Mathematical programming representations of the dynamics of continuous-flow production systems

Abstract

This study presents a mathematical programming representation of discrete-event systems with a continuous time and mixed continuous-discrete state space. In particular, continuous material flow production systems are considered. A mathematical programming representation is used to generate simulated sample realizations of the system and also to optimize control parameters. The mathematical programming approach has been used in the literature for performance evaluation and optimization of discrete material flow production systems. In order to show the applicability of the same approach to continuous material flow systems, this article focuses on optimal production flow rate control problems for a continuous material flow system with an unreliable station and deterministic demand. These problems exhibit most of the dynamics observed in various continuous flow productions systems: flow dynamics, machine failures and repairs, changing flow rates due to system status, and control. Moreover, these problems include decision variables related to the control policies and different objective functions. By analyzing the backlog, lost sales, and production and subcontracting rate control problems, it is shown that a mixed-integer linear programming formulation with a linear objective function and linear constraints can be developed to determine the simulated performance of the system. The optimal value of the control policy that optimizes an objective function that includes the estimated expected inventory carrying and backlog cost and also the revenue through sales can also be determined by solving a quadratic integer program with a quadratic objective function and linear constraints. As a result, it is shown that the mathematical programming representation is also a viable method for performance evaluation and optimization of continuous material production systems.