Designing retailer's replenishment policies for non‐instantaneous deteriorating items under fuzzy costs

In this paper, we discuss retailer's optimal replenishment policies for non‐instantaneous deteriorating items with partial backlogging under inflation over a finite horizon. The backlogging rate is a decreasing function of the waiting time up to the next replenishment. The objective of this model is to minimise the total cost of the retailer which includes the setup cost, holding cost, shortage cost and the opportunity cost due to lost sales. Here the total cost, time durations and the optimum number of replenishment are taken as decision variables. In the practical situation, it is not always possible that all the cost components in the total cost are known and have definite values. For reality, the cost components involved in the total cost of the retailer are fuzzified to a certain extent. Triangular fuzzy numbers are used to represent the mentioned costs. Signed distance method is used to defuzzify the triangular fuzzy numbers. Numerical examples are given to illustrate the model.