Production inventory model for controllable deterioration rate with shortages

This paper deals with an economic production quantity (EPQ) inventory model for deteriorating items under preservation technology. The preservation technology is used to protect the items from deterioration. Three different production levels are considered. It is assumed that initially the production rate is at a lower rate and it increases gradually over the period. This is just in order to reduce the holding cost by avoiding the larger stock quantity at the beginning of the production cycle. The shortages are permitted and fully backordered. The objective of the production inventory model is to determine the optimal production policy which minimizes the manufacturer's total cost. Theoretical results are established in order to demonstrate the existence of the optimal solution and a proper solution procedure is presented. A numerical example and sensitivity analysis are presented to validate the theoretical results. Also, some managerial insights are provided.