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Two-Machine No-Wait Flow Shop Scheduling with Missing Operation

Published: 01 November 1999 Publication History

Abstract

This paper considers the no-wait scheduling of n jobs in a two-machine flow shop, where some jobs require processing on the first machine only. The objective is to minimize the maximum completion time, or makespan. In view of its NP-hardness, we propose and analyze heuristic algorithms. Our main result is an O(n log n)-time heuristic which generates a schedule with makespan no more than 4/3 times that of an optimal schedule. This heuristic solves optimally the subproblem involving the jobs with no missing operations, using, for example, the well-known algorithm of Gilmore and Gomory, and then uses a list scheduling procedure to insert the remaining jobs in the schedule. A new proof technique is employed in the worst-case analysis, which has potential application in a variety of bin packing and scheduling problems.

Cited By

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  • (2019)Minimizing Makespan in No-Wait Job ShopsMathematics of Operations Research10.1287/moor.1050.015530:4(817-831)Online publication date: 1-Jan-2019
  • (2018)Two-stage no-wait hybrid flowshop scheduling with inter-stage flexibilityJournal of Combinatorial Optimization10.1007/s10878-017-0155-835:1(108-125)Online publication date: 21-Dec-2018

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cover image Mathematics of Operations Research
Mathematics of Operations Research  Volume 24, Issue 4
Nov. 1999
126 pages
ISSN:0364-765X
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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 November 1999

Author Tags

  1. Flow shop
  2. approximation
  3. list scheduling
  4. makespan

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Cited By

View all
  • (2019)Minimizing Makespan in No-Wait Job ShopsMathematics of Operations Research10.1287/moor.1050.015530:4(817-831)Online publication date: 1-Jan-2019
  • (2018)Two-stage no-wait hybrid flowshop scheduling with inter-stage flexibilityJournal of Combinatorial Optimization10.1007/s10878-017-0155-835:1(108-125)Online publication date: 21-Dec-2018

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