No-idle, no-wait: when shop scheduling meets dominoes, Eulerian paths and Hamiltonian paths

J.-C. Billaut, F. Della Croce (), F. Salassa and V. T’kindt
Additional contact information
J.-C. Billaut: Université de Tours
F. Della Croce: Politecnico di Torino
F. Salassa: Politecnico di Torino
V. T’kindt: Université de Tours

Journal of Scheduling, 2019, vol. 22, issue 1, No 4, 59-68

Abstract: Abstract In shop scheduling, several applications require that some components perform consecutively. We refer to “no-idle schedules” if machines are required to operate with no inserted idle time and to “no-wait schedules” if tasks cannot wait between the end of an operation and the start of the following one. We consider here no-idle/no-wait shop scheduling problems with makespan as the performance measure and determine related complexity results. We first analyse the two-machine no-idle/no-wait flow shop problem and show that it is equivalent to a special version of the game of dominoes which is polynomially solvable by tackling an Eulerian path problem on a directed graph. We present for this problem an O(n) exact algorithm. As a by-product, we show that the Hamiltonian path problem on a digraph G(V, A) with a special structure (where any two vertices i and j either have all successors in common or have no common successors) reduces to the two-machine no-idle/no-wait flow shop problem. Correspondingly, we provide a new polynomially solvable special case of the Hamiltonian path problem. Then, we show that also the m-machine no-idle/no-wait flow shop problem is polynomially solvable and provide an $$O(mn \log n)$$ O ( m n log n ) exact algorithm. Finally, we prove that the decision versions of the two-machine job shop problem and the two-machine open shop problem are NP-complete in the strong sense.

Keywords: No-idle/no-wait shop scheduling; Dominoes; Eulerian path; Hamiltonian path; numerical matching with target sums (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10951-018-0562-4

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