Continuous Review Inventory Model with Lost Sale Reduction and Ordering Cost Dependent on Lead Time for the Mixtures of Distributions

Abstract

This study considers a continuous review inventory system for inventory model involving lost sales reduction through capital investment cost function and the
reduction of lead time further reduces the ordering cost. To reduce the lost sales rate, two forms of capital investment cost function viz. logarithmic and power are employed. Two relationships between ordering cost and lead time viz. linear and logarithmic are considered. We develop four inventory models by taking dffierent combination of capital investment cost function and ordering cost lead time relationship. The objective of the study is to reduce the total related cost by simultaneously optimizing the order quantity, safety factor, fraction of the shortages during the stock-out period that will be lost and length of lead time. The lead time demand is assumed to follow a mixture of normal distribution. The optimal solution is derived by developing computer programs using the software MATLAB. We also provide four numerical examples to illustrate the models.