Minmax regret maximal covering location problems with edge demands

Baldomero-Naranjo, Marta; Kalcsics, Jörg; Rodríguez‐Chía, Antonio M.

doi:10.1016/j.cor.2020.105181

Cited by 15 publications

(8 citation statements)

References 44 publications

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“…More recently, Berman et al (2016) investigated two covering location problems on a network with edge-based demands, the first being the maximal covering location problem and the second being the obnoxious version in which the coverage is to be minimized. Baldomero-Naranjo et al (2021) considered the single-facility maximal covering location problem in which the demands are distributed along edges and are uncertain with only a known interval estimation; they proposed a minmax-regret maximal covering location problem and developed algorithms for finding the location that minimizes the maximal regret assuming special types of demand realization. One of the main differences between our model and those above is that ours addresses the situation in which both the origins and destinations of trips are distributed continuously along edges of the network, whereas in the above location models only the trip origins are distributed continuously, with the destinations being facilities given by a discrete set.…”

Section: Analytical Methods For Deriving Distance Distributions In Co...mentioning

confidence: 99%

Analytical method for deriving distance distributions in continuous networks in which travelers visit exactly one facility between origin and destination

Tanaka

Tanno

2022

JAMDSM

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In this paper, a method is developed for evaluating the locations of facilities in a network in which users visit exactly one facility on their way from origin to destination, such as the daily commute to work. The focus is on a continuous network in which the origins and destinations of trips are distributed uniformly and independently along edges of the network, and an analytical method is proposed for deriving the distance distributions. It is assumed that every traveler selects a route that minimizes the sum of the distance from origin to facility and the distance from facility to destination. Compared to a single summary index such as average distance, distance distributions contain rich information about the overall accessibility of facilities and so are useful for analyzing actual facility configurations and evaluating several planning alternatives. The proposed method can also be used to evaluate solutions obtained from facility location models that assume demands represented as flows traveling over a network. For the case of only one facility, a method is presented that uses an extended shortest-path tree rooted at the facility node. For the case of two or more facilities, an existing method is extended to obtain the shortest travel-length distribution in a continuous network in the case in which travelers visit exactly one facility on their way from origin to destination. By applying the proposed framework to an actual road network, it is found that the shapes of distributions differ greatly depending on the location of facilities and hence they are much more useful compared to using a single index such as the average distance.

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Section: Analytical Methods For Deriving Distance Distributions In Co...mentioning

confidence: 99%

Analytical method for deriving distance distributions in continuous networks in which travelers visit exactly one facility between origin and destination

Tanaka

Tanno

2022

JAMDSM

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“…Blanquero et al [26] studied the MCLP with regional demand on a network, in which demand is continuously distributed along the edge and the locations of p facilities are along the edges of a network. Baldomero-Naranjo et al [11] studied the single-facility minmax regret maximal covering location problem with demand distributed along the edges. Baldomero-Naranjo et al [13] further conducted another study on the upgrading version of the maximal covering location problem with edge length modifications on networks, by assuming that the length of the edges can be reduced at a cost.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Based on the present consideration, this location problem can be defined as the Edge Covering Location Problem (ECLP). The ECLP can be further subdivided into the Edge Set Location Covering Problem (ESCP) and the Edge Maximal Covering Location Problem (EMCLP) [10][11][12]. For the ESCP, its objective function is to minimize the construction costs or the number of facilities with the constraint that the entire demand must be totally covered [10,13].…”

Section: Introductionmentioning

confidence: 99%

Location of Railway Emergency Rescue Spots Based on a Near-Full Covering Problem: From a Perspective of Diverse Scenarios

Wang

Zhou

2023

Sustainability

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The location of railway emergency rescue spots is facing diverse scenarios including the location of new facilities and optimization of existing layouts with limited or non-limited conditions. Generally there will be heavily redundant covering ability if all the edge demands on a network are fully covered. Here, we first proposed a near-full covering model to balance investment in the facility and the actual coverage rate, and successfully applied this model in the optimal location of railway emergency rescue spots under diverse scenarios. We also developed a feasible solution that can select an effective algorithm or a greedy algorithm based on the total consumed time. With the constraint of a fixed coverage rate threshold, a larger coverage radius may lead to fewer facilities and higher relative redundancy. Flexible designs of the important node set where all the elements must be selected and the exclusive node set where all the elements cannot be selected are carried out to construct several scenarios. The comparative analysis shows that the optimal solution is an obvious improvement on the existing emergency rescue spot layout in the real railway network. This study provides an alternative version of the edge covering problem, and shows a successful application in the location problem of railway rescue spots.

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“…However, this assumption corresponds to ideal but usually unrealistic scenarios (the reader is referred to the examples of real applications of the above paragraph). Some works addressing network covering with continuous sets of both candidate locations and demand points are [12,13,14], for maximal covering, and [15,16,17], for set-covering. We focus on the latter variant, which we call the continuous set-covering problem.…”

Section: Introductionmentioning

confidence: 99%

Continuous Covering on Networks: Improved Mixed Integer Programming Formulations

Xu¹

2022

Preprint

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Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this work, we study the set-covering location problem when both candidate locations and demand points are continuous sets on a network. This variant has received little attention, and the scarce existing approaches have focused on particular cases, such as tree networks and integer covering radius. Here we study the general problem and present a Mixed Integer Linear Programming formulation (MILP) for networks with edges' lengths no greater than the covering radius. The model does not lose generality, as any edge not satisfying this condition can be partitioned into subedges of appropriate lengths without changing the problem. We propose a preprocessing algorithm to reduce the size of the MILP, and devise tight big-M constants and valid inequalities to strengthen our formulations.Moreover, a second MILP is proposed, which admits edges' lengths greater than the covering radius. As opposed to existing formulations of the problem (including the first MILP proposed herein), the number of variables and constraints of this second model does not depend on the lengths of the network's edges. This second model represents a scalable approach that particularly suits real-world networks, whose edges are usually greater than the covering radius. Our computational experiments show the strengths and limitations of our exact approach on both real-world and random networks. Our formulations are also tested against an existing exact method.

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Minmax regret maximal covering location problems with edge demands

Cited by 15 publications

References 44 publications

Analytical method for deriving distance distributions in continuous networks in which travelers visit exactly one facility between origin and destination

Analytical method for deriving distance distributions in continuous networks in which travelers visit exactly one facility between origin and destination

Location of Railway Emergency Rescue Spots Based on a Near-Full Covering Problem: From a Perspective of Diverse Scenarios

Continuous Covering on Networks: Improved Mixed Integer Programming Formulations

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