Approximation algorithms for bi-objective parallel-machine scheduling in green manufacturing

• Published in: Computers & industrial engineering Vol. 176; p. 108949
• Main Authors: Jiang, Yiwei, Tang, Xuelian, Li, Kai, Cheng, T.C.E., Ji, Min
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2023
• Subjects: Approximation algorithm; Green manufacturing; Parallel-machine scheduling; Worst-case ratio; Green manufacturing; Approximation algorithm; Worst-case ratio; Parallel-machine scheduling
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2022.108949

We consider bi-objective parallel-machine scheduling in green manufacturing to minimize the makespan and total processing cost. Each machine has a different constant processing cost per unit time. For the objective of minimizing the makespan, given a total cost budget, we provide an approximation algorithm with a worst-case ratio of 33+14≈1.686, which improves the previous bound of 2. For the objective of minimizing the total processing cost, subject to all the jobs must be completed before a given common deadline, we provide an approximation algorithm with a worst-case ratio of 2+r3, where r is the ratio of the maximum to the minimum processing cost per unit time on a machine. •We consider bi-objective parallel-machine scheduling in green manufacturing.•The goal is to minimize the makespan and total processing cost.•We propose an improved approximation algorithm for the first goal.•An approximation algorithm with the bound (2+r)/3 is given for the second goal.