Two-agent scheduling on uniform parallel machines with min-max criteria

Donatas Elvikis () and Vincent T’kindt ()

Annals of Operations Research, 2014, vol. 213, issue 1, 79-94

Abstract: We consider the problem of scheduling two agents A and B on a set of m uniform parallel machines. Each agent is assumed to be independent from the other: agent A and agent B are made up of n A and n B jobs, respectively. Each job is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size jobs, i.e. all jobs share the same processing time. Our goal is to minimize two maximum functions associated with agents A and B and referred to as $F_{max}^{A}=\max_{i\in A} f^{A}_{i}(C_{i})$ and $F_{max}^{B}=\max_{i\in B}f^{B}_{i}(C_{i})$ , respectively, with C i the completion time of job i and $f_{i}^{X}$ a non-decreasing function. These kinds of problems are called multi-agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of the strict Pareto optima for the $(F_{max}^{A}, F_{max}^{B} )$ criteria vector. In this paper we develop a minimal complete Pareto set enumeration algorithm with [InlineEquation not available: see fulltext.] time complexity and [InlineEquation not available: see fulltext.] memory requirements. Copyright Springer Science+Business Media, LLC 2014

Keywords: Multi-agent scheduling; Parallel machines; Pareto optimum (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-012-1099-0 (text/html)
Access to full text is restricted to subscribers.

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:213:y:2014:i:1:p:79-94:10.1007/s10479-012-1099-0

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

DOI: 10.1007/s10479-012-1099-0

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 ().