An exact approach for the redundancy allocation problem of homogeneous series-parallel multistate systems

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This paper develops an exact method for the redundancy allocation problem (RAP) for multistate homogeneous series-parallel systems. The problem aims to minimize the linear cost given the nonlinear reliability constraint on the system. We propose a simple 0-1 integer linear programming model and find optimal solutions for the test problems presented in previous research. The system has a finite number of performance levels varying from 0% (complete failure) to 100% (perfect function). Each level has a corresponding state probability. The system reliability is calculated using the universal generating function technique. Because of the complex nature of the problem, it is often solved by heuristics. By using an exact method, we are able to validate the solutions found by heuristics. Moreover, our method solves reasonable instances from the literature in just a few milliseconds.

, 19 pages

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