Optimization of price, lot size and backordered level in an EPQ inventory model with rework process

¹ School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
² Tecnológico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, 64849 Monterrey, N.L., Mexico
³ Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

^* Corresponding author: lecarden@tec.mx

Received: 2 September 2022
Accepted: 26 May 2023

Abstract

In traditional inventory models, the demand rate normally is considered as a constant value, while in marketing and pricing, it is dependent on the selling price. The present study introduces a new type of economic production quantity (EPQ) inventory model. This production-inventory model is among the aspects that make the management of inventories more realistic and practical for managers. The pricing policy, planned backorders, and the rework process are included in the EPQ inventory model. The main contribution is that, in the EPQ inventory model, the price serves as a critical factor that affects the size of demand to maximize total long-term profit. The primarily objective is to determine the optimum selling price, discrete values for the optimal lot size, and the level of optimal backorders so that the total profit is maximized. To accomplish the optimal value for the decision variables an algorithm is developed. The proposed algorithm provides an accurate solution for production managers to jointly decide on lot size, backorder size, and selling price. In addition, a numerical example is solved using real industry data. The results affirm that the total profit obtained using the production-inventory model increases significantly in comparison with the current situation. Furthermore, sensitivity analysis is carried out in order to describe the practical application of the suggested production-inventory model.