Modelling and analysis of uncertain hub maximal covering location problem in the presence of partial coverage

Abstract

The hub maximal covering location problem aims to find the best locations for hubs so as to maximize the total flows covered by predetermined number of hubs. Generally, this problem is defined in the framework of binary coverage. However, there are many real-life cases in which the binary coverage assumption may yield unexpected decisions. Thus, the partial coverage is considered by stipulating that the coverage of an origin-destination pair is determined by a non-increasing decay function. Moreover, as this problem contains strategic decisions in long range, the precise information about the parameters such as travel times may not be obtained in advance. Therefore, we present uncertain hub maximal covering location models with partial coverage in which the travel times are depicted as uncertain variables. Specifically, the partial coverage parameter is introduced in uncertain environment and the expected value of partial coverage parameter is further derived and simplified with specific decay functions. Expected value model and chance constrained programming model are respectively proposed and transformed to their deterministic equivalent forms. Finally, a greedy variable neighborhood search heuristic is presented and the efficiency of the proposed models is evaluated through computational experiments.