Minmax scheduling problems with a common due-window

Gur Mosheiov*, Assaf Sarig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


This paper focuses on a minmax due-window assignment problem. The goal is to schedule the jobs and the due-window such that the highest cost among all jobs is minimized. The objective function contains four cost components: for earliness, tardiness, due-window starting time and due-window size. We present a polynomial time solution for the case of a single machine and for a two-machine flow-shop. The cases of parallel identical machines and uniform machines are NP-hard, and simple heuristics and lower bounds are introduced and tested numerically. Scope and purpose. Contracts between suppliers and customers often contain a time interval (a due-window), such that goods delivered within this interval are considered to be on time and are not penalized. The due-window starting time and size are determined during sales negotiations with customers. A late and/or large due-window clearly makes the supplier less attractive, and hence the total cost function should increase in the due-window starting time and size. This paper focuses on due-window assignment problems on several classical machine settings: a single machine, a two-machine flow-shop and parallel identical and uniform machines.

Original languageAmerican English
Pages (from-to)1886-1892
Number of pages7
JournalComputers and Operations Research
Issue number6
StatePublished - Jun 2009

Bibliographical note

Funding Information:
This paper was supported in part by the Recannati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.


  • Common due-window
  • Earliness-tardiness
  • Minmax
  • Scheduling


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