Single machine scheduling with release dates and job delivery to minimize the makespan

Authors:
Lingfa Lu;Jinjiang Yuan;Liqi Zhang
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, Peoples Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, Peoples Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, Peoples Republic of China
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

In single machine scheduling with release dates and job delivery, jobs are processed on a single machine and then delivered by a capacitated vehicle to a single customer. Only one vehicle is employed to deliver these jobs. The vehicle can deliver at most c jobs at a shipment. The delivery completion time of a job is defined as the time at which the delivery batch containing the job is delivered to the customer and the vehicle returns to the machine. The objective is to minimize the makespan, i.e., the maximum delivery completion time of the jobs. When preemption is allowed to all jobs, we give a polynomial-time algorithm for this problem. When preemption is not allowed, we show that this problem is strongly NP-hard for each fixed c=1. We also provide a 53-approximation algorithm for this problem, and the bound is tight.