An EOQ Model for Items with Weibull Distribution Deterioration

Abstract

An inventory model is considered for deteriorating items with a variable rate of deterioration, where deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. Specifically, the Weibull distribution is used to represent the distribution of the time to deterioration. The EOQ formula is derived under conditions of constant demand, instantaneous delivery and no shortages, and it is shown that the results can be related to previously developed simpler models. A computer program is developed to provide the numerical solution and a numerical example is used to show the solution form and verify that the solution gives minimum total cost per unit time. An economic lot size model has been developed for situation in which the deterioration follows a Weibull distribution. The theoretical derivation was shown to reduce to the previous model found by Ghare and Schrader when the deterioration was exponential in nature and to a non deteriorating EOQ model when deterioration was made very small. A computer program was developed to provide a numerical solution and its use demonstrated on a numerical example. The computer program is available from the authors.