Polyhedral results for position-based scheduling of chains on a single machine

Markó Horváth and Tamás Kis ()
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Markó Horváth: Hungarian Academy of Sciences
Tamás Kis: Hungarian Academy of Sciences

Annals of Operations Research, 2020, vol. 284, issue 1, No 13, 283-322

Abstract: Abstract We consider a scheduling problem, where a set of unit-time jobs has to be sequenced on a single machine without any idle times between the jobs. Preemption of processing is not allowed. The processing cost of a job is determined by the position in the sequence, i.e., for each job and each position, there is an associated weight, and one has to determine a sequence of jobs which minimizes the total weight incurred by the positions of the jobs. In addition, the ordering of the jobs must satisfy the given chain-precedence constraints. In this paper we show that this problem is NP-hard even in a special case, where each chain consists of two jobs (2-chains). Further on, we study the polyhedron associated with the problem, and present a class of valid inequalities along with a polynomial-time separation procedure, and show that some of these inequalities are facet-defining in the special case of 2-chains. Finally, we present our computational results that confirm that separating these inequalities can significantly speed up a linear programming based branch-and-bound procedure to solve the problem with chains of two jobs.

Keywords: Scheduling; Polyhedra; Cutting planes (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-019-03180-8

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