Risk‐Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty

This paper considers a new risk‐control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculated without assuming a specific random distribution. In order to develop the risk control approach, a confidence interval‐based formulation is introduced. Using this interval, as well as minimizing the maximum value of worse edge costs, maximizing the minimum value of robust parameters to edge costs is introduced as objective functions in the risk‐control. Furthermore, in order to maintain the constructing spanning tree network entirely, the reliability for each edge is introduced, and maximizing the total reliability of spanning tree is assumed as the third objective function. The proposed model is a multiobjective programming problem, and hence, it is difficult to solve it directly without setting some optimal criterion. Therefore, satisfaction functions for each object and the integrated function are introduced, and the exact solution algorithm is developed by performing deterministic equivalent transformations. A numerical example is provided by comparing our proposed model with previous standard models.