A robust optimization model for p-median problem with uncertain edge lengths

Nikoofal, Mohammad E.; Sadjadi, Seyed Jafar

doi:10.1007/s00170-009-2503-z

Cited by 19 publications

(14 citation statements)

References 31 publications

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“…The goal is to maximize the overall profit. Nikoofal and Sadjadi (2010) avoid the most conservative solutions arising from considering box uncertainty by imposing a maximum total scaled variation for the uncertainty parameters. The authors address a p-median problem with interval uncertainty associated with the distances (or travel times).…”

Section: Robust Facility Location Problemsmentioning

confidence: 99%

Facility Location Under Uncertainty

Correia

Saldanha-da-Gama²

2015

Location Science

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In this chapter, we cover some essential knowledge on facility location under uncertainty. We put a major emphasis on modeling aspects related with discrete facility location problems. Different modeling frameworks are discussed. In particular, we distinguish between robust optimization, stochastic programming and chance-constrained models. We also discuss relevant aspects such as solution techniques, multi-stage stochastic programming models, scenario generation, and extensions of basic problems.

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Section: Robust Facility Location Problemsmentioning

confidence: 99%

Facility Location Under Uncertainty

Correia

Saldanha-da-Gama²

2015

Location Science

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“…Nikoofal and Sadjadi [13] used Bertimas and Sim's approach [5] to propose the robust model of the median hub location problem with uncertain travel cost. Taking advantage of Bertsimas and Sim's approach [5], Ghaffari-Nasab et al [14] proposed a robust model for the capacitated hub location problem (single allocationmultiple allocation) in which the demand change was uncertain.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Constraint (13) guarantees that for each origin and destination , only variables related to airports in set "′ can be non-zero, and the remaining variables are equal to zero. = 0∀ ∈ , ∈ ; ∀ = 1,2; ∈ − "′…”

Section: Constraintsmentioning

confidence: 99%

Development of a Model for Locating Hubs in a Competitive Environment under Uncertainty: A Robust Optimization Approach

Nourzadeh

Ebrahimnejad

Khalili‐Damghani

et al. 2020

IJE

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This article explores the development of previous models to determine hubs in a competitive environment. In this paper, by comparing parameters of the ticket price, travel time and the service quality of hub airports, airline hubs are divided into six categories. The degree of importance of travel time and travel cost are determined by a multivariate Lagrange interpolation method, which can play an important role in allocating travelers to follower airline hubs. Then, based on the seasonal demand of travelers, we consider travel demand as uncertain parameters. To determine the robust counterpart of this category of hub location models, a robust optimization method is used. Finally, models are tested in a case study. The central results show that the follower airline's income has a considerable growth and can absorb nearly 2% of travelers of the leader airline due to lower travel costs and travel time compared to that of leader airline.

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“…Baron et al [24] apply RO to the facility location problem by modeling demand uncertainty as box and ellipsoid in the fixed-charge problem. Nikoofal and Sadjadi [25] propose a robust p-median model with edge length uncertainty using an "uncertainty budget" to limit the total scaled variation of the uncertainty parameters. Lu and Sheu [26] present a robust vertex p-center model for locating urgent relief centers.…”

Section: Literature Reviewmentioning

confidence: 99%

A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

Zhou

2018

Symmetry

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In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

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A robust optimization model for p-median problem with uncertain edge lengths

Cited by 19 publications

References 31 publications

Facility Location Under Uncertainty

Facility Location Under Uncertainty

Development of a Model for Locating Hubs in a Competitive Environment under Uncertainty: A Robust Optimization Approach

A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

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