Simulation and optimization of continuous-flow production systems with a finite buffer by using mathematical programming

We present a mathematical programming approach for simulation and optimization of a general continuous-flow production system with an intermediate finite buffer. In this system, each station is represented with a discrete state space–continuous time process with given transition time distributions between the states and a set of flow rates associated with each discrete state. We develop a mathematical programming formulation to determine the critical time instances of the sample trajectory of the buffer that correspond to state transitions, buffer dynamics, and changing flow rates. We show that a simulated sample realization of the system is obtained by solving a mixed-integer linear program. The mathematical programming representation is also used to show that the production rate is a monotonically increasing function of the buffer capacity. We analyze the buffer capacity determination problem with the objective of determining the minimum buffer capacity that achieves a desired production rate and also with the objective of maximizing the profit. It is shown that the computational performance depends on the rates of change among system states and not on the number of states at each stage and on the buffer capacity. Our numerical results show a significant computational improvement compared with using a discrete-event simulation. As a result, the mathematical programming approach is proposed as a viable alternative method for performance evaluation and optimization of continuous-flow systems with a finite buffer.