Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment

Abstract

In multi-item, multi-objective constrained inventory models, objective goals, resource constraints, inventory costs and prices are assumed to be crisp and defined with certainty. In real-life, however, this is seldom the case. Due to the specific requirements and local conditions, the above goals and parameters are normally vague and imprecise, i.e. fuzzy in nature. Until now, a few people have attempted to solve such inventory problems. Impreciseness of objective goals and resource constraints have been expressed here by fuzzy membership functions and vagueness in inventory costs and prices by fuzzy numbers. Thus, the multi-item multi-objective constrained inventory problems reduce to fuzzy decision making problems which are solved by fuzzy non-linear programming (FNLP) and fuzzy additive goal programming (FAGP) methods. The exact fuzzy membership functions for goals and fuzzy number representations for inventory parameters can be obtained through past observations. Once these actual representations are available, the real-life inventory problems can be solved realistically which will be of much use for the management. In this paper, multi-item inventory models of deteriorating items with stock-dependent demand are developed in a fuzzy environment. Here, the objectives of maximizing the profit and minimizing the wastage cost are fuzzy in nature. Total average cost, warehouse space, inventory costs, purchasing and selling prices are also assumed to be vague and imprecise. The impreciseness in the above objective and constraint goals have been expressed by fuzzy linear membership functions and that in inventory costs and prices by triangular fuzzy numbers (TFN). Models have been solved by the fuzzy non-linear programming (FNLP) method based on Zimmermann [Zimmermann, H.-J., Fuzzy linear programming with several objective functions. Fuzzy Sets and Systems, 1978, 1, 46–55] and Lee and Li [Lee, E. S. and Li, R. J., Fuzzy multiple objective programming and compromise programming with Pareto optima. Fuzzy Sets and Systems, 1993, 53, 275–288]. These are illustrated with numerical examples and results of one model are compared with those obtained by the fuzzy additive goal programming (FAGP) [Tiwari, R. N., Dharmar, S. and Rao, J. R., Fuzzy goal programming: an additive model. Fuzzy Sets and Systems, 1987, 24, 27–34] method.