ability to eliminate the defeats of the methodologies available in the literature which can briefly be named as the disability in measuring total and partial efficiency simultaneously, being biased in giving importance to some sub-processes, lack of discrimination and disability in assessing unique efficiency scores for sub-processes. This paper’s novel approach is named as max-min optimization approach and is able to assess the unique and unbiased efficiency scores in a network structure for both total and partial efficiency simultaneously. To be more accurate, the efficiency assessment which are obtained by the methodology of this paper is unique. In addition, decision makers’ point of view plays no role in giving the priority to any sub-process and all the stages have the same importance in measuring the efficiency of a network structure. Last but not the least is that, since these sub-processes are connected, efficiency assessment should be done in a manner that takes into account the role of intermediate parameters and this consideration is done appropriately in this paper. Conclusion: In this paper, dynamic efficiency assessment of MMCI’s companies is measured by means of network data envelopment analysis. Since the approaches presented in literature have some weaknesses, this paper aims to develop a comprehensive network data envelopment analysis approach which is able to measure dynamic efficiency of DMUs in an appropriate manner. To do so, this research develops a novel methodology based on network data envelopment analysis. This approach is a multi-objective programming technique that measure total and partial efficiency of a network structure simultaneously in a unique and unbiased manner and is named as max-min approach. Finally, the max-min approach presented in this investigation is a proper methodology in assessing dynamic efficiency of a network structure in a period of time. References Cook, W. D., Zhu, J., Bi, G., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European Journal of Operational Research, 207(2), 1122-1129. KAO, C. (2016). Efficiency decomposition and aggregation in network data envelopment analysis. European Journal of Operational Research, 255, 778-786. TONE, K. & TSUTSUI, M. )2014(. Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42, 124-131.f
Journal of Production and Operations Management
University of Isfahan
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1
no.
2018
139
160
http://jpom.ui.ac.ir/article_22954_9d87d5a4c0390c7b9c03e635b4271ac0.pdf
dx.doi.org/10.22108/jpom.2018.92463.0
Optimization the Problem of Packing Rectangular Shapes by using Imperialist Competitive Algorithm
Motahreh
Kargar
PhD student, Department of Textile Engineering, Yazd University, Yazd, Iran
author
Pedram
Payvandy
Assistant professor, Department of Textile Engineering, Yazd University, Yazd, Iran
author
text
article
2018
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Packing is one of the well-known problems in operation research, especially in production planning. The main objective of studying the packing problem is to reduce the wastes of cutting through optimization of packing of pieces. Packing is a kind of NP-hard problem that the precise methods are not able to solve it. In this paper, in order to achieve an optimal packing of Non-guillotine cutting problems, the meta-heuristic emerging Imperialist Competitive Algorithm was used and the results were compared with the output of the genetic algorithm, which is the typical algorithm in solving packing problems. To achieve better solutions, the parameters of all meta-heuristics were calibrated with Taguchi experiment method. The efficacy of the proposed approach was tested on a set of instances, taken from the literature, and the results of the proposed algorithm were tested statistically by ANOVA. The results of this study showed that the meta-heuristic emerging Imperialist Competitive algorithm is more efficient and faster in solving packing problems. Introduction: Packing problems are problems which are difficult or sometimes impossible to solve exactly. Researchers have provided many different solutions based on heuristic and meta-heuristic to approximately solve these problems. Materials and Methods: Imperialist Competitive Algorithm is a new evolutionaryoptimization method which is inspired by imperialisticcompetition Atashpaz-Gargari (2007). Like other evolutionary algorithms, it startswith an initial population which is called country and isdivided into two types of colonies and imperialists which,together, form empires. Imperialistic competition among theseempires forms the proposed evolutionary algorithm. Duringthis competition, weak empires collapse and powerful onestake possession of their colonies. Imperialistic competitionconverges to a state in which there exists only one empire andcolonies have the same cost function value as the imperialist.The pseudo code of Imperialist competitive algorithm is asfollows: 1) Select some random points on the function and initializethe empires. 2) Move the colonies toward their relevant imperialist (Assimilation). 3) Randomly change the position of some colonies (Revolution). 4) If there is a colony in an empire which has lower costthan the imperialist, exchange the positions of thatcolony and the imperialist. 5) Unite the similar empires. 6) Compute the total cost of all empires. 7) Pick the weakest colony (colonies) from the weakestempires and give it (them) to one of the empires (Imperialistic competition). 8) Eliminate the powerless empires. 9) If stop conditions satisfied, stop, if not go to 2. After dividing all colonies among imperialists and creatingthe initial empires, these colonies start moving toward theirrelevant imperialist state which is based on assimilationpolicy Results and Discussion: In this study, in order to achieve an optimal packing of non-guillotine cutting problems, at first the meta-heuristic algorithm of Imperialist Competitive Algorithm was used. Then the results were compared with the output of the genetic algorithm which is the typical algorithm in solving packing problems. The results showed that ICA had the better fitness function average than GA. Also, ICA needs less number of function evaluations. Therefore ICA is faster than GA in solving permutation packing problems. References Atashpaz-Gargari, E., & Lucas, C. (2007). "Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition". IEEE Congress on Evolutionary Computation, 4661-4667 Ebrahimi, S., & Payvandy, P. (2013). "Optimization of the Link Drive Mechanism in a Sewing Machine Using Imperialist Competitive Algorithm". International Journal of Clothing Science and Technology, 26(3), 247 – 260. Bluma, C., & Schmid, V. (2013). "Solving the 2D bin packing problem by means of a hybrid evolutionary algorithm". Procedia Computer Science, 18, 899 – 908.
Journal of Production and Operations Management
University of Isfahan
2251-6409
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1
no.
2018
161
180
http://jpom.ui.ac.ir/article_22955_2cce494e5ceab63ccc29f604d2d10660.pdf
dx.doi.org/10.22108/jpom.2018.92481.0
Muti-Objective Optimization and Simulation Model To Design The Withdrawal Kanban Systems
Vahid
Baradaran
Assistant Professor, Industrial Engineering Department, Islamic Azad University, Tehran North Branch, Tehran, Iran
author
text
article
2018
per
The withdrawal Kanban system, by capability of data transferring in supply chain reduces different types of the waists such as inventories level and unnecessary movements. To achieve the aims of lean production, the parameters of the Kanban system such as the number of Kanban should be determined properly. The number of Kanban problem is a multi-objective problem which should met the aims of producers and suppliers simultaneously. In this paper, the objectives and constraints of withdrawal Kanban problem has been determined based on a case study in automobile supply chain. A mathematical integer multi-objective model with non-linear objects has been developed. Two sets of solutions are generated by the optimization model. A simulation model is developed to check the possibility and validity of solutions. The simulation studies show that one of the solutions can reduce up to 46 percent the inventory costs while increase 11 percent transportation costs compared to the current state. Introduction: Kanban as a scheduling system is an effective tool in lean manufacturing and pull production systems Kanban which helps to determine and order the quantity of allowed production and the amount of Semi-manufactured product allowed movement between workstations or supply chain components. By controlling the inventories at any point in the production and supply chain, Kanban could improve the efficiency. There are two types of Kanban: production Kanban and withdrawal Kanban. The production Kanban determines what to produce, when to produce it, and how much to produce in the workstations of manufacturing systems. While, the withdrawal Kanban determines the transfer time of different parts between various stations of the production line, or between the supply chain components. To be effective, the Kanban systems should be designed for a production system. The number of Kanban in cycle, the volume of each Kanban and the ordering point are the designing elements of Kanban. In this paper, designing the withdrawal Kanban including determining the optimal number of Kanban in cycle in supply chains is examined. Designing the withdrawal Kanban system in a supply chains affects the performance and satisfaction of supply chain components. The main contributions of this paper are: (1) Analysis of withdrawal Kanban in supply chains to identify the effects of the Kanban parameters on components of supply chain. (2) Developing a multi-objective optimization model to determine the optimal number of withdrawal Kanban by considering the objectives and constraints of the main manufacturer and supplies in the supply chain. (3) A discrete-event simulation model is constructed to compare the results of optimization model and other solutions in terms of performance indexes. Materials and Methods: A non-linear multi-objective mathematical model with four objectives is developed to determine the optimal number of withdrawal Kanban and type of vehicles which transport the Kanbans between supplies and manufacturer. The inventory, transportation, capital costs are the objective functions of the mathematical optimization model. The constraints such as vehicle capacities are considered in the mathematical model. The L-P metric method is used to convert the multi-objective model to single-objective mathematical model. The proposed model is used to design the withdrawal Kanban system in the production of an automobile component in Iran-Khodro. To evaluate the results of mathematical model and other models, a simulation model is developed. The case study are simulated with different scenarios based on the results of the proposed model, existing conditions, and other solutions. Finally, the results of simulation studies are compared Results and Discussion: The simulation studies show the solutions which obtained the proposed model compared to the current state, which can reduce up to 28 and 46 percent the capital and inventory costs, respectively. While the transportation costs will increase 11 percent. Conclusion: The Kanban system increase the efficiency of production system, if the Kanban system design properly. The design parameters of withdrawal Kanban system affect the performance and costs in a supply chain. By minimizing the capital, transportation and inventory costs in main manufacturer and suppliers of a supply chain, the optimal number of withdrawal Kanban in cycle is determined. The simulation model is proposed to evaluate the results of optimization model and measure the performance indexes of Kanban system before implementation. References Abdul Rahman, N. A., Sharif S. M. & Mashitah M. E. (2013). “Lean Manufacturing Case Study with Kanban System Implementation”. Procedia Economics and Finance, 7, 174 – 180. Azadeh, A., Layegh, J. & Pourankooh, P. (2010a). “Optimal Model for Supply Chain Controlled by kanban under JIT Philosophy by Integration of computer Simulation and Genetic Algorithm”. Basic and Applied Sciences, 4(3), 370-378. Belisario, L. S. & Pierreval, H. (2015). “Using genetic programming and simulation to learn how to dynamically adapt the number of cards in reactive pull systems”, Expert Systems with Applications, 42 (6), 3129-3141
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
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1
no.
2018
181
203
http://jpom.ui.ac.ir/article_22956_cfc0514135e94a3439f6c350bfa02cba.pdf
dx.doi.org/10.22108/jpom.2018.92445.0
Modeling Multi-Objective, Multi-Product and Multi-Period Supplier Selection Problem Considering Stochastic Demand
Mehdi
Seifbarghy
Associate Professor of Industrial Engineering Department, Faculty of Engineering, Alzahra University, Tehran, Iran
author
Foruzan
Naseri
Ph.D Student of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran
author
text
article
2018
per
In this paper, a multi-objective, multi-period and multi-product mixed integer programming model for the supplier selection and quota allocation problem under an all-unit quantity discount policy, constrained storage space and stochastic demand is considered. Also, due to the stochastic status of the demand, we use the Chance Constrained Programming (CCP) in order to transform the inventory balance equation to a stochastic position. Since the discount policy encourages the buyer to buy more while the storage capacity restricts, we require to consider both in the supplier selection and quota allocation problem; furthermore, different priorities for the objectives should be considered. We use the LP-metric method, goal programming and the novel solution technique called multi-choice goal programming in order to model the multi-objective problem. Furthermore, a numerical example using three modeling approaches, considering the different scenarios are solved. The differences in the scenarios are the importance of the objective function in terms of the decision maker. Results show if an objective function is prioritized, that objective will be closer to its optimal value.
Introduction: The evaluation and selection of suppliers is one of the interesting topics for many researchers. Esfandiari and Seifbarghy (2013) classified the research in the field of evaluation and supplier selection as follows:
The first class: mathematical programming models considering the cost objective function
The second class: mathematical programming programming considering two objective functions including minimizing cost and maximizing utility function.
The third class: mathematical programming considering at least three objective functions including minimizing cost, return items and delay in delivering products.
The forth class: phase models that deal with phase and vague data input such as demand and capacity.
The fifth class: models that consider different types of discount
The sixth class: models that considering the uncertainties of demand, capacity and ... .
The contributions of this paper are as follows:
Considering multi-period and multi-objective programming model for supplier selection and quota allocation problem under an all-unit quantity discount policy, constrained storage space and stochastic demand
Considering different multi-objective modeling techniques in the field of supplier selection
Using the Chance Constrained Programming (CCP) in order to transform the inventory balance equation to a stochastic position.
Materials and Methods: In this paper, a multi-objective, multi-period and multi-product mixed integer programming model for the supplier selection and quota allocation problem under an all-unit quantity discount policy, constrained storage space and stochastic demand is proposed. The Chance Constrained Programming (CCP) in order to transform the inventory balance equation to a stochastic position is used. The assumptions of this paper are as follows: the demand for each product has a normal distribution with specific mean and variance. Inventory holding and shortage costs of each unit product are independent of the price. The number of planning periods is distinct and limited. Suppliers offer all-unit quantity discount policy. The initial inventory level is zero. The remaining inventory of each period is transferable to subsequent periods. The load unit of each product is considered to be 1. The mathematical model of this paper is as follows:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
The objective function (1) minimizes costs. The first sentence is buying cost, the second sentence is ordering cost, the third sentence is holding cost and the forth sentence is shortage cost. The objective function (2) minimizes the average amount of returned products. The objective function (3) minimizes the average late delivery of products. Constraint (4) shows the warehouse capacity. Constraint (5), (6) and (7) are related to all-unit discount. Constraint (8) shows inventory balance equilibrium and constraint (9) and (10) show the variables of the model.
In this paper, three techniques including LP- metric, goal programming and multi-choice goal programming for modeling are used.
Results and Discussion: To solve numerical example using LP- metric, goal programming and multi-choice goal programming, different scenarios are considered. The difference in scenarios was determined in the importance of objective functions from decision makers’ point of view. The results showed that the LP-metric method is not an appropriate method for solving multi-objective problems. Also, the results showed that if the importance of an objective function is increased from decision maker point of view, that objective function is improved and other function get worse.
Conclusion: In this paper, a multi-objective, multi-period and multi-product mixed integer programming model for the supplier selection and quota allocation problem under an all-unit quantity discount policy, constrained storage space and stochastic demand were considered. The objective of this model is to minimize the costs, the returns and the delays. Also, due to the stochastic status of the demand, the Chance Constrained Programming (CCP) was used in order to transform the inventory balance equation to a stochastic position. Also, the three methods of LP-metric, goal programming and multi-choice goal programming were used. The results showed that if the importance of an objective function is increased from the decision maker’s point of view, that objective function improves and other functions get worse.
References
Seifbarghy, M., & Esfandiari, N. (2011). “Modeling and solving a multi-objective supplier quota allocation problem considering transaction costs”. Journal of Intelligent Manufacturing, 24(1), 201-209.
Esfandiari, N., &Seifbarghy, M. (2013). “Modeling a stochastic multi-objective supplier quota allocation problem with price dependent ordering”. Applied Mathematical Modelling, 37(8), 5790-580.
Razmi, J., & Maghool, E. (2009). “Multi-item supplier selection and lot-sizing planning under multiple price discounts using augmented -constrained and Tchebycheff method”. International Journal of Advanced Manufacturing Technology, 49(1-4), 379-392.
Journal of Production and Operations Management
University of Isfahan
2251-6409
9
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1
no.
2018
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http://jpom.ui.ac.ir/article_22957_8bd568b75995642ef9cd6778caa278ec.pdf
dx.doi.org/10.22108/jpom.2018.92472.0