A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging

Abstract

In this paper we study a continuous review inventory model. Five costs are considered as significant: deterioration, holding, shortage, opportunity cost due to the lost sales and the replenishment cost per replenishment which is linear dependent on the lot size. The deterioration of items occurs at a fixed rate independent of time. Demand rate is described by any logconcave function of time, which satisfies very mild conditions. The model allows for partial backlogging. The backlogging rate is an exponentially decreasing, time-dependent function specified by a parameter. For this model we derive results, which ensure the existence of a unique optimal policy and we propose an algorithm to find it. Numerical examples are given to illustrate the application of the algorithm. This paper extends the model studied by Bhunia and Maiti [Appl. Math. Model. 23 (1999) 301] by considering a more general demand rate function, introducing partial backlogging and relaxing the condition of replenishment cycles of equal lengths.