Optimal sustainable inventory policy for items with price-and-time-dependent demand rate

Abstract

This paper studies a sustainable inventory model for items whose demand rate is the product of a time- dependent function and a price-dependent function. The inventory system allows shortages during the product management period. Carbon emissions from transportation and storage are included in the model. The consideration of a demand rate that combines the effects of a price-algebraic function and a time-power function, with full backlogging and environmental constraints, is a novel and more realistic hypothesis and it should be studied. To determine the optimal inventory policy for this system can help to improve the efficiency and sustainability practices in inventory control. The objective is to determine a sustainable inventory policy that maximizes the average profit per unit time. We include the following significant components in the objective function: the average revenue, the ordering cost, the purchasing cost, the shipping cost, the holding cost, the shortage cost, and the carbon emissions costs in transportation and storage. To find the solution to this sustainable inventory problem, four scenarios are analyzed and, for each scenario, the optimal inventory policy is obtained. This policy determines the lot size, the optimal selling price, the maximum shortage, and the maximum profit per unit time. Some numerical examples are presented to illustrate the proposed methodology for determining the optimal policy of this sustainable inventory problem. We examine the effects on the best inventory policy when some parameters of the system are changed. Useful managerial insights derived from these results are proposed.