An inventory model for decaying items with Pareto distribution, time-dependent demand and shortages

Abstract

In this paper, we develop an EOQ model for time-varying demand with deterioration. We assumed that the deterioration of commodity follows a generalised Pareto distribution. Also, the shortage is allowed and fully backlogged. Keeping these assumptions under consideration, the mathematical expressions are obtained for carrying cost, shortage cost and deterioration cost. Inventory costs were used to constitute the total cost function. Subsequently, optimal time to consume physical stock, cycle time, and total cost per cycle were determined. The results are discussed with the help of numerical examples followed by a comparative analysis between quadratic demand rate and equivalent linear demand rate. A comparison of results obtained from numerical examples concludes that the optimum cost for quadratic demand is less than that of the linear demand model. Finally, sensitivity analysis is presented to describe the influence of changes in the parameters on optimal policies.