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<p>We consider the problem of minimizing the linear cost of a multistate homogeneous series–parallel system, subject to a nonlinear reliability constraint. We propose a simple 0-1 integer linear programming (ILP) model to determine optimal solutions for the test problems presented in previous research, considering that 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 multistate system (MSS) has a finite number of performance levels varying from 0% (complete failure) to 100% (perfect function), with each level associated with a 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. The mathematical programming model has a relatively simple structure. It is implemented easily 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • M. Ouzineb,
  • I. El Hallaoui,
  • M. Gendreau

摘要

We consider the problem of minimizing the linear cost of a multistate homogeneous series–parallel system, subject to a nonlinear reliability constraint. We propose a simple 0-1 integer linear programming (ILP) model to determine optimal solutions for the test problems presented in previous research, considering that 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 multistate system (MSS) has a finite number of performance levels varying from 0% (complete failure) to 100% (perfect function), with each level associated with a 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. The mathematical programming model has a relatively simple structure. It is implemented easily 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.