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Top2. Literature Review
In the last two decades, many researchers have investigated hub location problems; however, reliable hub location under uncertain environment is discussed newly and it is advanced field. In this section at first, the researches about classical and original hub location problems are reviewed. Then, we review in brief some related works to this paper, specifically those considering uncertainty and reliability. Furthermore, we review the researches about reliable hub location problem under uncertainty.
The first mathematical model in HLP was introduced by O’Kelly (1987). He presented a quadratic integer programming whose objective is to minimize the total delivery cost between nodes and locating a pre-specified number of hubs. The interested reader could review the papers by Campbell and O’Kelly (2012) and Farahani et al. (2013) to read full survey of hub location problems and its subcategories.
Hub covering and p-hub center problems are two new hub location problems proposed by Campbell (1994). Then, different formulation for the p-hub center problem was represented by Kara and Tansel (2000) and Ernst et al. (2009). In the p-hub center problem the main issue is time, which is mostly considered in cargo delivering systems.