SMT Solvers for Job-Shop Scheduling Problems: Models Comparison and Performance Evaluation

Abstract

The optimal assignment of jobs to machines is a common problem when implementing automated production systems. A specific variant of this category is the job-shop scheduling problem (JSP) that is known to belong to the class of NP-hard problems. JSPs are typically either formulated as Mixed Integer Linear Programming (MILP) problems and solved by general-purpose-MILP solvers or approached using heuristic algorithms specifically designed for the purpose. During the last decade a new approach, satisfiability (SAT), led to develop solvers with incredible abilities in finding feasible solutions for hard combinatorial problems on Boolean variables. Moreover, an extension of SAT, Satisfability Modulo Theory (SMT), allows to formulate constraints involving linear operations over integers and reals and some SMT-solvers have been also extended with an optimizing tool. Since the JSP is a well-known hard combinatorial problem, it is interesting to evaluate how SMT-solvers perform in solving it and how they compare to traditional MILP-solvers. We therefore evaluate state-of-the-art MILP and SMT solvers on benchmark JSP instances and find that general-purpose open-source SMT-solvers are competitive against commercial MILP-solvers.