Approximation schemes for parallel machine scheduling with non-renewable resources

• Published in: European journal of operational research Vol. 258; no. 1; pp. 113 - 123
• Main Authors: Györgyi, Péter, Kis, Tamás
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2017
• Subjects: Approximation schemes; Non-renewable resources; Parallel machines; Scheduling; Parallel machines; Scheduling; Approximation schemes; Non-renewable resources
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2016.09.007

•Parallel machine scheduling with non-renewable resources is considered.•A PTAS is devised for the makespan objective with arbitrary number of supply dates.•A PTAS is presented for the maximum lateness objective under some restriction.•APX-hardness is shown for the general case. In this paper the approximability of parallel machine scheduling problems with resource consuming jobs is studied. In these problems, in addition to a parallel machine environment, there are non-renewable resources, like raw materials, energy, or money, consumed by the jobs. Each resource has an initial stock, and some additional supplies at a-priori known moments in time and in known quantities. The schedules must respect the resource constraints as well. The optimization objective is either the makespan, or the maximum lateness. Polynomial time approximation schemes are provided under various assumptions, and it is shown that the makespan minimization problem is APX-complete if the number of machines is part of the input even if there are only two resources.