Optimal pricing, replenishment scheduling, and preservation technology investment policy for multi-item deteriorating inventory model under shortages

Abstract

In a wholesale shop, the retailer is required to keep an inventory of various ranges of a product due to uncertainty in consumer preferences and behavior. Different Economic Order Quantity (EOQ) models for each variety of a product are needed for optimum level of inventory. EOQ model decides how much stock a shopkeeper has to store, according to demand and deterioration of different items to optimize the inventory policy of multiple products. Items like fashion, food, vegetables, pharmaceuticals, etc., deteriorate in the retailer’s warehouse during storage. An investment is required in preservation technology to significantly reduce the deterioration rate, reduce economic losses, and increase business competitiveness. Here, a multi-item deteriorating EOQ model with a fixed cycle duration has been developed incorporating the preservation technology. The demands for the items are a quadratic function of the selling price, and shortages are allowed. The main objective is to determine the optimal selling price, investment under preservation, the time length up to zero inventory, order quantity of the proposed inventory model such that the overall profit will be maximized. First, we prove that the optimal selling price and investment in preservation exist and are unique. Next, the total profit per unit time is a concave function of selling price and preservation technology investment. An algorithm is designed to obtain the optimum joint policy. A numerical example has been given to illustrate the model, and sensitivity analysis is conducted, which gives some managerial insights.