Title: Fuzzy multi-objective linear programming for a stochastic hub maximal covering problem with uncertain shipments

Authors: Amir Ebrahimi Zade; Ahmad Sadegheih; Mohammad Mehdi Lotfi

Addresses: Department of Industrial Engineering, College of Engineering, Yazd University, P.O. Box 89195-741, Yazd, Iran ' Department of Industrial Engineering, College of Engineering, Yazd University, P.O. Box 89195-741, Yazd, Iran ' Department of Industrial Engineering, College of Engineering, Yazd University, P.O. Box 89195-741, Yazd, Iran

Abstract: When there are many origins and destinations in a network, the use of hubs helps to benefit from the economies of scale in transportation and considerable reduction in the number of required links. We propose a bi-objective mathematical model for a stochastic hub maximal covering problem formulated under two real-world assumptions. In many networks, there are some risks for the shipments among the nodes. In order to consider such risks, a second objective, in addition to maximising the utility of covered nodes, is aimed at maximising the safety of weakest path in the network. Also, similar to the real world situation, it is assumed that the transport times are normal random variables. An efficient nonlinear mixed-integer model is developed and after linearising, a fuzzy multi-objective linear programming method is applied to solve it. Notably, the single objective version of our model has smaller number of variables and equations than the previous ones. The computational results by establishing 24 test problems extracted from the Turkish dataset confirm: 1) the validity of proposed formulations for single objective hub maximal covering problem; 2) the satisfying performance of proposed bi-objective model in improving the safety of designed network.

Keywords: mathematical modelling; hub maximal covering problem; HMCP; safety; stochastic transport time; chance constraints; fuzzy multi-objective linear programming; fuzzy logic; uncertain shipments; uncertainty; network design.

DOI: 10.1504/IJISE.2016.077699

International Journal of Industrial and Systems Engineering, 2016 Vol.23 No.4, pp.482 - 499

Received: 18 Mar 2014
Accepted: 25 Oct 2014
Published online: 13 Jul 2016 *

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