Effect of advance payment on an inventory model for a deteriorating item considering expiration time of product, restricted shelf space and age dependent selling price with discount facility

Abstract

The life-time of a deteriorating product is a major issue in inventory management. In practise the quality as well as quantity of deteriorating product deteriorates over time and the quality (freshness) of the product influences the customer’s demand. With the consideration of product life time, we develop an inventory model with price and freshness dependent demand under advance payment system with discount facility. The selling price is freshness sensitive. Goal of our model are twofold. The first one is customer’s demand is dependent upon the newness/freshness state of the product as well as selling price of the product. In the last one stock level at the end of cycle is relaxed.  The solution process of projected optimization model is illustrated theoretically.  Couple of numerical examples and sensitivity analysis are provided to demonstrate the feature of the profit function. Concavity of the average profit function is shown by plotting graphs. This study shows that all parameters in the proposed maximization model significantly influence the optimal solution.