A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance

• Published in: Journal of combinatorial optimization Vol. 33; no. 4; pp. 1454 - 1468
• Main Authors: Mor, Baruch, Mosheiov, Gur
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2017; Springer Nature B.V
• Subjects: Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Theory of Computation; Two agents; Minmax; Scheduling; Common flow-allowance; Single machine
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-016-0049-1

We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.