Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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A Fuzzy Multi-Objective Linear Programming Model: A Case Study of an LPG Distribution Network

  • Ozyoruk, Bahar (Department of Industrial Engineering, Faculty of Engineering and Architecture, Gazi University) ;
  • Donmez, Nilay (Republic of Turkey Ministery of Science, Industry and Techology)
  • Received : 2013.09.04
  • Accepted : 2014.09.02
  • Published : 2014.09.30
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Abstract

Supply chain management is a subject that has an increasing importance due to the developments in the global markets and technology. In this paper, a fuzzy multi-objective linear programming model is developed for the supply chain of a company dealing with procurement, storage, filling, and distribution of liquefied petroleum gas (LPG) in Turkey. The model intends to determine the quantities of LPG to be procured, stored, filled to cylinders, and transported between the plants and demand centers for six planning periods. In this model, which aims to minimize both total costs (sum of procurement, storage, filling, and transportation costs) and total transportation distances, demand quantities of the main demand centers and decision maker's aspiration levels about objective functions are fuzzy. After comparing the results obtained from the model with those obtained by using different methods, it is concluded that the proposed method can be applied to real world problems practically and it may be used in this type of problems in order to generate an efficient solution.

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References

  1. Altiparmak, F., Gen, M., Lin, L., and Paksoy, T. (2006), A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers and Industrial Engineering, 51(1), 196-215. https://doi.org/10.1016/j.cie.2006.07.011
  2. Beamon, B. M. (1998), Supply chain design and analysis: models and methods, International Journal of Production Economics, 55(3), 281-294. https://doi.org/10.1016/S0925-5273(98)00079-6
  3. Bellman, R. E. and Zadeh, L. A. (1970), Decision-making in a fuzzy environment, Management Science, 17(4), 141-164. https://doi.org/10.1287/mnsc.17.4.B141
  4. Bilgen, B. and Ozkarahan, I. (2007), A mixed-integer linear programming model for bulk grain blending and shipping, International Journal of Production Economics, 107(2), 555-571. https://doi.org/10.1016/j.ijpe.2006.11.008
  5. Bylka, S. (1999), A dynamic model for the single-vendor, multi-buyer problem, International Journal of Production Economics, 59(1), 297-304. https://doi.org/10.1016/S0925-5273(98)00021-8
  6. Capar, I., Ulengin, F., and Reisman, A. (2003), A taxonomy for supply chain management literature, Paper presented at the 10th World Conference on Transport Research, Istanbul, Turkey, 64-68.
  7. Chanas, S. and Kuchta, D. (1998), Fuzzy integer transportation problem, Fuzzy Sets and Systems, 98(3), 291-298. https://doi.org/10.1016/S0165-0114(96)00380-6
  8. Chen, C. L. and Lee, W. C. (2004), Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices, Computers and Chemical Engineering, 28(6), 1131-1144. https://doi.org/10.1016/j.compchemeng.2003.09.014
  9. Chen, S. P. and Chang, P. C. (2006), A mathematical programming approach to supply chain models with fuzzy parameters, Engineering Optimization, 38(6), 647-669. https://doi.org/10.1080/03052150600716116
  10. Dhaenens-Flipo, C. and Finke, G. (2001), An integrated model for an industrial production-distribution problem, IIE Transactions, 33(9), 705-715.
  11. Eksioglu, S. D., Eksioglu, B., and Romeijn, H. E. (2007), A Lagrangean heuristic for integrated production and transportation planning problems in a dynamic, multi-item, two-layer supply chain, IIE Transactions, 39(2), 191-201. https://doi.org/10.1080/07408170600733244
  12. El-Wahed, W. F. A. (2001), A multi-objective transportation problem under fuzziness, Fuzzy Sets and Systems, 117(1), 27-33. https://doi.org/10.1016/S0165-0114(98)00155-9
  13. El-Wahed, W. F. A. and Lee, S. M. (2006), Interactive fuzzy goal programming for multi-objective transportation problems, Omega, 34(2), 158-166. https://doi.org/10.1016/j.omega.2004.08.006
  14. Farrag, M. A., El-Metwally, M. M., and El-Bages, M. S. (1999), A new model for distribution system planning, International Journal of Electrical Power and Energy Systems, 21(7), 523-531. https://doi.org/10.1016/S0142-0615(98)00059-3
  15. Garcia, J. M., Lozano, S., and Canca, D. (2004), Coordinated scheduling of production and delivery from multiple plants, Robotics and Computer-Integrated Manufacturing, 20(3), 191-198. https://doi.org/10.1016/j.rcim.2003.10.004
  16. Gen, M. and Syarif, A. (2005), Hybrid genetic algorithm for multi-time period production/distribution planning, Computers and Industrial Engineering, 48(4), 799-809. https://doi.org/10.1016/j.cie.2004.12.012
  17. Hannan, E. L. (1981), Linear programming with multiple fuzzy goals, Fuzzy Sets and Systems, 6(3), 235-248. https://doi.org/10.1016/0165-0114(81)90002-6
  18. Hu, C. F. And Fang, S. C. (1999), Solving fuzzy inequalities with piecewise linear membership functions, IEEE Transactions on Fuzzy Systems, 7(2), 230-235. https://doi.org/10.1109/91.755403
  19. Hussein, M. L. (1998), Complete solutions of multiple objective transportation problems with possibilistic coefficients, Fuzzy Sets and Systems, 93(3), 293-299. https://doi.org/10.1016/S0165-0114(96)00216-3
  20. Kanyalkar, A. P. and Adil, G. K. (2005), An integrated aggregate and detailed planning in a multi-site production environment using linear programming, International Journal of Production Research, 43(20), 4431-4454. https://doi.org/10.1080/00207540500142332
  21. Kikuchi, S. (2000), A method to defuzzify the fuzzy number: transportation problem application, Fuzzy Sets and Systems, 116(1), 3-9. https://doi.org/10.1016/S0165-0114(99)00033-0
  22. Kim, T., Hong, Y., and Chang, S. Y. (2006), Joint economic procurement: production-delivery policy for multiple items in a single-manufacturer, multipleretailer system, International Journal of Production Economics, 103(1), 199-208. https://doi.org/10.1016/j.ijpe.2005.06.005
  23. Lai, Y. J. and Hwang, C. L. (1992), A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49(2), 121-133. https://doi.org/10.1016/0165-0114(92)90318-X
  24. Lee, Y. H. and Kim, S. H. (2002), Production-distribution planning in supply chain considering capacity constraints, Computers and Industrial Engineering, 43(1), 169-190. https://doi.org/10.1016/S0360-8352(02)00063-3
  25. Li, L. and Lai, K. K. (2000), A fuzzy approach to the multiobjective transportation problem, Computers and Operations Research, 27(1), 43-57. https://doi.org/10.1016/S0305-0548(99)00007-6
  26. Liang, T. F. (2006), Distribution planning decisions using interactive fuzzy multi-objective linear programming, Fuzzy Sets and Systems, 157(10), 1303-1316. https://doi.org/10.1016/j.fss.2006.01.014
  27. Min, H. and Zhou, G. (2002), Supply chain modeling: past, present and future, Computers and Industrial Engineering, 43(1), 231-249. https://doi.org/10.1016/S0360-8352(02)00066-9
  28. Mokashi, S. D. and Kokossis, A. C. (2003), Application of dispersion algorithms to supply chain optimisation, Computers and Chemical Engineering, 27(7), 927-949. https://doi.org/10.1016/S0098-1354(02)00232-6
  29. Nishi, T., Konishi, M., and Ago, M. (2007), A distributed decision making system for integrated optimization of production scheduling and distribution for aluminum production line, Computers and Chemical Engineering, 31(10), 1205-1221. https://doi.org/10.1016/j.compchemeng.2006.10.006
  30. Ozdamar, L. and Yazgac, T. (1999), A hierarchical planning approach for a production-distribution system, International Journal of Production Research, 37(16), 3759-3772. https://doi.org/10.1080/002075499190031
  31. Petrovic, D., Roy, R., and Petrovic, R. (1999), Supply chain modelling using fuzzy sets, International Journal of Production Economics, 59(1), 443-453. https://doi.org/10.1016/S0925-5273(98)00109-1
  32. Pundoor, G. (2005), Integrated production-distribution scheduling in supply chains, Ph.D. dissertation, University of Maryland, College Park, MD.
  33. Sarmiento, A. M. and Nagi, R. (1999), A review of integrated analysis of production-distribution systems, IIE Transactions, 31(11), 1061-1074.
  34. Shih, L. H. (1997), Planning of fuel coal imports using a mixed integer programming method, International Journal of Production Economics, 51(3), 243-249. https://doi.org/10.1016/S0925-5273(97)00078-9
  35. Shih, L. H. (1999), Cement transportation planning via fuzzy linear programming, International Journal of Production Economics, 58(3), 277-287. https://doi.org/10.1016/S0925-5273(98)00206-0
  36. Tanaka, H. (1984), A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics, 3, 185-194.
  37. Verma, R., Biswal, M. P., and Biswas, A. (1997), Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions, Fuzzy Sets and Systems, 91(1), 37-43. https://doi.org/10.1016/S0165-0114(96)00148-0
  38. Wang, R. C. and Liang, T. F. (2004), Application of fuzzy multi-objective linear programming to aggregate production planning, Computers and Industrial Engineering, 46(1), 17-41. https://doi.org/10.1016/j.cie.2003.09.009
  39. Wang, R. C. and Liang, T. F. (2005), Aggregate production planning with multiple fuzzy goals, International Journal of Advanced Manufacturing Technology, 25(5-6), 589-597. https://doi.org/10.1007/s00170-003-1885-6
  40. Wang, W., Fung, R. Y., and Chai, Y. (2004), Approach of just-in-time distribution requirements planning for supply chain management, International Journal of Production Economics, 91(2), 101-107. https://doi.org/10.1016/S0925-5273(03)00212-3
  41. Xie, Y., Petrovic, D., and Burnham, K. (2006), A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand, International Journal of Production Economics, 102(1), 37-50. https://doi.org/10.1016/j.ijpe.2005.01.016
  42. Zadeh, L. A. (1965), Fuzzy sets, Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  43. Zimmermann, H. J. (1978), Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1(1), 45-55. https://doi.org/10.1016/0165-0114(78)90031-3

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