Preemptive Possibilistic Linear Programming:Application to Aggregate Production Planning

Authors: Phruksaphanrat B.

Abstract:

This research proposes a Preemptive Possibilistic Linear Programming (PPLP) approach for solving multiobjective Aggregate Production Planning (APP) problem with interval demand and imprecise unit price and related operating costs. The proposed approach attempts to maximize profit and minimize changes of workforce. It transforms the total profit objective that has imprecise information to three crisp objective functions, which are maximizing the most possible value of profit, minimizing the risk of obtaining the lower profit and maximizing the opportunity of obtaining the higher profit. The change of workforce level objective is also converted. Then, the problem is solved according to objective priorities. It is easier than simultaneously solve the multiobjective problem as performed in existing approach. Possible range of interval demand is also used to increase flexibility of obtaining the better production plan. A practical application of an electronic company is illustrated to show the effectiveness of the proposed model.

Keywords: Aggregate production planning, Fuzzy sets theory, Possibilistic linear programming, Preemptive priority

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334153

References:

[1] F. Hanssmann and S.W. Hess, "A linear programing approach to production and employment scheduling," Management science, vol. 1, pp. 46-51, 1960.
[2] D.A. Goodman, "A goal programing approach to aggregate planing of production and workfore," Management science, vol. 20, pp. 1569- 1575, 1974.
[3] S. Eilon, "Five approach to agregate production planing," AIIE Transection, vol. 7, pp. 118-131, 1975.
[4] S.M., Masud, C.L. Hwang, . "An aggregate production planing model and application of three multiple objective decision method," International of production research, vol. 18, pp. 123-138, 1980.
[5] R.C. Wang, Liang T.F., "Applying possibilistic linear programing to aggregate production planing," Int.J. of Production economics, vol. 98, pp. 328-341, 2005.
[6] H.J. Zimmermann, " Description and optimization of fuzzy system," Int. J. of Gernaral system, vol. 2, pp. 209-215, 1976.
[7] H.J. Zimmermann, " Fuzzy programming and linear programming with several objective functions," Fuzzy Sets and Systems, vol. 1, pp. 45-56, 1978.
[8] RE. Bellman, LA. Zadeh. " Decision making in fuzzy environment," Manage Sci, vol. 17, pp. 141-164, 1970.
[9] R.C. Wang, Liang T.F., "Application of fuzzy multi-objective linear programming to aggregate production planing," Computer & Industrial Engineering, vol. 46, pp. 17-41, March 2004.
[10] T. F. Liang, "Distribution planning decision using interactive fuzzy multiobjective linear programming," Fuzzy set and systems, vol.157, pp. 1303-1316, May 2006.
[11] J. Tang, D. Wang and R.Y.K.Fung, "Fuzzy formulation for multiproduct aggregate production planning," Production planning and control, vol 11, pp.670-676, 2000.
[12] L.A. Zadeh , " Fuzzy sets as a basis theory of possibility," Fuzzy set and System, vol. 1, pp. 3-28, 1978.
[13] E. Muela, G. Schweickardt and F. Garces, "Fuzzy possibilistic model for medium-term power geration planning with environment criteria," Energy policy, vol. 35, pp.5643-5655, 2007.
[14] P. M. Vasant, N.N. Barsoum and A. Bhattacharya, "Possibilistic optimization in planning decision of construction industry," Int. J. Production Economics, vol. 111, 2008.
[15] Y.J. Lai and R.C. Wang, "A new approach to some possibilistic linear programming problems," Fuzzy sets and systems, vol. 49, pp. 121-133, 1992.
[16] H.-M. Hsu and W.-P. Wang, " Possibilistic programming in production planning of assemble-to-order environment," Fuzzy Sets and Systems, vol.119, pp. 59-70, 2001.
[17] S.A.Torabi and E.Hassini, "An interaticve possibilistic programming approach for multiple objective supply chain master planning," Fuzzy Sets and Systems, vol. 159, pp. 193-214, 2008.
[18] M.A.Parra, A.B. Terol, B.P. Gladish and M.V.R. Uria, "Solving multiobjective possibilistic problem through compromise programming," European Journal of Operational Research, vol. 164, pp.748-759, 2005.
[19] M.S. Pishvaee and S.A. Torabi, "A possibilistic programming approach for closed loop supply chain network design under uncertainty," Fuzzy Sets an Systems, vol. 161, pp.1609-1613, 2010.
[20] D.Ozgen, S. Onut, B.Gulsun, U.R. Tuzkaya and G. Tuzkaya, "A twophase possibilistic linear programming methodology for multi-objective supplier evaulation and order allocation problems," Information Sciences, vol. 178, pp. 485-500, 2008.
[21] Y.P.Li and G.H.Huang, "An interval-based possibilistic programming method for waste management with cost minimization and environment-impact abatement under uncertainty," Science of the total environment, vol. 408, pp. 4296-4308, 2010.
[22] O. Kabak and F.Ulengin, "Possibilistic linear-programming approach for supply chain networking decisions," European journal of operational research, vol. 209, pp. 253-264, 2011.
[23] Y.-J. Lai nad C.-L. Hwang, Lecture notes in economics and mathematical systems: Fuzzy multiple objective decision making, methods and applications. Springer: Great Britain, 1996.
[24] P. Surapati and R.T.Kumar, "Multiobjective transportation model with fuzzy parameters: Priority based fuzzy goal programming approach," Journal of transporation system engineering and information technology, vol. 8, pp. 40-48, June 2008.