On scheduling with non-increasing time slot cost to minimize total weighted completion time

Yingchao Zhao (), Xiangtong Qi () and Minming Li ()
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Yingchao Zhao: Caritas Institute of Higher Education
Xiangtong Qi: Hong Kong University of Science and Technology
Minming Li: City University of Hong Kong

Journal of Scheduling, 2016, vol. 19, issue 6, No 10, 759-767

Abstract: Abstract This paper addresses a recent open scheduling problem which aims to minimize the summation of total weighted completion time and the total machine time slot cost. Focusing on the case of non-increasing time slot cost with non-preemptive jobs, we show that the problem can be solved in polynomial-time when the time slot cost decreases with certain patterns, including linearly decreasing, decreasing concave, and decreasing convex cases. Different methodologies are used for three cases. For the linearly decreasing case, we can classify all the jobs into three categories and schedule the job sets one by one. For the decreasing concave case, we calculate each job’s worst starting time and try to make them far away from their worst starting times. For the decreasing concave case, we calculate each job’s best starting time and let them start close to their best starting times. Finally, we show that the problem is NP-hard in the strong sense when the time slot cost decreases in an arbitrary way.

Keywords: Operations research; Scheduling; Time slot cost; Total weighted completion time (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10951-015-0462-9

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