This paper presents a hierarchical location and sizing problem in the presence of joint partial coverage and unreliable facilities. We consider a 3-level hierarchical production-distribution system of a supply chain n...
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This paper presents a hierarchical location and sizing problem in the presence of joint partial coverage and unreliable facilities. We consider a 3-level hierarchical production-distribution system of a supply chain network in which the lowest level facilities act as the first points of contact for customers and the upper level facilities supply the lower level facilities. For the problem, we first develop an integer non-linear program which determines the number, location, and size of two types of facilities as well as their primary and backup assignments within the network such that the weighted total demand coverage is maximized under budget constraints. Adopting a special network mapping technique, we then develop an equivalent mixed integer linear programming formulation. Next, we propose two competing piece -wise linear approximations, one based on a separable programming approach and the other on a tangent line approximation method. We finally assess the performance of the three proposed formulations via numerical experiments carried out for a variety of problem instances with different sizes under three op-timality gap settings and two linearization approximation error level alternatives. Our results show that both approximations are promising and outperform the exact formulation both in terms of computation time and solution quality. (c) 2023 Elsevier Ltd. All rights reserved.
The facility location problem (FLP) has broad applications in transportation, ranging from siting electric vehicle charging stations to positioning emergency vehicles. The spatial facility location problem (SFLP) cons...
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ISBN:
(纸本)9781467365970
The facility location problem (FLP) has broad applications in transportation, ranging from siting electric vehicle charging stations to positioning emergency vehicles. The spatial facility location problem (SFLP) considers continuous demand of a region where facilities can be placed anywhere. One of the approaches to solving the SFLP is to aggregate the demand into discrete points first and then solve the corresponding point-based FLP as a surrogate model. The model performance, however, is measured by the percentage of the continuous space actually covered. The solution to the classic FLP is often not unique. In this paper, we explore how the behavior of the solution to the FLP would affect the quality of the coverage to the spatial demand. We examine in detail the property of the surrogate model and identify the key contributing factor that would affect the quality of the solution to the original coverage problem for covering continuous spatial demand. Our goal is to find a surrogate model that is detailed enough to capture all the key elements of the problem and achieve the desired accuracy level, yet has the size that can be handled by the existing computing power.
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