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

TL;DR

This paper applies Answer-Set Programming with difference logic to optimize lexicographical makespan in parallel machine scheduling, improving robustness and demonstrating competitive performance with existing solvers.

Contribution

It introduces a novel ASP-based approach with multi-shot solving and heuristics for complex scheduling with robustness considerations.

Findings

ASP with difference logic effectively models timing constraints.

Multi-shot solving improves solution quality for large instances.

ASP competes well with CP and MIP solvers on industrial-sized problems.

Abstract

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 KRR paradigm for this problem and is competitive with state-of-the-art CP and MIP solvers. Under consideration in Theory and Practice of Logic Programming (TPLP).