Several 2‐facility location problems on networks with equity objectives

Kalcsics, Jörg; Nickel, Stefan; Puerto, Justo; Rodríguez‐Chía, Antonio M.

doi:10.1002/net.21568

Cited by 12 publications

(4 citation statements)

References 37 publications

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“…Similar results have been obtained for various location problems, including covering problems [10,24,25,33], center problems [44], median problems [1,35], or other facility location problems [27,29,34,38], as well as flow/shortest path problems [17,26,42].…”

Section: Introductionsupporting

confidence: 73%

On the complexity of the upgrading version of the maximal covering location problem

Baldomero‐Naranjo,

Kalcsics,

Rodríguez‐Chía

2024

Networks

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In this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP‐hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in time for uniform weights and NP‐hard for non‐uniform weights. On paths, the single facility problem is solvable in time, while the ‐facility problem is NP‐hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo‐polynomial algorithm is developed for the single facility problem on trees with integer parameters.

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Section: Introductionsupporting

confidence: 73%

On the complexity of the upgrading version of the maximal covering location problem

Baldomero‐Naranjo,

Kalcsics,

Rodríguez‐Chía

2024

Networks

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“…9.4). Only recently Kalcsics et al (2014) started looking into polynomial cases of multi-facility multicriteria location problems on networks.…”

Section: Other Multicriteria Location Problems On Networkmentioning

confidence: 99%

Location Problems with Multiple Criteria

2015

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This chapter analyzes multicriteria continuous, network, and discrete location problems. In the continuous framework, we provide a complete description of the set of weak Pareto, Pareto, and strict Pareto locations for a general Q-criteria location problem based on the characterization of three criteria problems. In the network case, the set of Pareto locations is characterized for general networks as well as for tree networks using the concavity and convexity properties of the distance function on the edges. In the discrete setting, the entire set of Pareto locations is characterized using rational generating functions of integer points in polytopes. Moreover, we describe algorithms to obtain the solutions sets (the different Pareto locations) using the above characterizations. We also include a detailed complexity analysis. A number of references has been cited throughout the chapter to avoid the inclusion of unnecessary technical details and also to be useful for a deeper analysis.

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“…Indeed, the majority of the papers list some measures that could or have been used in FLPs (i.e., Erkut 1993;Marsh and Schilling 1994;L opez-de-los-Mozos and Mesa 2001; L opez-delos-Mozos, Mesa, and Puerto 2008;Miyagawa 2014;Kalcsics et al 2015). They attempt to complete an exhaustive list of equality measures and to define some properties that show the differences among the several measures.…”

Section: Introductionmentioning

confidence: 99%

Exploring Similarities in Discrete Facility Location Models with Equality Measures

Barbati¹,

Bruno

2017

Geographical Analysis

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There have been a number of discrete facility location models that deal with the use of some equality measures of the distances between the facility and the users. They have been used to guarantee a similar level of equity among the users that may be affected in a positive or in a good way from a facility. These models have been formulated trying to adapt equality measures taken from contexts different from the location one. This way, every measure is very specific to the particular application and it is not highlighted why a measure should be selected and what is the contribution to the equity distribution among the users that can provide. In this article, we propose a facility location problem in which we have to locate a given number of facilities among a set of potential facilities, optimizing an equality measure. We propose a computational study to test the similarities and the differences of a good number of measures with more than a single facility to locate and we point out which measures produce similar results and how they depend on each other.

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Several 2‐facility location problems on networks with equity objectives

Cited by 12 publications

References 37 publications

On the complexity of the upgrading version of the maximal covering location problem

On the complexity of the upgrading version of the maximal covering location problem

Location Problems with Multiple Criteria

Exploring Similarities in Discrete Facility Location Models with Equality Measures

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