Minimizing weighted earliness-tardiness and due-date cost with unit processing-time jobs

Gur Mosheiov*, Uri Yovel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

The classical single-machine scheduling and due-date assignment problem of Panwalker et al. [Panwalker, S.S., Smith, M.L., Seidmann, A., 1982. Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research 30(2) (1982) 391-399] is the following: All n jobs share a common due-date, which is to be determined. Jobs completed prior to or after the due-date are penalized according to a cost function which is linear and job-independent. The objective is to minimize the total earliness-tardiness and due-date cost. We study a generalized version of this problem in which: (i) the earliness and tardiness costs are allowed to be job dependent and asymmetric and (ii) jobs are processed on parallel identical machines. We focus on the case of unit processing-time jobs. The problem is shown to be solved in polynomial (O(n4)) time. Then we study the special case with no due-date cost (a classical problem known in the literature as TWET). We introduce an O(n3) solution for this case. Finally, we study the minmax version of the problem, (i.e., the objective is to minimize the largest cost incurred by any of the jobs), which is shown to be solved in polynomial time as well.

Original languageAmerican English
Pages (from-to)528-544
Number of pages17
JournalEuropean Journal of Operational Research
Volume172
Issue number2
DOIs
StatePublished - 16 Jul 2006

Keywords

  • Assignment problem
  • Due-date assignment
  • Earliness-tardiness
  • Scheduling

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