Abstract
This paper addresses the problem of scheduling n jobs on m identical parallel machines so as to minimize the completion time variance. Properties of optimal solutions are derived first. Then, complexity results are obtained, which show that the problem is NP-complete in the strong sense when m is arbitrary, and NP-complete in the ordinary sense when m is fixed. Two algorithms are proposed. The first algorithm can generate an optimal solution in time O(n2mPm(P - Pm)m-1/[mm(m - 1)!]2), where P is the sum of all the processing times and Pm is the sum of the first m largest processing times. The second algorithm can find a near-optimal solution in time O(nPm(P - Pm)m-1/mm(m - 1)!). It is further shown that the relative error of the near-optimal solution is guaranteed to approach zero at a rate O(n-2) as n increases.
Original language | English |
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Pages (from-to) | 55-70 |
Number of pages | 16 |
Journal | Discrete Applied Mathematics |
Volume | 84 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - 15 May 1998 |
Keywords
- Completion time variance
- Dynamic programming
- NP-completeness
- Scheduling
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics