MATLAB Code of A proposed mathematical model for bi-level programming model in supplier selection based on decreasing procurement cost and increasing customer satisfaction levels

Description

Abstract

Suitable suppliers Selection can substantially reduce purchasing costs and increase the competitiveness of the organization, because in most industries, the cost of raw materials and component products, a major portion of the cost of the product.

In planning a surface, there is a central decision and why this type of planning a centrally planned to say.

The two-level planning is a useful tool for modeling decentralized decision problems. This problem has two optimization problems with two level from authority levels that one of them is part of the constraints of other problem.  Decision-making at a lower level (the follower is called) has to function under the parameters given by the decision-making level (the leader is called) is optimal.

The research has two main decisions that minimize the cost of materials included in the Supply Chain Procurement and also to raise the maximum level of product quality and customer satisfaction.

Purchasing department on issues such as sourcing, selection of suppliers and supply chain management is related to the maximum level of customer satisfaction is also related to the needs of our customers.

The study is based on the literature that there is something similar to this, we will answer the question:

Is reached by the two levels can be selected suppliers?

References :

Croom, S., Romano, P., Giannakis, M., Supply chain management: an analytical framework for critical literature review. European Journal of Purchasing & Supply Management, 6(1), 67-83(2000).

2. Huijun, S., Ziyou, G., Jianjun, W., A bi-level programming model and solution algorithm for the location of logistics distribution centers, AppliedMathematical Modelling, NO. 32, pp. 610–616, 2008.
3. Stevens, Graham C.,Integrating the Supply Chain, International Journal Of Physical Distribution and Logistics Managemant.19(8),3-8, 1989.
4. Handfield, R.B, Nchols, E.L,JR, Introduction to supply chain management. Prentice Hall, New Jersey, 1999.
5. Teylor,D., Global cases in logistics and supply chain management. Prentice Hall, New Jerssey, 5-7, 1997.
6. Thomas, D.J, Griffin, P.M. coordinated supply chain management, European Journal of Operations Research, 94, 1-15, 1996.
7. Simchi-Levi., D, Kaminsky., Designing and managing the supply chain, Mc Graw-Hill, Singapore, P.45-47, (2000).
8. Wadhwa, Vijay, and A., Ravi Ravindran. Vendor Selection in Outsourcing. Computers & operations research, 34.12: 3725-3737, 2007 .
9. Aissaoui, N., Haouari, M., & Hassini, E., Supplier selection and order sizing modeling: A review .Journal of Computers & Operations Research, 34, 3516- 3540, 2007.
10. Telgen, J., Inzicht en overzicht: de uitdagingen van Besliskunde enlnkoop management. Academical address at the University of Twente, Enschede, The Netherlands. (1994).
11. Qyayle, M., Purchasing and Supply Chain Management: Strategies and Realities. (9th ed.), IRM Press, 2006.
12. Cavinato J., & Kauffman R., The purchasing handbook: A Guide for the Purchasing and Supply Professional. (0^th Ed.), McGraw-Hill, 2000.
13. De Boer, L ., Operations research in support of purchasing. Design of a toolbox for supplier selection. Ph.D. Thesis, University of Twente, Enschede, The Netherlands, 1998.
14. C.Kolstad, A review of the Literature on bi-Level mathematical programming, Technical Report LA-10284-MS,US-32, US-32, Los Alamos Laboratory,1985.
15. Shih, H.S., Wen, U.P., Lee, E.S., Lan, K.M., Hsiao, H.C., A Neural Network Approach to Multiobjective and Multilevel Programming Problems, Computers and Mathematics with Applications, NO. 48, pp. 95-108, 2004.
16. Ghodsypour, S.H., A decision support system for supplier selection integrating analytical hierarchy process with operations research methods. Thesis (Ph.D) , Univ.of Nottingham, Dept of manufacturing engineering and operations management, U.K. 1996.
17. Dickson, G.W., An Analysis of Vendor Selection Systems and Management. Journal of Purchasing. 2(1), 5-17, 1966.
18. Verma R., Pullman M.E; An analysis of the supplier selection process; International Journal of Management Science, Vol. 26, No. 6., 1998.
19. Weber, C.A., Current, J.R., & Benton, W.E., Vendor Selection Criteria and Methods.,European Journal of Operation Research, 50, 2-18, 1991.
20. zhang, zh, lei, j., cao, N., To, k Ng and keng po, Evolution of supplier selection criteria and methods., P.P. 1-19, 2004.
21. Gaballa, A.A., Miniman cost allocation of tenders. Operational Research Quarely25(3), 389-398, 1974.
22. Hong, J.D., Hayya Jc., Just-in time purchasing single or multiple sourcing?; International Journal of Production Economics, Vol. 27, 1992.
23. Ghodsypour, S. H., O’Brien, C., A decision support system for reducing the number of suppliers and managing the supplier partnership in a JIT/TQM environment. Proceedings of the Third International Symposium on Logistics, University of Padua, Padua, Italy, 1997.
24. Ghodsypour, S ,H. and O’Brien, C., A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming, International Journal of Production Economics, Vol. 56-57, P.P. 199-212, 1998
25. Karpak, B., Kumcu, E., and Kasuganti, R., “Purchasing materials in the supply chain: managing a multi-objective task” , European journal of purchasing & supply management, 7(3), -21-1, 2001.
26. Weber ,C.A., Current, J.R., Desai, A., An optimization approach to determining the number of vendors to employ. Supply Chain management: an International Journal 5 (2), PP:90-98, 2000
27. Ghodsypour , S. H. and O’Brien, C., The Total cost of logistics in supplier selection, under conditions of multiple souring, multiple criteria and capacity constraint, International Journal of Production Economics, Vol. 73, P.P. 15-27,2001.
28. Kumar M., Vrat P., Shankar R., A fuzzy goal programming approach for vendor selection problem in a supply chain; Computers & industrial Engineering, Vol.46, 2004.
29. franklin L.f-h.hl. h-l., “ The voting analytic hierarchy process method for selecting supplir” , International Journal of Production Economics,(Article in press), 2005.
30. Zam S.,Sevkil M.,Tarim, M.,Fuzzy analytic hierarchy based approach for supplier selection, International Journal of Production, Vol. 73, P.P. 15-29, 2005.
31. A.Amid, S.H.Ghodsypour, C.O Brien., Fuzzy multiobjective Linear model for supplier selection in a supply chain, Int. J.Production Economics 104 394-407, (2006).
32. Amid. A, Ghodsypour. S.H, O’Brien. C. A Weighted Additive Fuzzy Multi-Objective Model for the Supplier Selection Problem Under Price Breaks in a Supply Chain. International Journal Production Economics, 323-332,2009.
33. Ho . W.xiaowei. X. Prasanta, K.D., Multi-criteria decision making approaches for supplier evaluation and selection: A Literature review, European Journal of Operational Reserch 202,16-24, 2010.
34. Juo, R,. Wang. Y. and Tien, F., “ Integration of artificial neural network and MADA methods for green supplier selection”, Journal of Cleaner Production, 18(12), 1161-1170, 2010.
35. Zeydan, Mithat, Cuneyt Colpan, and Cemal Cobanoglu., “A combined methodology for supplier selection and performance evaluation. Expert System with Applications 38.3: 2741-2751,(2011).
36. Desheng Dash Wu, Yidong Zhang, Dexiang Wu, David L.Olson., “Fuzzy multi objective programming for supplier selection and risk modeling: A possibility approach”, European Journal of Operational Research 200 774-787, 2010.
37. Amid, S.H.Ghodsypour, C.O Brien., “ A weigted max-min model for fuzzy multi-objective supplier selection in a supply chain”, Int. J.Production Economics 131 139-145, 2011.
38. Mafakheri, Fereshteh, Michel Breton, and Ahmed Ghoniem “ supplier selection-order allocation: A two-stage multiple criteria dynamic programming approach. “ International Journal of Production Economics 132.1:52-57, 2011.
39. Beyza Ahlatcioglu Ozkok, Fatma Tiryaki., “ A compensatory fuzzy approach to multi-objective Linear supplier selection problem with multiple-item”, Expert Systems with Applications 11363-11368, 2011.
40. Krishnendu Shaw, Ravi Shankar, Surendra S. Yadav, Lakshman S. Thakur.,Supplier selection using fuzzy AHP and fuzzy multi-objective Linear programming for developing Low carbon supply chain, Expert System with Applications 8182-8192, 2012.
41. Saman Hassanzadeh Amin, Guoqing Zhang., An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach, Expert System with Applications 678-6791, (2012).
42. Huseyin Selcuk, Kilic., An intergrated approach for supplier in multi-item/multi-supplier environment, Applied Mathematical Modelling 7752-7763, (2013).
43. Devika Kannan, Roohollah Khodaverdi, Laya Olfat, Ahmad Jafarian, Ali Diabat., Integrated fuzzy multi criteria decision making method and multiobjective programming Approach for supplier selection and order allocation in a green supply chain, Journal of Cleaner Production 355e367,(2013).
44. Guo, Cong, and Xueping Li., “A multi-echelon inventory system with supplier selection and order allocation under stochastic demand.” International Journal of Production Economics 37-47, (2014).
45. Deng, S. Aydin, R., Kwong, C.K., Auang,Yun., Integrated product line design and supplier selection: A multi-objective optimization paradigm. Cumputer & Industrial Engineering , Volum 70, pages 150-158, 2o14.
46. Aksoy,Ash., Sucky,Eric.,öztürk, Nursel., Dynamic strategic supplier selection system with fuzzy logic. Procidia- social and behavioral sciences 109, 1059-1063, 2014.
47. Savard G, Gavuvin J.,” The steepest descent direction for the nonlinear bilevel programming problem, “ Operations Reserch Letters 15:265-272, (1994).
48. Vicent LN, Calamai PH., Bilevel and multi- level programming: abibiography review. Journal of Global Optimization 5(3): 291-306, 2003.
49. Closon B, Macrotte P, Savard G., “ A trust-region method for nonlinear programming: algorithm and computational experience,” Computational Optimization and Applications 30(3): 211-227, 2005
50. Jeroslow RG.,” The polynomial hierarchy and a simple model for competitive analysis,” Mathemtical programming 32:146-164, 1985.
51. Migdalas, A., Bilevel programming in traffic planning:models, methods and challenge. Journal of Global Optimization,. 7(4):p.381- 405,1995.
52. Kazempour, S., A.J. Conejo, and C. Ruiz, Strategic generation investment using a complementarity approach. Power System, IEEE Transportations on, 26(2): p. 940-948, 2011.
53. K.Shimizu. “Two-level decision problems and their new solution methods by a penally method”, volume 2 of Control seience and technology for the progress of society, pages 1303 1308. IF AC, 1982.
54. Dao Lizhu, Quing Xu, Quing Xu, Zhenghua Lin, “A homotopy method for solving bilevel programming problem, Nonlinear Analysis 57, 917-928, (2004)
55. S.Saati, A.Memariani, “Bi-Level Programming and Recent approach of applied mathematics, N:2, pp.22-35. 2004.
56. Wan Zhongping, Wang Guangmin, Lv Yibing., “A dual-relax penalty function approach for solving nonlinear bilevel program” Acta Mathematica Scientia,31B(2):652–660,2011
57. Zhongping Wan, Lijun Mao, Guangmin Wang,” Estimation of distribution algorithm for a class of nonlinear bilevel programming problems” Information Sciences 256 (2014) 184–196.
58. Willams, J.F. , “On the optimality of integer Lot size rations economic Lot size determination in multi-stage assembly systems. “Management Science, Vol.28.PP. 1341-1349, (2000).
59. Modarres, M. and Teimory. E., “ Optimal solution in a constrained distribution system. “ IIE Transaction. Vol. 15, 2002.
60. Modarres, M. and Teimory. E., “Generalization of mulri-retailer distribution systems.. “Journal of Production Plannig and control. Vol.8, 1997.
61. Fujiwara,O. Soewandi, H. and Sedarage. D “An optimal ordering and issuing policy for a teo-stage inventory system for perishable product. “European Journal of Operational Reserch. Vol.99.412-423, (1997).
62. Mitra, S.,. Analysis of a two-echelon inventory system with returns. Omega The international journal of management science.,Vol. 37, PP. 106 – 115, 2009.
63. Zhao, Z. , Gu ,X., Particle swarm optimization based algorithm for bilevel programming problems. Proceedings of the Sixth international Conference on intelligent Systems Design and Applications, IEEE, 2006.
64. Leblanc, L.J. Boyce, and D.E., A bilevel programming algorithm for exact solution of the network design problem with user- optimal flows. Transportation Research Part B: Methodological,20(3): p. 259-265,1986.
65. Saharidis, G.,The berth scheduling problem with customer differentiation: a new methodological approach based on hierarchical optimization. The International Journal of Advanced Manufacturing Technology, 46(1-4): p. 377-393.
66. Clark, P.A. and A.W. Westerberg, Optimization for design problems having more than one objective. Computers & Chemical Engineering, 7(4): p. 259- 278, 1983.
67. Clark, P.A. and A.W. Westerberg, Bilevel programming for steady- state chemical process design. Fundanentals and algorithms. Computers & Chemical Engineering, 14(1): P. 87-97, 1990.
68. Nicholls, M.G., Alumimum Production Modeling- A Nonlinear Bilevel Programming Approach. Operations research, 43(2): p. 208-218, 1995.
69. Mitsos, A., G.M. Bollas, and P.I. Barton, Bilevel optimization formulation for parameter estimation in liquid- liquid phase equilibrium problems. Chemical Engineering science, 64(3):p. 548- 559, 2009.
70. Dempe, S., V. Kalashnikov, and R.Z. Rios – Mercado, Discrete bilevel programming: Application to a natural gas cash- out problem.European Journal of Operational Research. 166(2): p.469-488,2009.
71. Lukac, Z., K. Soric, and V.V. Rosenzweig, Production planning problem with sequence dependent setups as a bilevel programming problem. European Journal of Operational Research, 187(3): p. 1504- 1512, 2008.
72. Kis, T. and A. Kovacs, on bilevel machine scheduling problems. R spectrum, 34(1): p. 43-68, 2012.
73. kucukaydin, H., N. Aras, and I. Kuban Altinel, Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution. European Journal of Operational Research, 208(3): p. 206-220, 2011.
74. He, l., Huang, G., Lu, H., Greenhouse gas emission control in integrated municipal solid waste management through mixed integer bilevel decision- making. Journal of hazardous materials, 193: p. 112-119, 2011.
75. Jia, S. and Wan, Z., A penalty function method for solving ill- posed bilevel programming problem via weighted summation. Journal of system science and complexity, 26(6): p. 1019-1027, 2013.
76. Ma, Y., and Xu, J., A novel multiple decision- maker model for resource- costrained project scheduling problems. Canadian Journal of Civil Engineering , 41(999): p. 500-511, 2014.
77. Ryu, J.- H., Dua. V., and Pistikopoulos, E.N., A bilevel programming fromework for enterprise- wide process networks under uncertainty. Computers & chemical Engineering, 28(6): p. 1121-1129, 2004.
78. Amouzegar, M.A. and Moshirvaziri, K., Determining optimal pollution control policies: An application of bilevel programming. European Journal of Operational Research, 119(1): p. 100-120, 1999.
79. Mokhlesian, M. and Zegordi, S.H.,Application of multidibisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct,competitive supply chain the International Journal of Advanced Manufacturing Technology,71(9-12): p. 1975-1989, 2014.
80. Bracken, J. and Mcgill, J.T. Dfence applications of mathematical programs with optimization problems in the constraints. Operations research, 22(5): p.1086-1096, 1974.
81. Cassidy, R., Kirby, M. and Raike, W., Efficient distribution of resources through three levels of government. Management science, 17(8): p. B-462- B- 473, 1971.
82. Choudhary, D. and Shankar, R. A goal programming model for joint decision making of inventory lot-size, supplier selection and carrier selection, Computers & Industrial Engineering. (2014)
83. Rezaei, J. and Davoodi, M. A deterministic, multi-item inventory model with supplier selection and imperfect quality. Applied Mathematical Modelling, 32, 2106-2116,(2008).