A Parallel Machine Scheduling Problem Maximizing Total Weighted Early Work

Byung-Cheon Choi (), Myoung-Ju Park (), Kyung Min Kim () and Yunhong Min
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Byung-Cheon Choi: School of Business, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea
Myoung-Ju Park: Department of Industrial and Management Systems Engineering, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Kyunggi-do 17104, Korea
Kyung Min Kim: Department of Industrial Management and Engineering, Myongji University, 116 Myongji-ro, Choein-gu, Yongin-si, Gyeonggido 17058, Korea
Yunhong Min: Graduate School of Logistics, Incheon National University, 119, Academy-ro, Yeonsu-gu, Incheon, Gyeonggi-do 22012, Korea

Asia-Pacific Journal of Operational Research (APJOR), 2021, vol. 38, issue 06, 1-16

Abstract: We consider the total weighted early work maximization problem on identical machines in parallel such that the weights are identical, or the due date is the same. First, we present an approach to solve the case with a fixed number of machines in pseudo-polynomial time. Then, we develop approximation algorithms for the two cases with identical weights and with a common due date. For the case with identical weights, furthermore, we show that the parallel-machine and a single-machine cases are strongly NP-hard and weakly NP-hard, respectively, even if the due date of each job is equal to the processing time multiplied by a constant.

Keywords: Scheduling; early work; computational complexity; approximation algorithm (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S021759592150007X

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