Noncooperative Game on Scheduling: The Single Machine Case

Authors:	Wang Changjun, Shanghai Jiaotong University, China Xi Yugeng, Shanghai Jiaotong University, China
Topic:	5.2 Manufacturing Modelling for Management and Control
Session:	Production Planning and Scheduling - I
Keywords:	Manufacturing system. Production costs, Scheduling algorithms, Nash games, Multiobjective optimizations.

Abstract

Considering the diversified requirements of modern manufacturing, the paper studies a group of scheduling problems where jobs and machine have independent performance objectives. Based on noncooperative game, it is modeled as a two-layer optimization problem. In job-layer, the jobs’ strategies resulted from competition for machine resource achieve Nash Equilibrium (NE), while in machine-layer, machine induces the NE to some global optimum by indirectly influencing jobs’ selfish behaviors. Referring to Lagrangian relaxation, an iterative algorithm is developed to solve the problem. Numerical example is also given for illustration.