×

A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment. (English) Zbl 1159.90532

Summary: In this study, a fuzzy multi-objective joint replenishment inventory model of deteriorating items is developed. The model maximizes the profit and return on inventory investment (ROII) under fuzzy demand and shortage cost constraint. We propose a novel inverse weight fuzzy non-linear programming (IWFNLP) to formulate the fuzzy model. A soft computing, differential evolution (DE) with/without migration operation, is proposed to solve the problem. The performances of the proposed fuzzy method and the conventional fuzzy additive goal programming (FAGP) are compared. We show that the solution derived from the IWFNLP method satisfies the decision maker’s desirable achievement level of the profit objective, ROII objective and shortage cost constraint goal under the desirable possible level of fuzzy demand. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

Software:

Genocop
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Science, 17, B141-B164 (1970) · Zbl 0224.90032
[2] Chang, P. T.; Yao, M. J.; Huang, S. F.; Chen, C. T., A genetic algorithm for solving a fuzzy economic lot-size scheduling problem, International Journal of Production Economics, 102, 265-288 (2006)
[3] Chen, L. H.; Tsai, F. C., Fuzzy goal programming with different importance and priorities, European Journal of Operational Research, 133, 548-556 (2001) · Zbl 1053.90140
[4] Chiou, J. P.; Wang, F. S., Hybrid method of evolutionary algorithms for static and dynamic optimization problems with application to a fed-batch fermentation process, Computers and Chemical Engineering, 23, 1277-1291 (1999)
[5] Deb, K., An efficient constraint handling method for genetic algorithms, Computer Methods in Applied Mechanics and Engineering, 186, 311-338 (2000) · Zbl 1028.90533
[6] Dey, J. K.; Kar, S.; Maiti, M., An interactive method for inventory control with fuzzy lead-time and dynamic demand, European Journal of Operational Research, 167, 381-397 (2005) · Zbl 1075.90003
[7] Lam, S. M.; Wong, D. S., A fuzzy mathematical model for the joint economic lot size problem with multiple price breaks, European Journal of Operational Research, 95, 611-622 (1996) · Zbl 0926.90004
[8] Lee, E. S.; Li, R. J., Fuzzy multiple objective programming and compromise programming with Pareto optima, Fuzzy Sets and Systems, 3, 275-288 (1993) · Zbl 0807.90130
[9] Maity, K.; Maiti, M., Numerical approach of multi-objective optimal control problem in imprecise environment, Fuzzy Optimization and Decision Making, 4, 313-330 (2005) · Zbl 1110.49020
[10] Mandal, N. K.; Roy, T. K.; Maiti, M., Multi-objective fuzzy inventory model with three constraints: A geometric programming approach, Fuzzy Sets and Systems, 150, 87-106 (2005) · Zbl 1075.90005
[11] Z. Michalewicz, Genetic Algorithms; Z. Michalewicz, Genetic Algorithms · Zbl 0763.68054
[12] Mondal, S.; Maiti, M., Multi-item fuzzy EOQ models using genetic algorithm, Computers and Industrial Engineering, 44, 105-117 (2002)
[13] Otake, T.; Min, K. J., Inventory and investment in quality improvement under return on investment maximization, Computers and Operations Research, 28, 113-124 (2001) · Zbl 1017.90003
[14] Rosenberg, D., Optimal price-inventory decisions profit vs ROII, IIE Transactions, 23, 17-22 (1991)
[15] Rosenthal, R. E., Concepts theory and techniques: Principles of multi-objective optimization, Decision Sciences, 16, 133-152 (1985)
[16] Roy, T. K.; Maiti, M., Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment, Computers and Operations Research, 25, 1085-1095 (1998) · Zbl 1042.90511
[17] Sakawa, M.; Yauchi, K., An interactive fuzzy satisfying method for multi-objective nonconvex programming problems through floating point genetic algorithms, European Journal of Operational Research, 117, 113-124 (1999) · Zbl 0998.90073
[18] Schroeder, R. G.; Krishnan, R., Return on investment as a criterion for inventory model, Decision Sciences, 7, 697-704 (1976)
[19] R. Storn, On the usage of differential evolution for function optimization, in: Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, New Frontiers in Fuzzy Logic and Soft Computing, 1996, pp. 519-523.; R. Storn, On the usage of differential evolution for function optimization, in: Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, New Frontiers in Fuzzy Logic and Soft Computing, 1996, pp. 519-523.
[20] Storn, R.; Price, K. V., Minimizing the real functions of the ICEC ‘96 contest by differential evolution, IEEE Conference on Evolutionary Computation, 842-844 (1996)
[21] Storn, R.; Price, K. V., Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11, 341-359 (1997) · Zbl 0888.90135
[22] Tiwari, R. N.; Dharmar, S.; Rao, J. R., Fuzzy goal programming – an additive model, Fuzzy Sets and Systems, 24, 27-34 (1987) · Zbl 0627.90073
[23] Wang, J.; Shu, Y. F., Fuzzy decision modeling for supply chain management, Fuzzy Sets and Systems, 150, 107-127 (2005) · Zbl 1075.90532
[24] Xie, Y.; Petrovic, D.; Burnham, K., A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand, International Journal of Production Economics, 102, 37-50 (2006)
[25] Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45-55 (1978) · Zbl 0364.90065
[26] Zimmermann, H. J., Fuzzy mathematical programming, Computers and Operations Research, 10, 291-298 (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.