Bounded parallel-batch scheduling on single and multi machines for deteriorating jobs

Authors:
Cuixia Miao;Yuzhong Zhang;Zhigang Cao
Affiliations:
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, Peoples Republic of China;School of Management, Qufu Normal University, Rizhao, Shandong 276826, Peoples Republic of China;Key Laboratory of Management Decision and Information Systems AMSS, CAS, Beijing 100190, Peoples Republic of China
Venue:
Information Processing Letters
Year:
2011

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Abstract

We consider the bounded parallel-batch scheduling problem in which the processing time of a job is a simple linear function of its starting time. The objective is to minimize the makespan. When the jobs have identical release dates, we present an optimal algorithm for the single-machine problem and an fully polynomial-time approximation scheme for the parallel-machine problem. When the jobs have distinct release dates, we show that the single-machine problem is NP-hard and present an optimal algorithm for one special case.