A multi-item inventory model with random replenishment intervals, fuzzy costs and resources under Possibility and Necessity Measure

Abstract

This paper presents a multi-product multi-period inventory problem with random replenishment intervals and fuzzy costs under space and shortage level constraints. Since the costs (purchasing, holding and backordering) related to inventory system are often imprecise and the replenishment intervals are random in real life, the proposed model is also fuzzy-random Here, the replenishment intervals are taken to be i.i.d random variables and the fuzzy costs are Trapezoidal fuzzy number (TrFN). Using the probability distribution between replenishment epochs the fuzzy-random model is transformed to a fuzzy expected profit model and then using fuzzy arithmetic under function principle the optimistic and pessimistic values of the objective function are obtained. The optimum order quantities for maximum profit are determined with the help of Generalised Reduced Gradient (GRG) method. To illustrate the solution procedure a numerical solution is provided.