Solving the median problem with continuous demand on a network

Blanquero, Rafael; Carrizosa, Emilio

doi:10.1007/s10589-013-9574-3

Cited by 11 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, a series of networks of medium size, obtained e.g. from [6,18], were solved for a small number p of facilities: p = 2, 3, 4. In order to analyze the impact of p on the running times, we have tested our method on a small network, the Sioux-Falls, taken from [23].…”

Section: Computational Resultsmentioning

confidence: 99%

“…[6,7], the nonlinear optimization problem of deciding where to locate them. However, full inspection of all p-uples of edges will be doable only for very small networks.…”

Section: Division Rulementioning

confidence: 99%

“…Solving such (MCLP) yields as an optimal solution selecting the edges f * 1 = (1, 2) and f * 2 = (4, 6), and the edgesets (4,5), (4,6), (5,6), (6, 7)}, where, in case of ties in d * , edges have been allocated randomly. With such definition of E 1 , E 2 , three supersets are obtained as split of the starting superset S 0 , namely (E 1 , 2), (E 1 , 1; E 2 , 1), (E 2 , 2), represented in Figure 2.…”

Section: Initial Supersetsmentioning

confidence: 99%

See 2 more Smart Citations

Maximal Covering Location Problems on networks with regional demand

Blanquero

Carrizosa

G.-Tóth

2016

Omega

Self Cite

View full text Add to dashboard Cite

Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a network so that the expected demand covered is maximized, where demand is continuously distributed along the edges. This MINLP has a combinatorial part (which edges of the network are chosen to contain facilities) and a continuous global optimization part (once the edges are chosen, which are the optimal locations within such edges).A branch and bound algorithm is proposed, which exploits the structure of the problem: specialized data structures are introduced to successfully cope with the combinatorial part, inserted in a geometric branch and bound.Computational results are presented, showing the appropriateness of our procedure to solve covering problems for small (but nontrivial) values of p.

show abstract

Section: Computational Resultsmentioning

confidence: 99%

“…[6,7], the nonlinear optimization problem of deciding where to locate them. However, full inspection of all p-uples of edges will be doable only for very small networks.…”

Section: Division Rulementioning

confidence: 99%

Section: Initial Supersetsmentioning

confidence: 99%

See 1 more Smart Citation

Maximal Covering Location Problems on networks with regional demand

Blanquero

Carrizosa

G.-Tóth

2016

Omega

Self Cite

View full text Add to dashboard Cite

show abstract

“…As second extension, both approaches could be applied to dierent p-facility location problems on networks, such as the p-median problem with continuous demand on a network [7].…”

Section: Discussionmentioning

confidence: 99%

p-facility Huff location problem on networks

Blanquero¹,

Carrizosa²,

G.-Tóth³

et al. 2016

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

Abstract. The p-facility Hu location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the eld of continuous location, in this paper we study the p-facility Hu location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be solved by a branch and bound algorithm. We propose two approaches for the initialization and division of subproblems, the rst one based on the straightforward idea of enumerating every possible combination of p edges of the network as possible locations, and the second one dening sophisticated data structures that exploit the structure of the combinatorial and continuous part of the problem. Bounding rules are designed using DC (dierence of convex) and Interval Analysis tools.In our computational study we compare the two approaches on a battery of 21 networks and show that both of them can handle problems for p ≤ 4 in reasonable computing time.

show abstract

“…Second, one can also assume that users are distributed along the edges of the network, as e.g. in Blanquero and Carrizosa (2013) for median problems and Blanquero et al (2014) for covering problems. Since the much easier problems discussed in Blanquero and Carrizosa (2013) and Blanquero et al (2014) call for the use of nonlinear mixed integer programming tools, it is expected that this source location problem will be, at least, as hard.…”

mentioning

confidence: 99%