A chance constrained programming approach for uncertain p-hub center location problem

•We first investigate the p-hub center problem with subjective imprecision.•We formulate a chance constrained programming model for uncertain p-hub center location problem.•We give the analytical forms of the proposed model base on uncertainty theory.•We present principle of nearby and design a hybrid intelligent algorithm to solve the uncertain p-hub center models.

The p-hub center location problem aims to locate p hubs and allocate other nodes to these hub nodes in order to minimize the maximal travel time. It is more important for time-sensitive distribution systems. Due to the presence of uncertainty, more researches are recently focused on the problem in non-deterministic environment. This paper joins the research stream by considering travel times as uncertain variables instead of random variables or fuzzy ones. The goal is to model the p-hub center problem based on experts' subjective belief in the case of lack of data. The uncertain distribution of the maximal travel time is first derived and then a chance constrained programming model is formulated. The deterministic equivalent forms are further given when the information of uncertainty distributions is provided. A hybrid intelligent algorithm is designed to solve the proposed models and numerical examples are presented to illustrate the application of this approach and the effectiveness of the algorithm.