An EOQ model of an item with imprecise seasonal time via genetic algorithm

Here, an inventory model of an item during its seasonal time is considered where duration of the season of the item is imprecise in nature in non‐stochastic sense, i.e., fuzzy in nature. Demand of the item is price dependent and unit cost of the 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 constant during the remaining part of the season. The model is formulated to maximise the average proceeds out of the system from the planning horizon which is fuzzy in nature. As optimisation of fuzzy objective is not well defined, optimistic/pessimistic return of the objective function (using possibility/necessity measure of fuzzy event) is optimised. 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 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 the model. The model is illustrated with some numerical examples and some sensitivity analyses have been done. In a particular case when planning horizon is crisp the model is solved via RRGA.