Bi-criteria and tri-criteria analysis to minimize maximum lateness makespan and resource consumption for scheduling a single machine

Liron Yedidsion

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We analyze two single machine scheduling problems for the case where job processing times are controllable, by allocating continuous and non-renewable resources to the processing operations. The first problem to analyze is constructing the trade-off curve between maximum lateness and total resource consumption; an O(n2) computational time optimization algorithm was constructed to solve this problem. This algorithm was extended to solve the second problem, which is to construct the trade-off surface between maximum lateness, makespan, and total resource consumption. As part of this algorithm we identify a plane in the 3D field that is formed by the three criteria, which is parallel only to the maximum lateness, and calculate the optimal makespan and total resource consumption as functions of points on this plane. The extended algorithm keeps the same complexity of O(n2) time. Both algorithms are very robust as they solve the problem for a very large set of resource consumption functions which has to follow only some mild (and commonly acceptable) conditions. Moreover, as far as we know, this is the first research of its kind in the field of multi-objective scheduling to present an algorithm that constructs a 3D trade-off surface.

Original languageEnglish
Pages (from-to)665-679
Number of pages15
JournalJournal of Scheduling
Volume15
Issue number6
DOIs
StatePublished - 1 Dec 2012
Externally publishedYes

Keywords

  • Bi-criteria
  • Convex resource allocation
  • Makespan
  • Maximum lateness
  • Multi-objective
  • Single machine scheduling
  • Tri-criteria

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