On Optimization of Dynamical Material Flow Systems Using Simulation

Up until now risk analysis, as a rule, ended with the estimation of the risks. Further improvements -- optimal design, risk control, dynamic risk management -- require many more efforts. Essential difficulties are connected with the discontinuous or nonsmooth behavior of performance functions with respect to the control and (or) random parameters due to possible failures of the system's parts. Usually, the systems also include discrete event elements -- logical rules can change the structure of the system if some constraints are not satisfied, for example safety constraints. These problems require new formal analysis tools which will include dynamics, stochastics, nonsmoothness and discontinuity.
In this paper, the authors consider a simple example of such a problem with the aim to explore the possibilities for its analysis. The problem is comprised of optimizing a material flow system based on an efficient use of simulation. The material flow system may be a production system, a distribution system or a pollutant-deposit/removal system. The important characteristic which is considered in this paper is that one of the components of the dynamic system is unreliable. This characteristic leads to simulation models in which criteria are discontinuous with respect to the optimization parameters. This makes it difficult to use the standard methods for the estimation of gradients of the expected criteria values. A method is introduced which overcomes the difficulty. From a formal point of view the problem can be viewed as a mixed integer stochastic optimization problem.

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