An optimal replenishment of fuzzy inventory model for time dependent deteriorating item with fuzzy planning horizon

Abstract

This paper deals with an inventory model for single deteriorating item during its seasonal time where lifetime of an item has an upper limit. Deterioration rate increases with time and depends on the duration of lifetime left. Demand of the item is price dependent and unit cost of item is time dependent. Unit cost is a decreasing function at the beginning of the season and an increasing function at the end of the season and is constantduring the remaining part of the season. So, the inventory model is formulated to maximize the average proceeds out of the system from the imprecise planning horizon. As the optimization of fuzzy objective is not well defined, optimistic/pessimistic return of the objective function (using possibility/necessity measure of the fuzzy event) is optimized. A fuzzy simulation process is proposed to evaluate this optimistic/pessimistic return. A genetic algorithm (GA) is developed based on entropy theory where region of the search space gradually decreases to a small neighbourhood of the optima. This is named as region reducing genetic algorithm (RRGA) and is used to solve this model when planning horizon is crisp. As simulation based region reducing genetic algorithm, called fuzzy simulation based region reducing genetic algorithm (FSRRGA) is developed to solve the fuzzy objective value. The model is illustrated with some numerical examples and some sensitivity analyses have been performed.