Simulation-based optimization vs. mathematical programming: A hybrid approach for optimizing scheduling problems

With the increasing computing power of modern processors, exact solution methods (solvers) for the optimization of scheduling problems become more and more important. Based on the mixed integer programming (MIP) formulation of a scheduling problem, it will be analyzed how powerful the present solvers of this problem class are and up to which complexity real scheduling problems are manageable. For this, initially some common benchmark problems are investigated to find out the boundaries for practical application. Then, the acquired results will be compared with the results of a conventional simulation-based optimization approach under comparable time restrictions. As a next step, the general advantages and disadvantages of both approaches were analyzed. As the result, a coupling of the discrete event simulation system and an MIP solver is presented. This coupling automatically generates an MIP-formulation for the present simulation model which can be solved externally by an MIP solver. After the external optimization process follows a backward transformation of the results into the simulation system. All features of the simulation system (like Gantt-Charts, etc.) could be used to check or to illustrate these results. To perform the coupling for a wide range of simulation models, it has to be defined which general constraints the model has to satisfy.