Abstract

A single-item inventory model for delayed deteriorating items with inventory level dependent demand rate and time-dependent holding cost

Y. M. Baraya* and B. Sani.

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Abstract The purpose of this paper is to propose an optimal replenishment policy for an inventory system for delayed deteriorating items with inventory level dependent demand rate and linear time dependent holding cost by taking an exponential decay type of deterioration. In the proposed model, infinite replenishment rate is assumed and shortages are not allowed. The model is formulated as a profit maximization problem. Numerical examples are given to illustrate the model, followed by a sensitivity analysis of the decision variables with regard to changes in the model parameters. The results indicate that the effect of stock dependent demand parameter and holding cost parameter on the profit is significant. On examining the effect of system parameters on the decision variables, it was found that optimum ordering quantity and net profit per unit time are sensitive to the over estimation and under estimation of the parameters ordering cost, stock dependent demand parameter and instantaneous rate of holding cost while they are more or less insensitive to the parameters of fresh product time, unit purchase cost and rate of deterioration. The model developed in this paper helps to determine the optimum inventory policies for stock dependent demand rate items under linear time dependent holding cost and delayed exponential decay type of deterioration. This model represents many real-life situations especially in perishable items such as food products and deteriorating items as in medicines, among others. Keywords: Inventory model, Delayed deterioration, stock dependent demand, linear-time holding cost.

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