A multi-objective robust optimization model for the capacitated P-hub location problem under uncertainty

Ahmad Makui,Ahmad Nikui,Ehsan Jahani,Mohammad Rostami

doi:10.5267/j.msl.2011.12.014

Ahmad Makui, Ahmad Nikui + Show 2 more

Open Access

https://doi.org/10.5267/j.msl.2011.12.014

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Abstract

Uncertainty plays an important role on many engineering problems and there is a growing interest in having reliable solutions especially for problems with sensitive parameters. The paper presents a robust optimization (RO) model for multi-objective operation of capacitated P-hub location problems (MCpHLP) under uncertainty set. There are, at least, two parameters in any P-hub problems, which are under uncertainty. The first one is associated with demand and the second one is the amount of time required to process commodities. We present a scenario based robust optimization technique, where these two items are considered under various scenario and a RO is implemented to find reliable solutions. The implementation of the proposed RO model is demonstrated for an example using weighting method.

Highlights

Hubs are special facilities that are serving as switching in transportation and multistage distribution systems
We present a scenario based robust optimization technique, where these two items are considered under various scenario and a RO is implemented to find reliable solutions
Louveaux (1986) reviewed existed uncertain location problems models where all the facility location problems were considered in the first step of decision-making and distribution pattern was regarded as the second step

Summary

Introduction

Hubs are special facilities that are serving as switching in transportation and multistage distribution systems. O'kelly (1987) presented the first recognized mathematical formulation for a hub location problem by studying an airline passenger networks. His formulation was considered with the single allocation p-median allocation problem. The first article addressed the hub location under uncertainty was presented by (Marianov & Serra, 2003) He used the M/D/c queuing models with a capacity constraint for a plane on landing. To the best of our knowledge, among studies conducted on robust optimization hub location problems, there is only one paper has been published. Huang Jia (2009) presented a robust model for hub location to minimize sum of transportation costs without considering capacity constraints and the resulted problem was solved by multi-objective genetic algorithm.

Robust optimization

Modeling

Solution Process

Experiment

Conclusion