Single allocation hub location problem considering zero-one uncertain demands

Hubs are special facilities used as switching, transferring, and sorting points in many distribution systems. Instead of serving each origin-destination pair directly, the hub facility concentrates flow to take advantage of the resulting economic savings. Flows from the same source combine with different destinations on their path to a hub and combine with flows that have different sources but have the same destination. The accumulation of flows takes place in the path from the origin to the hub and from the hub to the destination, as well as between the hubs. These types of systems, commonly known as hub-and-spoke, are studied in the form of hub location problems. In this paper, we develop the single allocation hub location problem with uncertain zero-one demands, in which the amount of demand between each origin-destination pair is considered as a Bernoulli random variable with a definite probability p. Due to the fact that this problem has not been studied in the literature so far, a new mathematical model of mixed integer programming type is developed for the problem and is solved using GAMS software. Also, the results of solving different test problems from the CAB data set are examined and the effect of different parameters on the optimal solution of the problem is examined.