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Hybrid Monte – Carlo Analytic Methods for resources optimization

By A. Dubi , Ben Gurion University

System Engineering is the science of predicting the behavior of systems over time. It was demonstrated in the past that this is an extremely complex problem resulting a need for the solution of a multi dimensional set of simultaneous integral equations. The awareness of this is slowly but clearly penetrating the industrial world and the use of the Monte Carlo Method, which is the only viable approach for the above problem, is becoming more and more acceptable. This, however, does not help much in the optimization of resources.
The complexity of System engineering problems, the need in an Integral equation for realistic industrial problems, the viability of the Monte Carlo method and the difficulty involved in approaching resource optimization problems will be discussed and explained.
A straight forward gradient search Monte Carlo optimization may require thousands or hundreds of thousands of calculations. This is impractical as each calculation may last hours of computer time. For many years it was believed that this is an insurmountable problem. A new approach was recently developed that may give hope.
The approach is based on a general relation between the system performance function and the waiting time resulting from lack of resources (Spare parts, men power or any other resource). This connection utilizes the concept of sensitivity, i.e. the "contribution of each component type to the loss of performance" – These concepts will be explained and the general nature of the functional relation will be demonstrated. A simple yet generally accurate model for the relation between the waiting time and quantities of resources will be established and an analytic general relation between the performance and resources will be obtained. This relation provides a tool for fast optimization requiring a small number of MC calculations while the parameters of the functional relation are obtained from these MC calculation. This provides, therefore a self optimizing MC mechanism. This mechanism was already realized for practical class of problems involving a single field of complex systems. This new capability will be demonstrated on a realistic problem and its extension to Multiple field cases will be discussed.