Title: Solving an EPQ model with Lagrange interpolating polynomial function via game theory approach

Authors: Anup Khan; Sujit Kumar De; Prasun Kumar Nayak

Addresses: Department of Computer Science, Midnapore College (Autonomous), West Bengal – 721101, India ' Department of Mathematics (UG and PG), Midnapore College (Autonomous), West Bengal – 721101, India ' Department of Mathematics (UG and PG), Midnapore College (Autonomous), West Bengal – 721101, India

Abstract: This article briefly discusses about classical economic production quantity (EPQ) model using game theoretic approach via Lagrange multiplier. It involves two stages of computations, in first stage, we develop a Mond-Weir dual of the EPQ cost minimisation problem with the help of weak and strong duality theory. Secondly, we have formulated an equivalent matrix game problem using Preda's framework. The problem has been solved under convex optimisation, the game theoretic approach and Lagrange interpolating polynomial optimisation respectively with the help of a novel solution algorithm. The numerical illustration shows that a saddle point exists locally but for global optimality some duality gaps have been found. However, this study explains the role of Lagrange multiplier towards optimising the objective function and its corresponding range of variations also. Finally, we have done sensitivity analysis and graphical illustration to justify the novelty of this new approach.

Keywords: EPQ model; matrix game; Lagrange interpolating polynomial; optimisation.

DOI: 10.1504/IJMOR.2024.141471

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.1, pp.1 - 24

Received: 21 Mar 2023
Accepted: 04 Apr 2023
Published online: 16 Sep 2024 *

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