Abstract
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 ∈ ℕ. 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.
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© 1995 Springer-Verlag Berlin Heidelberg
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Crama, Y., Spieksma, F.C.R. (1995). Scheduling jobs of equal length: Complexity, facets and computational results. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_58
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DOI: https://doi.org/10.1007/3-540-59408-6_58
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