Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

• Published in: Journal of scheduling Vol. 22; no. 6; pp. 623 - 634
• Main Authors: Györgyi, Péter, Kis, Tamás
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2019; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Business and Management; Calculus of Variations and Optimal Control; Optimization; Completion time; Complexity; Job shops; Mathematical analysis; Operations Research/Decision Theory; Optimization; Polynomials; Production scheduling; Renewable resources; Resource scheduling; Supply Chain Management; Weight; Single-machine scheduling; Approximation algorithms; Non-renewable resources
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-019-00601-1

In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.