Effects of memory on inventory control and pricing policy for imperfect production with rework process

Indian Institute of Technology Roorkee, Roorkee 247667, India

^* Corresponding author: psingh@ma.iitr.ac.in

Received: 18 July 2022
Accepted: 12 November 2024

Abstract

Fractional calculus is a pertinent way to study the memory effect in an inventory model for investigating its dynamical behavior. Since inventory management is a memory-dependent process, fractional calculus approach may be employed to discover some fruitful insights and can help to gain more profit. In realistic scenarios, the manufacturing process cannot be perfect, and it delivers some faulty units due to many inevitable reasons. In literature, an imperfect production inventory problem under the memory effect has not been studied. Our study aims to investigate the memory effect on a production inventory system. In this article, a fractional order inventory control problem is formulated by considering an imperfect manufacturing process and price-sensitive demand. The faulty units are repaired through a rework process. Caputo fractional derivatives and integrals are used to consider the memory effect. Due to the nonlinear cost elements in the formulated problem, optimal pricing and production policies are investigated by using a quasi-Newton optimization algorithm and particle swarm optimization approach. The managerial implications of the proposed study are discussed with the help of numerical illustrations. The numerical outcomes suggest that consideration of memory in the inventory system boosts the profitability of the firm.