Scheduling with two competing agents to minimize total weighted earliness

Enrique Gerstl (), Baruch Mor and Gur Mosheiov
Additional contact information
Enrique Gerstl: The Hebrew University
Baruch Mor: Ariel University
Gur Mosheiov: The Hebrew University

Annals of Operations Research, 2017, vol. 253, issue 1, No 11, 227-245

Abstract: Abstract We study a single machine scheduling problem with two competing agents and earliness measures. Given a common deadline for all the jobs of both agents, the objective function is minimizing the total weighted earliness of the first agent, subject to an upper bound on the maximum earliness of the jobs of the second agent. This problem was recently proved to be NP-hard, leaving the question of the complexity class open. We introduce a pseudo-polynomial dynamic programming algorithm, implying that the problem is NP-hard in the ordinary sense. An extensive numerical study indicates that the dynamic programming is very effective for solving medium size instances. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. The dynamic programming algorithm is extended to any (given) number of agents, proving NP-hardness in the ordinary sense of the general multi-agent setting. Finally, we study the inverse problem of minimizing the maximum earliness of one agent subject to an upper bound on the maximum total weighted earliness of the second agent. We introduce a pseudo-polynomial dynamic programming algorithm, a simple greedy-type heuristic and a lower bound. Our numerical tests verify that the heuristic produces very small optimality gaps.

Keywords: Two-agent scheduling; Single machine; Earliness; Dynamic programming (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-016-2310-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2310-5

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-016-2310-5

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().