Scheduling problems with two competing agents to minimize minmax and minsum earliness measures

• Published in: European journal of operational research Vol. 206; no. 3; pp. 540 - 546
• Main Authors: Mor, Baruch, Mosheiov, Gur
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Artificial intelligence; Completion time; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Cost engineering; Cost reduction; Earliness; Exact sciences and technology; Flow control; Microprocessors; Multi-agent scheduling; Multi-agent scheduling Single machine Earliness; Operational research; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Production scheduling; Schedules; Scheduling; Scheduling, sequencing; Single machine; Software; Studies; Upper bounds; Multi-agent scheduling; Earliness; Single machine; Costs; Polynomial time; Upper bound; Multiagent system; Processor scheduling; Minimax method; NP hard problem; Artificial intelligence; Completion time; Execution time
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.03.003

A relatively new class of scheduling problems consists of multiple agents who compete on the use of a common processor. We focus in this paper on a two-agent setting. Each of the agents has a set of jobs to be processed on the same processor, and each of the agents wants to minimize a measure which depends on the completion times of its own jobs. The goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents. We consider measures of minmax and minsum earliness. Specifically, we focus on minimizing maximum earliness cost or total (weighted) earliness cost of one agent, subject to an upper bound on the maximum earliness cost of the other agent. We introduce a polynomial-time solution for the minmax problem, and prove NP-hardness for the weighted minsum case. The unweighted minsum problem is shown to have a polynomial-time solution.