Two-agent single-machine scheduling with cumulative deterioration

• Published in: 4OR Vol. 17; no. 2; pp. 201 - 219
• Main Authors: Chen, Ren-Xia, Li, Shi-Sheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Completion time; Deterioration; Industrial and Production Engineering; Job shops; Lateness; Operations research; Operations Research/Decision Theory; Optimization; Polynomials; Production scheduling; Research Paper; Scheduling; Upper bounds; Cumulative deterioration; Two-agent; Single-machine; Scheduling; 90B35
• ISSN: 1619-4500; 1614-2411
• DOI: 10.1007/s10288-018-0388-0

We address cumulative deterioration scheduling in which two agents compete to perform their respective jobs on a single machine. By cumulative deterioration we mean that the actual processing time of any job of the two agents is a linear increasing function of the total normal processing times of already processed jobs. Each agent desires to optimize some scheduling criterion that depends on the completion times of its own jobs only. We study several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. The aim is to find an optimal schedule that minimizes the objective value of one agent while maintaining the objective value of the other agent not exceeding a fixed upper bound. For each problem under study, we design either a polynomial-time or a pseudo-polynomial-time algorithm to solve it.