Mathematical programming formulations for approximate simulation of multistage production systems

Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This new way of representing discrete event systems paves the way to the creation of simpler mathematical programming models that reduce the complexity of the system analysis. The paper proposes an approximate representation for a class of production systems characterized by several stages, limited buffer capacities and stochastic production times. The approximation exploits the concept of a time buffer, modeled as a constraint that put into a temporal relationship the completion times of two customers in a sample path. The main advantage of the proposed formulation is that it preserves its linearity even when used for optimization and, for such a reason, it can be adopted in simulation–optimization problems to reduce the initial solution space. The approximate formulation is applied to relevant problems such as buffer capacity allocation in manufacturing systems and control parameters setting in pull systems.