Inventory Control Model with Time-Linked Holding Cost, Salvage Value and Probabilistic Deterioration following Various Distributions

Abstract

This paper proposes a study on inventory model for time linked holding cost and salvage value with probabilistic deterioration following various distributions. Shortage is assumed to be partially backlogged. Demand rate is time linked. Deterioration is a continuous random variable following some probabilistic distributions. We consider the uniform and triangular distributions. An expression for average total cost is derived as an Economic Order Quantity problem. Using the probabilistic distribution, the average total cost function is divided into two models - Model I, and Model II. To explain the solution procedure, two numerical examples are provided for both models. The convex property for the concerned average total cost functions is justified with the help of graphs in three dimensions. The optimal results are compared graphically for both the models.