### G-2023-32

# Integer linear programming for a constant demand in redundancy allocation multistate series-parallel problem

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We consider the problem of minimizing the linear cost of multistate homogeneous series-parallel system 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 considering a constant demand corresponds to the maximum demand in the study period. The decision variables are the number of components in each subsystem, and the choice of components. 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. The mathematical programming model has a relatively simple structure. It is implemented immediately with the help of a mathematical programming language and an integer linear programming software. Moreover, our method solves reasonable instances from the literature in just a few milliseconds.

Published **August 2023**
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16 pages

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**G2332.pdf**
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