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Compact Scheduling of Open Shops

In: A Book of Open Shop Scheduling

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  • Wieslaw Kubiak

    (Memorial University of Newfoundland)

Abstract

This chapter concentrates on compact and cyclic compact open shop scheduling. Compact scheduling is motivated by timetabling and cyclic compact scheduling by just-in-time systems. A compact schedule requires each job to be processed in a no-wait fashion and each machine to process operations without idle time. Compact schedules do not always exist. The chapter presents smallest instances for which compact schedules do not exist and tests to determine whether compact schedules exist for a given degree Δ. Such tests run in polynomial time for open shop instances with Δ ≤ 4 but become NP-complete for Δ = 5. The minimization of makespan over all compact schedules has polynomial-time solution only for Δ ≤ 3, and it is open even for (3, 4)-biregular open shops where every job has length equal 3 and each machine workload equal 4. Deficiency has been proposed as a measure of deviation from compactness. However, the problem of minimizing deficiency is not only NP-hard in the strong sense but also the existing integer programming (IP) and constraint programming (CP) models can hardly solve problems of size n + m = 10 in reasonable time.

Suggested Citation

  • Wieslaw Kubiak, 2022. "Compact Scheduling of Open Shops," International Series in Operations Research & Management Science, in: A Book of Open Shop Scheduling, chapter 0, pages 205-232, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-91025-9_9
    DOI: 10.1007/978-3-030-91025-9_9
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