Unrelated machine scheduling with time-window and machine downtime constraints: An application to a naval battle-group problem

Youngho Lee, Hanif D. Sherali

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

This paper deals with an unrelated machine scheduling problem of minimizing the total weighted flow time, subject to time-window job availability and machine downtime side constraints. We present a zero-one integer programming formulation of this problem. The linear programming relaxation of this formulation affords a tight lower bound and often generates an integer optimal solution for the problem. By exploiting the special structures inherent in the formulation, we develop some classes of strong valid inequalities that can be used to tighten the initial formulation, as well as to provide cutting planes in the context of a branch-and-cut procedure. A major computational bottleneck is the solution of the underlying linear programming relaxation because of the extremely high degree of degeneracy inherent in the formulation. In order to overcome this difficulty, we employ a Lagrangian dual formulation to generate lower and upper bounds and to drive the branch-and-bound algorithm. As a practical instance of the unrelated machine scheduling problem, we describe a combinatorial naval defense problem. This problem seeks to schedule a set of illuminators (passive homing devices) in order to strike a given set of targets using surface-to-air missiles in a naval battle-group engagement scenario. We present computational results for this problem using suitable realistic data.

Original languageEnglish
Pages (from-to)339-365
Number of pages27
JournalAnnals of Operations Research
Volume50
Issue number1
DOIs
Publication statusPublished - 1994 Dec 1
Externally publishedYes

Fingerprint

Lower bounds
Machine scheduling
Time windows
Linear programming
Schedule
Integer programming
Valid inequalities
Optimal solution
Flow time
Cutting planes
Branch and bound algorithm
Upper bound
Integer
Scenarios
Air

Keywords

  • Lagrangian relaxation
  • strong integer programming formulation
  • time-window constraints
  • Unrelated machine scheduling

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

Cite this

Unrelated machine scheduling with time-window and machine downtime constraints : An application to a naval battle-group problem. / Lee, Youngho; Sherali, Hanif D.

In: Annals of Operations Research, Vol. 50, No. 1, 01.12.1994, p. 339-365.

Research output: Contribution to journalArticle

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