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A deteriorating multi-item inventory model with fuzzy costs and resources based on two different defuzzification techniques. (English) Zbl 1187.90029

Summary: Normally inventory models of deteriorating items, such as food products, vegetables, etc. involve imprecise parameters, like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation, etc. In this paper, we aim to provide two defuzzification techniques for two fuzzy inventory models using (i) extension principle and duality theory of non-linear programming; and (ii) interval arithmetic. On the basis of Zadeh’s extension principle, two non-linear programs parameterized by the possibility level \(\alpha \) are formulated to calculate the lower and upper bounds of the minimum average cost at \(\alpha \)-level, through which the membership function of the objective function is constructed. In interval arithmetic technique the interval objective function has been transformed into an equivalent deterministic multi-objective problem defined by the left and right limits of the interval. This formulation corresponds to the possibility level, \(\alpha = 0.5\). Finally, the multi-objective problem is solved by a multi-objective genetic algorithm (MOGA). The model has been illustrated through a numerical example and solved for different values of possibility level, \(\alpha \) through extension principle and for \(\alpha = 0.5\) via MOGA. As a particular case, the results have been obtained for the inventory model without deterioration. Results from two methods for \(\alpha = 0.5\) are compared.

MSC:

90B05 Inventory, storage, reservoirs
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C46 Optimality conditions and duality in mathematical programming
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