Abstract

A PARTIAL BACKLOGGING INVENTORY MODEL FOR DETERIORATIN ITEM WITH STOCK-DEPENDENT DEMAND AND TIME VARYING HOLDING COST

Idris Samaila* and Y. M. Baraya

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Abstract This model investigates instantaneous deterioration rate with linear time dependent holding cost and partial backlogging rate. Most literature on deterministic inventory models considered holding cost to be constant while others considered variable holding cost with complete backlogging where deterioration is non-instantaneous. In real life situation, deterioration of some items starts immediately the stock arrives and also backlogging cannot always be complete due to dynamic nature of human being. The inventory policy is to determine the optimal replenishment policy in order to maximize the profit function. The necessary and sufficient conditions for optimality were determined. Then Numerical examples with the help of Newton Raphson iteration method and sensitivity analysis were carried out to show the workability of the model. It has been found out from the results of the model that the changes in stock dependent demand rate, holding cost, deterioration rate, replenishment size, shortage cost and partial backlogging rate do have a great impact on the optimal replenishment policy. Keywords: Deterioration, partial backlogging rate, shortage cost

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