A note on a due-date assignment on a two-machine flow-shop

Motty Birman, Gur Mosheiov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We address a due-date assignment and scheduling problem in a two-machine flow-shop setting. Our objective is to find both the job schedule and the common due-date which minimize maximum earliness, tardiness and due-date costs. We introduce an efficient (O(n2 log n)) solution, based on repetitive use of the well-known Johnson Algorithm. Careful determination of the due-date in the course of sales negotiations with a customer is clearly an important task for the firm. A late due-date reflects a lower service level and incurs an obvious penalty for the supplier. For a given due-date, there are penalties associated with jobs completed early or late. This paper addresses a Just-In-Time scheduling problem incorporating all these cost components. The machine setting assumed is a two-machine flow-shop. We show that an optimal solution (i.e., both an optimal due-date value and an optimal job schedule) can be found in polynomial time.

Original languageAmerican English
Pages (from-to)473-480
Number of pages8
JournalComputers and Operations Research
Issue number3
StatePublished - Mar 2004

Bibliographical note

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


  • Due-date assignment
  • Earliness-tardiness
  • Flow-shop
  • Scheduling


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