Robust cold standby redundancy allocation for nonrepairable series–parallel systems through Min-Max regret formulation and Benders’ decomposition method

This article deals with a redundancy allocation problem in series–parallel systems with a cold standby strategy, in which component time to failure follows an exponential distribution that has constant hazard rate. Examples of this kind of system are systems composed of electronic components (e.g. transistors, capacitors, resistors and integrated circuits) used in control systems, power generators and the like, which needs to be supported by standby components to prevent unexpected failures. In this article, the reliability of each component is imprecise in terms of interval data, and only the lower and upper bounds of reliabilities are known. The problem is formulated through Min-Max regret criterion, which is commonly used to define robust solutions. The resulted problem formulation contains unlimited numbers of constraints, and Benders’ decomposition method is implemented to deal with the given problem. This method is compared with an enumeration method and a stochastic search method called genetic algorithm to show its effectiveness. The results show that the proposed Benders’ decomposition method is conducive to the same results in a reasonable amount of time. The performance of the proposed model using Benders’ decomposition method is also examined over different problem sizes, and the associated results are analyzed. The results show that for large-sized problems, Benders’ decomposition method is converged with fewer numbers of cuts, and therefore, it is time-economic for solving such problems.