Efficiency in constrained continuous location

Ndiaye, Malick; Michelot, Christian

doi:10.1016/s0377-2217(97)00184-7

Cited by 8 publications

(10 citation statements)

References 17 publications

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“…. , n) we get Theorem 4.2 in [11]. There, the constrained solution set is the projection of the unconstrained solution set.…”

Section: The Casementioning

confidence: 87%

“…3(a). Since F 2 is constructed to be strictly quasiconvex, we have that WE(F 1 , F 2 ) is a connected curve joining (0, 0) and (11,11) consisting of the consecutive tangent points between the level sets of F 1 and F 2 . We can see that the tangent points between the level sets of F 1 and those of F 2 defined by (4), (5), (6) and (7) are represented in Fig.…”

Section: The Casementioning

confidence: 99%

“…Then, since the weakly efficient set is connected there must exist infinitely many intersections of WE(F 1 , F 2 ) with the segment defined by (0, 0) and (11,11).…”

Section: The Casementioning

confidence: 99%

“…Other references devoted to study modifications of the Point-Objective location models are [3][4][5][6][7][8][9][10][11][12][13], among others. It is worth noting that from the above references only [3][4][5][6][7][8]11] consider the constrained case. Moreover, these references study the particular case of the Point-Objective location problem where distances are measured with the same norm.…”

Section: Introductionmentioning

confidence: 99%

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Quasiconvex constrained multicriteria continuous location problems: Structure of nondominated solution sets

Puerto¹,

Rodríguez‐Chía²

2008

Computers & Operations Research

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In this paper, we consider constrained multicriteria continuous location problems in two-dimensional spaces. In the literature, the continuous multicriteria location problem in two-dimensional spaces has received special attention in the last years, although only particular instances of convex functions have been considered. Our approach only requires the functions to be strictly quasiconvex and inf-compact. We obtain a geometrical description that provides a unified approach to handle multicriteria location models in two-dimensional spaces which has been implemented in MATHEMATICA. ᭧

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“…. , n) we get Theorem 4.2 in [11]. There, the constrained solution set is the projection of the unconstrained solution set.…”

Section: The Casementioning

confidence: 87%

Section: The Casementioning

confidence: 99%

“…Then, since the weakly efficient set is connected there must exist infinitely many intersections of WE(F 1 , F 2 ) with the segment defined by (0, 0) and (11,11).…”

Section: The Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasiconvex constrained multicriteria continuous location problems: Structure of nondominated solution sets

Puerto¹,

Rodríguez‐Chía²

2008

Computers & Operations Research

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“…In pure attracting models, characterizations of strict efficient, efficient and weak efficient solutions have been obtained in terms of Q δ sets (Durier 1990;Durier and Michelot 1986;Ndiaye and Michelot 1998;Ndiaye 1996). These sets, induced by a norm (see Durier and Michelot 1986) and closely related to the geometry of the unit ball B := {x ∈ X: γ (x) ≤ 1}, play also an important role to give necessary conditions for efficiency in presence of repulsive demand points.…”

Section: Necessary Conditions For Efficiency In Terms Of Q δ Setsmentioning

confidence: 99%

Efficiency for continuous facility location problems with attraction and repulsion

2008

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The paper deals with the problem of locating new facilities in presence of attracting and repulsive demand points in a continuous location space. When an arbitrary norm is used to measure distances and with closed convex constraints, we develop necessary conditions of efficiency. In the unconstrained case and if the norm derives from a scalar product, we completely characterize strict and weak efficiency and prove that the efficient set coincides with the strictly efficient set and/or coincides with the weakly efficient set. When the convex hulls of the attracting and repulsive demand points do not meet, we show that the three sets coincide with a closed convex set for which we give a complete geometrical description. We establish that the convex hulls of the attracting and repulsive demand points overlap iff the weakly efficient set is the whole space and a similar result holds for the efficient set when we replace the convex hulls by their relative interiors. We also provide a procedure which computes, in the plane and with a finite number of demand points, the efficient sets in polynomial time. Concerning constrained efficiency, we show that the process of projecting unconstrained weakly efficient points on the feasible set provides constrained weakly efficient points.

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