Production planning for controllable deteriorating items with price and stock dependent demand rate

Document Type : Research Paper


Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, A Central University, Sagar M.P., India


In this paper, an Economic Production Quantity (EPQ) inventory model for deteriorating items with price-stock dependent demand rate under complete and partial backlog is developed, in which the deterioration rate is controlled by investment in preservation technology. To fulfil the demand and to reduce the shortage we have considered the production rate proportional to the selling price of the product. This study is to maximize the total profit for seasonal deteriorating items by simultaneously determining the optimal selling price, the optimal production and the optimal preservation technology cost when the producer invests in the preservation technology to reduce the deterioration rate. We first show that for any given number of the production cycle, optimal selling price and preservation technology cost exists and are unique. Next, we show that the total profit is a jointly concave function of selling price and preservation technology cost. We provide some conditions to determine an optimal solution that maximizes profits for the EPQ model. We then provide a simple algorithm to figure out the optimality of total profit for the proposed model. Mathematical theorems are developed to determine optimal inventory policy. Numerical results demonstrate the advantages of the preservation technology, and further show the effects of different system parameters on the optimal variables and the maximal total profit. Finally, some managerial implications are provided.


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Volume 13, Issue 2
July 2022
Pages 1419-1446
  • Receive Date: 09 April 2020
  • Revise Date: 11 August 2020
  • Accept Date: 28 September 2020