A special class of extended multicriteria location problems

Alzorba, Shaghaf; Günther, Christian; Popovici, Nicolae

doi:10.1080/02331934.2013.869810

Cited by 6 publications

(2 citation statements)

References 20 publications

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“…The following preparation allows us to characterize the set χ Eff (G(R 2 ); R q + ) of efficient solutions of the multi-objective location problem (MOLP). In the literature, several characterizations of the set efficient solutions of location problems have been obtained; see, e.g., [50,52,53]. We will adapt here the approach proposed by the authors in [53] which is based on the dual norm to the Manhattan-norm, namely the maximum-norm defined for any (x 1 , x 2 ) ∈ R 2 by…”

Section: 31mentioning

confidence: 99%

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

2023

J. Nonlinear Var. Anal.

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Continuity of the objective functions and compactness of their domain are classical assumptions widely used to obtain existence results for solutions of optimization problems. Due to the lack of compactness in general spaces, under some moderate assumptions concerning the objective function and the feasible set, we derive existence results for vector-valued optimization problems and corresponding results for associated scalarized problems in this paper. Furthermore, we apply our results to special vector-valued approximation problems, especially to multi-objective location problems where the whole set of efficient solutions can be generated by a geometric primal-dual algorithm. Moreover, by using the nonlinear scalarizing functional introduced by Gerstewitz, we perform an optimization according to the preferences of a decision maker on the generated set of efficient solutions from which we derive a single solution of this set that corresponds to the preferences of the decision maker.

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Section: 31mentioning

confidence: 99%

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

2023

J. Nonlinear Var. Anal.

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“…The most basic and likewise famous problems are known as the p-median, the p-center, and the covering problem (see Laporte et al 2015). Nowadays research in this field mostly extends these basic models, often by coupling other fields of theoretical or practical interest, for example, multicriteria location planning (Kalcsics et al 2014;Alzorba et al 2015), robust location planning (Baron et al 2011;Carrizosa and Nickel 2003), or combining locational decisions and routing (see for example the survey Drexl and Schneider 2015).…”

Section: Introductionmentioning

confidence: 99%

Interdicting facilities in tree networks

Fröhlich

Ruzika

2021

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This article investigates a network interdiction problem on a tree network: given a subset of nodes chosen as facilities, an interdictor may dissect the network by removing a size-constrained set of edges, striving to worsen the established facilities best possible. Here, we consider a reachability objective function, which is closely related to the covering objective function: the interdictor aims to minimize the number of customers that are still connected to any facility after interdiction. For the covering objective on general graphs, this problem is known to be NP-complete (Fröhlich and Ruzika In: On the hardness of covering-interdiction problems. Theor. Comput. Sci., 2021). In contrast to this, we propose a polynomial-time solution algorithm to solve the problem on trees. The algorithm is based on dynamic programming and reveals the relation of this location-interdiction problem to knapsack-type problems. However, the input data for the dynamic program must be elaborately generated and relies on the theoretical results presented in this article. As a result, trees are the first known graph class that admits a polynomial-time algorithm for edge interdiction problems in the context of facility location planning.

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Location Problems with Multiple Criteria

2019

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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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A special class of extended multicriteria location problems

Cited by 6 publications

References 20 publications

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

Interdicting facilities in tree networks

Location Problems with Multiple Criteria

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