Facility Location Under Uncertainty

Correia, Isabel; Saldanha-da-Gama, Francisco

doi:10.1007/978-3-030-32177-2_8

Cited by 32 publications

(24 citation statements)

References 85 publications

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“…Some temporally extended models of the FLP have also been developed: The dynamic facility location problem (DFLP) deals with fluctuating demands [20,21], and some studies have examined FLPs in which factors other than demand behave in a stochastic manner [22,23]. The multi-stage uncapacitated facility location problem (MSUFLP) was formulated as a model that studies routes that pass through multiple facilities [18].…”

Section: Facility Location Problemmentioning

confidence: 99%

Evacuation Shelter Scheduling Problem

Shimizu¹,

Suwa²,

Iwata³

et al. 2022

Proceedings of the Annual Hawaii International Conference on System Sciences

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Evacuation shelters, which are urgently required during natural disasters, are designed to minimize the burden of evacuation on human survivors. However, the larger the scale of the disaster, the more costly it becomes to operate shelters. When the number of evacuees decreases, the operation costs can be reduced by moving the remaining evacuees to other shelters and closing shelters as quickly as possible. On the other hand, relocation between shelters imposes a huge emotional burden on evacuees.In this study, we formulate the "Evacuation Shelter Scheduling Problem," which allocates evacuees to shelters in such a way to minimize the movement costs of the evacuees and the operation costs of the shelters. Since it is difficult to solve this quadratic programming problem directly, we show its transformation into a 0-1 integer programming problem. In addition, such a formulation struggles to calculate the burden of relocating them from historical data because no payments are actually made. To solve this issue, we propose a method that estimates movement costs based on the numbers of evacuees and shelters during an actual disaster. Simulation experiments with records from the Kobe earthquake (Great Hanshin-Awaji Earthquake) showed that our proposed method reduced operation costs by 33.7 million dollars: 32%.

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Section: Facility Location Problemmentioning

confidence: 99%

Evacuation Shelter Scheduling Problem

Shimizu¹,

Suwa²,

Iwata³

et al. 2022

Proceedings of the Annual Hawaii International Conference on System Sciences

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“…The integration of probabilistic programming ( Charnes & Cooper, 1959;Prékopa, 1995 ) with Location Analysis has its roots in the seminal paper by ReVelle and Hogan (1989) focusing the location of emergency facilities see ( Birge & Louveaux, 2011;Correia & Saldanha-da-Gama, 2015;Snyder, 2006 ). In fact, like in that work, most of the related literature emerges from the need to locate emergency facilities.…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling the shelter site location problem using chance constraints: A case study for Istanbul

Kınay

Kara

Saldanha-da-Gama

et al. 2018

European Journal of Operational Research

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In this work, we develop and test a new modeling framework for the shelter site location problem under demand uncertainty. In particular, we propose a maxmin probabilistic programming model that includes two types of probabilistic constraints: one concerning the utilization rate of the selected shelters and the other concerning the capacity of those shelters. By invoking the central limit theorem we are able to obtain an optimization model with a single set of non-linear constraints which, nonetheless, can be approximated using a family of piecewise linear functions. The latter, in turn, can be modeled mathematically using integer variables. Eventually, an approximate model is obtained, which is a mixed-integer linear programming model that can be tackled by an off-the-shelf solver. Using the proposed reformulation we are able to solve instances of the problem using data associated with the Kartal district in Istanbul, Turkey. We also consider a large-scale instance of the problem by making use of data for the whole Anatolian side of Istanbul. The results obtained are presented and discussed in the paper. They provide clear evidence that capturing uncertainty in the shelter site location problem by means of probabilistic constraints may lead to solutions that are much different from those obtained when a deterministic counterpart is considered. Furthermore, it is possible to observe that the probabilities embedded in the probabilistic constraints have a clear influence in the results, thus supporting the statement that a probabilistic programming modeling framework, if appropriately tuned by a decision maker, can make a full difference when it comes to find good solutions for the problem.

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“…In another set of facility location problems, the uncertainty is in the customer demands. Correia and Saldanha da Gama survey facility location under demand uncertainty. They first discuss the stochastic uncapacitated facility location problem, then review the stochastic capacitated facility location problem including chance‐constrained variants.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The SUFL problem can be viewed as a special case of the SConFL problem without the requirement that open facilities have to be connected. Correia and Saldanha da Gama state the SUFL problem and provide a deterministic equivalent formulation which we arrive at from Formulation (19) by eliminating the

y_{i j}

variables.…”

Section: Computational Experimentsmentioning

confidence: 99%

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An inexact sample average approximation approach for the stochastic connected facility location problem

Bardossy

Raghavan

2017

Networks

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The sample average approximation (SAA) approach is a widely used technique, based on Monte‐Carlo simulation, often applied to large‐scale stochastic optimization problems. In this approach, a set of sample average problems with multiple copies of sampled scenarios are generated and solved exactly. In other words, there is an implicit assumption that the sample average problems are solvable to optimality. In some instances, however, the sample average problems might be NP‐hard problems, often difficult or impractical to solve to optimality. In this article, we broaden the scope of the SAA approach and show that even without solving the sample problems to optimality, by combining a heuristic and a lower bounding approach, high‐quality solutions with tight confidence bounds on the optimal solution value can be obtained. We demonstrate this “inexact SAA approach” on two problems. First, we apply it to the Stochastic Connected Facility Location (SConFL) problem, the motivating application for this article, that arises in the design of telecommunications networks. As an additional application, we also use it for the Stochastic Uncapacitated Facility Location (SUFL) problem. Our computational results demonstrate the effectiveness of the inexact SAA approach. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 19–33 2017

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Facility Location Under Uncertainty

Cited by 32 publications

References 85 publications

Evacuation Shelter Scheduling Problem

Evacuation Shelter Scheduling Problem

Modeling the shelter site location problem using chance constraints: A case study for Istanbul

An inexact sample average approximation approach for the stochastic connected facility location problem

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