A bi-objective hub maximal covering location problem considering time-dependent reliability and the second type of coverage

Abstract

The hub location problem seeks to find the best location for hubs and the assignment of non-hub nodes to hubs. The hub location problem appears in a variety of applications including airline systems, cargo delivery systems, and telecommunication network design. In this paper, a bi-objective hub maximal covering location problem is presented considering time-dependent reliabilities. The two objective functions are: (i) maximizing the weighted network reliability and (ii) maximizing the total flow in a hub network, where the type of coverage used for locating is the second type. Additionally, the transportation cost between each pair of nodes is assumed to be an uncertain parameter. Chance constrained programming is employed to formulate the bi-objective problem. The model is transformed into a single-objective model using the goal attainment method – a technique in multi-objective decision making procedures. As the problem belongs to the class of NP-hard problems, a genetic algorithm is developed to solve it. Since there is no benchmark available in the literature, a simulated annealing algorithm is developed as well in order to validate the results obtained. The response surface methodology is utilized to tune the parameters of both algorithms in order to find better solutions. Some numerical examples are presented to investigate the efficiency of the proposed algorithms. Finally, the results obtained using the two algorithms are compared by the technique for order preference by similarity to the ideal solution.

Keywords:

• Hub maximal covering
• time-dependent reliability
• chance constraint
• genetic algorithm
• simulated annealing
• response surface methodology

JEL Classification:

• C610

Acknowledgements

The authors are thankful for the constructive comments of anonymous reviewers. Taking care of the comments certainly improved the presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.