A multi-warehouse partial backlogging inventory model for deteriorating items under inflation when a delay in payment is permissible

Abstract

In this paper we develop a multi-item multi-warehouse inventory model for dete-riorating items for m secondary warehouses (SWs) and one primary warehouse (PW) withdisplayed stock and price dependent demand under permissible delay in payment. Items aresold from PW which is located at the main market and due to large stock and insufficient spaceof existing PW, excess items are stored at m SWs of finite capacity. Due to different preserv-ing facilities and storage environment, inventory holding cost is considered to be different indifferent warehouses. Here the demand of items is a deterministic function of correspondingselling price and the displayed inventory. Shortages are allowed and partially backlogged.The items of SWs are transported to the PW in continuous release pattern and associatedtransportation cost is proportional to the distance from PW to SWs. Here Mi (< Ti , cycletime) be the period of permissible delay in settling account for ith item, without the interestcharges. But if the retailer settles the account after Mi , he will have to pay with interest percycle for the inventory not sold after the due date Mi . A single objective inventory problemis solved numerically by developing Genetic algorithm and the maximum average profit andthe corresponding optimum decision variables are evaluated. Finally the model is illustratedusing a numerical example. A sensitivity analysis of the optimal solution with respect to theparameters of the system is carried out.