Multistate series-parallel system expansion-scheduling subject to availability constraints

This paper addresses the multistage expansion problem for multistate series-parallel systems. The study period is divided into several stages. At each stage the demand distribution is predicted in the form of a cumulative demand curve. The additional elements chosen from a list of available products can be included into any system-component at any stage to increase the total system capacity and/or reliability. Each element is characterized by its capacity (productivity), availability, and cost. The objective is to minimize the sum of costs of the investments over the study period while satisfying reliability constraints at each stage. To solve the problem, a genetic algorithm is used as an optimization tool. The solution encoding technique allows the genetic algorithm to manipulate integer strings representing multistage expansion planes. A solution quality index comprises both reliability and cost estimations. The procedure based on the universal generating function is used for evaluating the availability of multistate series-parallel systems. An example illustrates finding the optimal expansion plan for a coal-transportation system of a power station.