Simulation optimization with mathematical programming representation of discrete event systems

Optimization-via-simulation consists in applying iteratively two detached models until an optimality condition is reached: a simulation model for predicting the system performance, and a model for generating potential optimal solutions. Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This paper proposes explicit mathematical programming representations for jointly simulating and optimizing discrete event systems. The main advantage of such models is the rapidity of searching for the optimal solution, given to the explicit knowledge of objective function and constraints. Three types of formulations are proposed for solving the buffer allocation problem in flow lines with finite buffer capacities: an exact mixed integer linear model, an approximate LP model and a stochastic programming model. Numerical analysis shows that the computational time required to solve resource allocation problems can be significantly reduced by using the proposed formulations.