New lower and upper bounds for scheduling around a small common due date

J.A. Hoogeveen, H. Oosterhout, S.L. van de Velde

Research output: Contribution to journalArticleAcademicpeer-review

22 Citations (Scopus)
28 Downloads (Pure)


We consider the single-machine problem of scheduling n jobs to minimize the sum of the deviations of the job completion times from a given small common due date. For this NP-hard problem, we develop a branch-and-bound algorithm based on Lagrangian lower and upper bounds that are found in O(n log n) time. We identify conditions under which the bounds concur; these conditions can be expected to be satisfied by many instances with n not too small. In our experiments with processing times drawn from a uniform distribution, the bounds concur for n ≥ 40. For the case where the bounds do not concur, we present a refined lower bound that is obtained by solving a subset-sum problem of small dimension to optimality. We further develop a 4/3-approximation algorithm based upon the Lagrangian upper bound.
Original languageEnglish
Pages (from-to)102-110
JournalOperations research
Issue number1
Publication statusPublished - 1994


Dive into the research topics of 'New lower and upper bounds for scheduling around a small common due date'. Together they form a unique fingerprint.

Cite this