Mathematical programming representation for approximate model of flow lines

Mathematical programming representation has been recently used to describe the behavior of discrete event systems as well as their formal properties. This paper proposes an approximate mathematical programming model for the simulation of flow lines with finite buffer capacities. The approximation exploits the concept of time buffer, modeled as a constraint that put into a temporal relationship the completion times of two jobs in a sample path. The system performance estimated by the approximate formulation are between two extreme values calculated from the solution of a linear programming model. When the linear model is coupled with a buffer optimization model, the extreme values represent the upper and lower bounds containing the optimal solution. The main advantage of the proposed formulation is that it preserves its linearity even when used for buffer optimization.