Bicriterion Single Machine Scheduling with Resource Dependent Processing Times

• Published in: SIAM journal on optimization Vol. 8; no. 2; pp. 617 - 630
• Main Authors: Cheng, T. C. Edwin, Janiak, Adam, Kovalyov, Mikhail Y.
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.05.1998
• Subjects: Algorithms; Approximation; Cybernetics; Dynamic programming; Job shops; Pareto optimum; Scheduling
• ISSN: 1052-6234; 1095-7189
• DOI: 10.1137/S1052623495288192

A bicriterion problem of scheduling jobs on a single machine is studied. The processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job. A solution is specified by a sequence of the jobs and a resource allocation. The quality of a solution is measured by two criteria, F1 and F2. The first criterion is the maximal or total (weighted) resource consumption, and the second criterion is a regular scheduling criterion depending on the job completion times. Both criteria have to be minimized. General schemes for the construction of the Pareto set and the Pareto set $\epsilon$-approximation are presented. Computational complexities of problems to minimize F1 subject to F_2\le K$ and to minimize F2 subject to $F_1\le K$, where K is any number, are studied for various functions F1 and F2. Algorithms for solving these problems and for the construction of the Pareto set and the Pareto set $\epsilon$-approximation for the corresponding bicriterion problems are presented.