Coordination mechanisms for scheduling games with machine modification

Abstract

This paper studies scheduling games with machine modification. A set of jobs is to be processed on a set of identical machines. An initial schedule before the modification of machines is given as a prior. Then some machines are removed and some new machines are added. Each job has the right either to stay on its original machine if the machine is not removed, or to move to another machine. The choices of all jobs after the machine modification constitute a new schedule. The individual cost of each job is its completion time, which is determined by the scheduling policy that the machines follow. We present properties of the Nash equilibriums under generalizations of the classical scheduling policies such as LPT, SPT and Makespan. For the social cost of minimizing the makespan, we establish the Price of Anarchy and Price of Stability of the games, and majorities of the parametric bounds are tight for each combination of the number of final machines, the number of added machines and the number of removed machines.

A Coordination Mechanism for Scheduling Game on Parallel-Batch Machines with Deterioration Jobs

“…All the policies of the machines are named as a coordination mechanism [12,13]. More studies on coordination mechanism for scheduling game problem can be found in Chen and Tan [14], Ye et al [15], Chen and Xu [16], and He and Tan [17].…”

Dynamic scheduling of a picking robot with limited buffer and rejection: an industrial case study

“…Making such complex decisions appropriately requires advanced optimization approaches. Such approaches often perform well for complex industrial decision processes such as integrated decisions (Solano‐Blanco et al., 2020), multiple objectives (Bissoli et al., 2021), or when random event disturb the plan (He and Tan, 2020). In a multirobot context, Briand et al.…”