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

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.

Authors:

• Ömer Faruk Baykoç
• Ümit Sami Sakalli

Keywords:

• Aggregate production planning
• Blending
• brasscasting
• possibilistic programming.

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.