Optimal Aggregate Production Planning with Fuzzy Data

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 α is formulated to calculate the bounds of the optimal performance measure at α . Then the membership function of the optimal performance measure is constructed by enumerating different values of α . 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

[1]  Raul Poler,et al.  Models for production planning under uncertainty: A review ☆ , 2006 .

[2]  Rafik A. Aliev,et al.  Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management , 2007, Inf. Sci..

[3]  S. Chanas.  The use of parametric programming in fuzzy linear programming , 1983 .

[4]  C. Hwang,et al.  An aggregate production planning model and application of three multiple objective decision methods , 1980 .

[5]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[6]  Tien-Fu Liang,et al.  Application of fuzzy multi-objective linear programming to aggregate production planning , 2004, Comput. Ind. Eng..

[7]  Reay-Chen Wang,et al.  Applying possibilistic linear programming to aggregate production planning , 2005 .

[8]  A. Bonaert.  Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[9]  B DantzigGeorge.  Linear Programming Under Uncertainty , 1955 .

[10]  Reay-Chen Wang,et al.  Aggregate production planning with multiple objectives in a fuzzy environment , 2001, Eur. J. Oper. Res..

[11]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[12]  Rasaratnam Logendran,et al.  Aggregate production planning — A survey of models and methodologies , 1992 .

[13]  Udatta S. Palekar,et al.  Aggregate production planning for a continuous reconfigurable manufacturing process , 2005, Comput. Oper. Res..

[14]  Stephen C. H. Leung,et al.  A goal programming model for aggregate production planning with resource utilization constraint , 2009, Comput. Ind. Eng..

[15]  Richard Y. K. Fung,et al.  Fuzzy modelling and simulation for aggregate production planning , 2003, Int. J. Syst. Sci..

[16]  Mohammad Ali Soukhakian,et al.  A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning , 2009, Comput. Ind. Eng..

[17]  John Bevan,et al.  Operations Management: Strategy and Analysis (2nd Edition) , 1992 .

[18]  José Rui Figueira,et al.  An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming , 2006 .

[19]  Kin Keung Lai,et al.  A stochastic programming approach for multi-site aggregate production planning , 2006, J. Oper. Res. Soc..

[20]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[21]  C. Hwang,et al.  Fuzzy Mathematical Programming: Methods and Applications , 1995 .

[22]  Geoff Buxey,et al.  A managerial perspective on aggregate planning , 1995 .

[23]  Germaine H. Saad.  An overview of production planning models: structural classification and empirical assessment , 1982 .

[24]  Richard Y. K. Fung,et al.  Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities , 2003, IEEE Trans. Syst. Man Cybern. Part A.

[25]  Jiafu Tang,et al.  Fuzzy formulation for multi-product aggregate production planning , 2000 .