Open Access

ARTICLE

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Peng Liu^1,*, Ke Xu^1,2, Hua Gong^1,2

1 School of Management, Shenyang University of Technology, Shenyang, 110870, China
2 School of Science, Shenyang Ligong University, Shenyang, 110159, China

* Corresponding Author: Peng Liu. Email:

Computers, Materials & Continua 2023, 76(1), 239-258. https://doi.org/10.32604/cmc.2023.038232

Received 02 December 2022; Accepted 10 April 2023; Issue published 08 June 2023

Abstract

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry, the coordinated scheduling problem of parallel machine production and transportation is investigated. The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance. A non-cooperative game model is established, considering the competition and self-interest behavior of jobs from different customers for machine resources. The job from different customers is mapped to the players in the game model, the corresponding optional processing machine and location are mapped to the strategy set, and the makespan of the job is mapped to the payoff. Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model. A Nash equilibrium solution algorithm based on the genetic algorithm (NE-GA) is designed, and the effective solution of approximate Nash equilibrium for the game model is realized. The fitness function, single-point crossover operator, and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium. Rules are also designed to avoid the generation of invalid offspring chromosomes. The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes. Compared with other algorithms such as heuristic algorithms (FCFS, SPT, and LPT), the simulated annealing algorithm (SA), and the particle swarm optimization algorithm (PSO), experimental results show that the proposed NE-GA algorithm has obvious performance advantages.

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Keywords

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