Closed-loops systems have been analyzed by means of Markov theory, discrete event simulation models, renewal theory and random walks. The dynamics of discrete event systems (DES) has been recently addressed with the mathematical programming technique. In particular, DESs are mapped into a mixed integer linear programming (MILP) formulation, the optimal solution of which represents the trajectory of the DES itself, i.e., the output of a standard simulation. This paper proposes approximate linear programming–based models to simulate and optimize the closed–loop system behavior. The approximation has been obtained by relaxing the constraints that keep the number of parts circulating in the system constant. In the relaxed model,
the fixed population aspect, which characterizes the system, is indirectly modeled by means of continuous time variables that limit the entering (leaving) of parts into (from) the system. The main advantage of the proposed approximate simulation model is that it preserves its linearity even when used for optimization.
Numerical experiments show the accuracy of the proposed models for the optimal pallet allocation problem
