Mixed-integer versus constraint programming solvers: An extensive comparison with job shop scheduling problem

This paper compares free/open-source and commercial solvers of mixed-integer programming (MILP) and constraint programming (CP) in the classic job shop scheduling problem (JSSP)  with makespan and total flowtime minimization. We implemented a MILP model and solved it with CPLEX, Gurobi, and HIGS solvers, and we also implemented and solved CP models with IBM CP, Hexaly, and OR-Tools solvers. We conducted computational experiments using 80 well-known Taillard instance sets. The extensive computational experience shows that the MILP model is promising for solving small-sized instances, and the CP model got the best average relative deviation and superior performance in large-sized instances. The solver IBM CP got the best average results.