Scheduling jobs of equal length: Complexity, facets and computational results

  • Yves Crama
  • Frits C. R. Spieksma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 920)


Given are n jobs, which have to be performed on a single machine within a fixed timespan 1,2,⋯T. The processing time (or length) of each job equals p, p. The processing cost of each job is an arbitrary function of its start-time. The problem is to schedule all jobs so as to minimize the sum of the processing costs.

This problem is proved to be NP-hard, already for p=2 and 0–1 processing costs. On the other hand, when T=np+c, with c constant, the problem can be solved in polynomial time. A partial polyhedral description of the set of feasible solutions is presented. In particular, two classes of facet-defining inequalities are described, for which the separation problem is polynomially solvable. Also, we exhibit a class of objective functions for which the inequalities in the LP-relaxation guarantee integral solutions.

Finally, we present a simple cutting plane algorithm and report on its performance on randomly generated problem instances.


scheduling computational complexity polyhedral description 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Yves Crama
    • 1
  • Frits C. R. Spieksma
    • 2
  1. 1.Faculté d'EconomieUniversité de LiègeLiègeBelgium
  2. 2.Department of MathematicsUniversity of LimburgMaastrichtNetherlands

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