Sample average approximation applied to the capacitated-facilities location problem with unreliable facilities

Gade, Dinakar; Pohl, Edward A.

doi:10.1243/1748006xjrr246

Cited by 14 publications

(10 citation statements)

References 24 publications

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“…The SAA approximates the true optimal value by solving generated samples of stochastic parameters, and it is used in the reliable facility location problem with a large number of scenarios (Gade and Pohl 2009;Shen et al 2011;Aydin and Murat 2013). The steps of SAA procedure are as follows (Kleywegt et al 2001).…”

Section: Sample Average Approximationmentioning

confidence: 99%

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

Yahyaei

Bashiri

2017

J Ind Eng Int

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The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of scenarios grows exponentially with the number of facilities. To alleviate this issue, two approaches are applied simultaneously. The first approach is to apply sample average approximation to approximate the two stochastic problem via sampling. Then, by applying the multiple cuts Benders decomposition approach, computational performance is enhanced. Numerical studies show the effective performance of the SAA in terms of optimality gap for small problem instances with numerous scenarios. Moreover, performance of multi-cut Benders decomposition is assessed through comparison with the classic version and the computational results reveal the superiority of the multi-cut approach regarding the computational time and number of iterations.

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Section: Sample Average Approximationmentioning

confidence: 99%

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

Yahyaei

Bashiri

2017

J Ind Eng Int

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“…Equation (17) fixes the number of facilities to establish, and equation (18) forces the dummy facility used to model balking to be among them. Constraints (19) and (20) ensure that if a customer goes to a failing facility at a given level r < p, it leaves that facility in the next level.…”

Section: A Binary Formulation For the Homogeneous Casementioning

confidence: 99%

“…For instance, problems with correlated failures are studied in Berman et al [11] and Li et al [23], problems with capacitated facilities in Gade and Pohl [17] and Aydin and Murat [5], and the possibility of installing non-failing facilities at a larger cost has also been explored (e.g. Lim et al [26]).…”

Section: Introductionmentioning

confidence: 99%

“…Constraints (28) and (29) are equivalent to (17) and (18) in formulation F2 of the RpMF; they set the number of facilities to open and force the dummy facility representing the loss of a customer being one of them. Constraints (30) are flow conservation constraints at nodes in F. If no facility is settled at location j ∈ F , the whole demand h j must leave node j, otherwise, the expected flow leaving node j is equal to the probability that j fails times the flow at j, which is equal to the entering flow, plus the demand at j. Analogous constraints for nodes in NF are given by equations (31).…”

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confidence: 99%

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The reliable p -median problem with at-facility service

Albareda-Sambola

Hinojosa

Puerto

2015

European Journal of Operational Research

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This paper deals with a discrete facility location model where service is provided at the facility sites. It is assumed that facilities can fail and customers do not have information on failures before reaching them. As a consequence, they may need to visit more than one facility, following an optimized search scheme, in order to get service. The goal of the problem is to locate p facilities in order to minimize the expected total travel cost. The paper presents two alternative mathematical programming formulations for this problem and proposes a matheuristic based on a network flow model to provide solutions to it. The computational burden of the presented formulations is tested and compared on a test-bed of instances.

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“…They also provide a concise and well-described explanation of the value of considering risk and reliability in a supply chain network design. Similarly, Gade and Pohl [4] consider a capacitated facility location problem with unreliable facilities and redundant facility *Corresponding author: Bell Engineering, Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA. email: epohl@uark.edu locations and provide solution approaches for such systems using a sample average approximation algorithm.…”

Section: Introductionmentioning

confidence: 99%

Modelling and analysis of risk and reliability for a contingency logistics supply chain

Miman

Pohl

2008

Proceedings of the Institution of Mechanical Engineers, Part O:

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Contingency logistic supply chain design and performance are very important for rare events such as natural disasters, terrorist attacks, and other emergency conditions. Although there is ample work on the evaluation of supply chain systems in terms of their profitability and efficiency, there is little work on the effectiveness of the response time of the supply chain, as well as quantitative measures for the robustness of the design and the reliability of the supply chain. Depending on the contingency, the perceived risk may be different for different situations. The level of risk aversion is dependent on the decision maker and the uncertainties associated with the supply and demand for the contingency. In this study the risk associated with shortages due to the uncertainties in supply and demand in the supply chain are modelled using distortion. In addition, a numerical analysis is performed and the sensitivity of the parameters in a contingency logistic supply chain is analysed. Methods to improve the effectiveness of the contingency operation are examined by efficiently allocating available resources, supplies, and time, as well as modelling the decision maker's perception associated with the failure of a particular node. An array of optimization models are formulated and discussed. Each of these models enables a decision maker to examine a variety of trade-offs in a contingency logistics supply chain. For example, one model examines the acquisition of mitigation strategies and the reallocation of resources while taking into consideration the decision maker's risk aversion. The main contribution of this paper is the establishment of an analysis framework for modelling and analysing the risk and reliability of contingency logistic supply chains.

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Sample average approximation applied to the capacitated-facilities location problem with unreliable facilities

Cited by 14 publications

References 24 publications

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

The reliable p -median problem with at-facility service

Modelling and analysis of risk and reliability for a contingency logistics supply chain

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