Game Theory-Based Mathematical Planning Model for Integrated Production Planning in Supply Chains

Abstract

In the face of intensifying global competition, the efficient management of supply chains has become paramount across practical industries. The intricate nature of supply chain processes, often compounded by extensive computational requirements, presents significant challenges in achieving effective Supply Chain Management (SCM). This article proposes an innovative approach to integrated production planning (IPP), aiming to address these challenges. Inspired by game theory, widely acknowledged for its applications in amalgamating heat and mass converter networks, the proposed approach seamlessly integrates demand and supply data. This integration offers supply chain planners deeper insights into the SCM process, facilitating streamlined reprogramming and decision-making. The framework is substantiated through the presentation of two illustrative case studies. The first involves a single-product scenario, while the second showcases the processing of multiple products on a single processor. Notably, the results obtained from these case studies align consistently with solutions derived from equivalent optimization problems solved using the GAMS. Furthermore, this article introduces a production sequencing algorithm tailored to the second case study. The novel algorithm significantly reduces computation time, achieving a remarkable one-sixth reduction compared to prior methodologies. This reduction underscores the potential for heightened computational efficiency within the proposed framework. In conclusion, the findings of this study demonstrate the efficacy of the game theory-based approach in yielding optimal comprehensive plans and serving as a promising foundation for enhancing computational efficiency through the adept application of mixed programming formulas.