Answer-Set Programming for Lexicographical Makespan Optimisation in Parallel Machine Scheduling

We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost r...

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Bibliographic Details
Published inTheory and practice of logic programming Vol. 23; no. 6; pp. 1281 - 1306
Main Authors EITER, THOMAS, GEIBINGER, TOBIAS, MUSLIU, NYSRET, OETSCH, JOHANNES, SKOČOVSKÝ, PETER, STEPANOVA, DARIA
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.11.2023
Subjects
Algorithms
answer-set programming
Constraint modelling
Employment
Integer programming
Knowledge representation
lexicographical optimisation
Linear programming
Mixed integer
parallel machine scheduling
Release dates
Schedules
Scheduling
Subject specialists
Variables
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Summary:We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of answer-set programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising knowledge representation and reasoning (KRR) paradigm for this problem and is competitive with state-of-the-art constraint programming (CP) and Mixed-Integer Programming (MIP) solvers.
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ISSN:1471-0684
1475-3081
1475-3081
DOI:10.1017/S1471068423000017