Optimal Aggregate Production Planning with Fuzzy Data

Authors: Wen-Lung Huang, Shih-Pin Chen

Abstract:

This paper investigates the optimization problem of multi-product aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh-s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level a is formulated to calculate the bounds of the optimal performance measure at a . Then the membership function of the optimal performance measure is constructed by enumerating different values of a . Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.

Keywords: fuzzy data, aggregate production planning, membership function, parametric programming

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334548

References:

[1] Aliev, R.A., Fazlollahi, B., Guirimov, B.G. and Aliev, R.R., 2007. Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Information Sciences, 177, 4241-4255.
[2] Bazaraa, M.S., Jarvis, J.J. and Sherali, H.D., 2005. Linear Programming and Network Flows, 3rd ed. New Jersey: John Wiley & Sons.
[3] Bazaraa, M.S., Sherali, H.D. and Shetty, C.M., 1993. Nonlinear Programming: Theory and Algorithm, 2nd ed. Singapore: John Wiley & Sons.
[4] Buxey, G., 1995. A managerial perspective on aggregate planning. International Journal of Production Economics, 41, 127-133.
[5] Chanas, S., 1983, The use of parametric programming in fuzzy linear programming, Fuzzy Sets and Systems, 11, 229-241.
[6] Dantzig, G.B., 1955. Linear programming under uncertainty. Management Science, 1, 197-206.
[7] Fung, R.Y.K., Tang, J. and Wang, D., 2003. Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 33, 302-313.
[8] Gomes da Silva, C., Figueira, J., Lisboa, J. and Barman, S., 2006. An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming. Omega, 34, 167-177.
[9] Jain, A. and Palekar, U.S., 2005. Aggregate production planning for a continuous reconfigurable manufacturing process. Computers & Operations Research, 32, 1213-1236.
[10] Jamalnia, A. and Soukhakian, M.A. A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning. Computers & Industrial Engineering (2008), doi:10.1016/j.cie.2008.09.010.
[11] Kaufmann, A., 1975. Introduction to the Theory of Fuzzy Subsets, vol. 1. New York: Academic Press.
[12] Klir, G. and Yuan, B., 2002. Fuzzy Sets Theory and Fuzzy Logic: theory and Application. Taiwan: Person Education.
[13] Krajewski, L.J. and Ritzman L.P., 1999. Operations Management: Strategy and Analysis. Singapore: Addison-Wesley.
[14] Lai, Y.J. and Hwang, C.L., 1992. Fuzzy Mathematical Programming: Methods and Applications. Berlin: Springer.
[15] Leung, S.C.H. and Chan, S.S.W., 2009. A goal programming model for aggregate production planning with resource utilization constraint. Computers & Industrial Engineering, 56, 1053-1064.
[16] Leung, S.C.H., Wu, Y. and Lai, K.K., 2006. A stochastic programming approach for multi-site aggregate production planning. Journal of the Operational Research Society, 57, 123-132.
[17] Lingo User-s Guide, 1999. Chicago: LINDO Systems Inc.
[18] Masud, A.S.M. and Hwang, C.L., 1980. An aggregate production planning model and application of three multiple objective decision methods. International Journal of Production Research, 18, 741-752.
[19] Mula, J., Poler, R., Garcıá-Sabater, J.P. and Lario, F.C., 2006. Models for production planning under uncertainty: A review. International Journal of Production Economics, 103, 271-285.
[20] Nam, S.J. and Logendran, R., 1992. Aggregate production planningÔÇöa survey of models and methodologies. European Journal of Operational Research, 61, 255-272.
[21] Saad, G., 1982. An overview of production planning model: Structure classification and empirical assessment. International Journal of Production Research, 20, 105-114.
[22] Tang, J., Wang, D. and Fang, R.Y.K., 2000. Fuzzy formulation for multi-product aggregate production planning. Production Planning and Control, 11, 670-676.
[23] Tang, J., Fung, R.Y.K. and Yung, K.L., 2003. Fuzzy modelling and simulation for aggregate production planning. International Journal of Systems Science, 34, 661-673.
[24] Wang, R.C. and Fang, H.H., 2000. Aggregate production planning in a fuzzy environment. International Journal of Industrial Engineering, 7, 5-14.
[25] Wang, R.C. and Fang, H.H., 2001. Aggregate production planning with multiple objectives in a fuzzy environment. European Journal of Operational Research, 133, 521-536.
[26] Wang, R.C. and Liang, T.F., 2004. Application of multi-objective linear programming to aggregate production planning. Computers and Industrial Engineering, 46, 17-41.
[27] Wang, R.C. and Liang, T.F., 2005. Applying possibilistic linear programming to aggregate production planning. International Journal of Production Economics, 98, 328-341.
[28] Zadeh, L.A., 1965. Fuzzy sets. Information and Control, 8, 338-353.
[29] Zadeh, L.A., 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.
[30] Zimmermann, H.J., 2001. Fuzzy Sets Theory and its Applications, 4th ed., Boston: Kluwer-Nijhoff.