A game theory model based on Gale-Shapley for dual-resource constrained (DRC) flexible job shop scheduling

Abstract

Most job shops in practice are constrained by both machine and labor availability. Worker assignment in these so-called Dual Resource Constrained (DRC) job shops is typically solved in the literature via the use of meta-heuristics, i.e. "when" and "where" rules, or heuristic assignment rules. While the former does not necessarily lead to optimal results, the latter suffers from high computational time and complexity, especially when there is a large number of workstations. This paper uses game theory to propose a new worker assignment rule for DRC job shops. The Gale-Shapley model (also known as the stable marriage problem) forms a 'couple' made up of a worker and machine following a periodic review strategy. Simulation is used to evaluate and compare the proposed model to "when" and "where" rules previously proposed in the literature. Simulation experiments under different conditions demonstrate that the Gale-Shapley model provides better results for worker assignments in complex DRC systems, particularly when the workers have different efficiency levels. The implications of the findings for research and practice are outlined.

A Review of Game Theory Models to Support Production Planning, Scheduling, Cloud Manufacturing and Sustainable Production Systems

“…Renna et al [26] studied the dual resource scheduling problem in job-shop manufacturing systems. They proposed a Gale-Shapley model to support worker assignment for dual resource-constrained job-shop problems.…”

Production, maintenance and resource scheduling: A review

“…The overall conclusion, for all shops, is to let workers operate in the department where they are most efficient, until all work at that department is exhausted. More recently, Renna, Thürer, & Stevenson (2020) consider the same problem, using game theory as an approach to solve the worker assignment problem. They show an increased performance compared to more traditional 'when' and 'where' rules.…”