An Aggregate Production Planning Model for Brass Casting Industry in Fuzzy Environment

Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

Abstract:

In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075780

References:

[1] Ashayeri J., van Eijs A.G.M. and Nederstigt P., (1994). Blending modeling in a process manufacturing: A case study. European Journal of Operational Research, 72, 460-468.
[2] Kim J. and Lewis R. L., (1987). A large scale linear programming application to least cost charging for foundry melting operations. American Foundrymens- Society Transactions, 95, 735-744.
[3] Rong, A. and Lahdelma R., (2008). Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production. European Journal of Operational Research, 186, 953-964.
[4] Sakalli U. S. and Birgoren B., (2009). A spreadsheet-based decision support tool for blending problems in brass casting industry, Computers & Industrial Engineering, 56, 724-735.
[5] Zadeh L. A., (1965). Fuzzy Sets. Information and Control, 8, 338- 353.
[6] Zimmermann H.-J., (1976). Description and optimization of fuzzy systems. International Journal of General Systems, 2, 209-215.
[7] Wang R.C. and Liang T.F, (2005). Applying possibilistic linear programming to aggregate production planning. Int. J. Production Economics, 98, 328-341.
[8] Lee Y. Y., (1990). Fuzzy set theory approach to aggregate production planning and inventory control. Ph.D. Dissertation. Department of I.E., Kansas State University.
[9] Tang J., Wang, D. and Fung, R. Y. K., (2000). Fuzzy formulation for multi-product aggregate production planning. Production Planning and Control, 11(7), 670-676.
[10] Wang R. C. and Fang, H. H., (2000). Aggregate production planning in a fuzzy environment. International Journal of Industrial Engineering/Theory, Applications and Practice, 7(1), 5-14.
[11] 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.
[12] 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 (12-13), 661-673.
[13] Zadeh L.A., (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.
[14] Buckley J.J., (1988). Possibilistic linear programming with triangular fuzzy numbers. Fuzzy Sets and Systems, 26, 135-138.
[15] Buckley J.J., (1989). Solving possibilistic linear programming problems. Fuzzy Sets and Systems, 31, 329-341.
[16] Lai Y.J. and Hwang C.L., (1992). A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems, 49, 121-133.
[17] Hsieh S. and Wu M., (2000). Demand and cost forecast error sensitivity analyses in aggregate production planning by possibilistic linear programming models. Journal of Intelligent manufacturing, 11, 355-364.
[18] Tang J., Wang D. and Fung R.Y.K., (2001). Formulation of general possibilistic linear programming problems for complex systems. Fuzzy Sets and Systems, 119, 41-48.
[19] Hsu H.M. and Wang W.P., (2001). Possibilistic programming in production planning of assemble-to-order environments. Fuzzy Sets and Systems, 119, 59-70.
[20] Liang T. F., (2007). Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives. Production Planning & Control, 18(7), 548-560.
[21] Lai Y.-J. and Hwang C.-L., (1992). Fuzzy Mathematical programming, Springer-Verlag Berlin Heidelberg, USA, Newyork.
[22] Hwang C.L. and Yoon K., (1981). Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, Heidelberg.
[23] Zimmermann, H.-J., (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45-55.
[24] Hop N. V., (2007). Solving fuzzy (stochastic) linear programming problems using superiority and inferiority, Information Sciences, 177, 2971-2984.