An approximation algorithm for the maximization version of the two level uncapacitated facility location problem

Bumb, A.F.

doi:10.1016/s0167-6377(01)00087-6

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…Constraints (6) ensure that each vendor makes a profit of at least r min units. Constraints (7)- (9) state that the variables are binary.…”

Section: Formulations and Complexitymentioning

confidence: 99%

“…Aardal et al [2] propose some facet defining and valid inequalities for the polytope associated with the two level uncapacitated facility location problem. Approximation algorithms are studied by Aardal et al [1], Ageev [3], Ageev et al [4], Bumb [9], Bumb and Kern [10], Gabor and van Ommeren [14], Guha et al [16], Meyerson et al [22], Shmoys et al [26], Zhang [32], and Zhang and Ye [33]. Branch and bound algorithms are given by Kaufman et al [18], Ro and Tcha [25], Tcha and Lee [29], and Tragantalerngsak et al [31].…”

Section: Introductionmentioning

confidence: 99%

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The vendor location problem

Çınar

Yaman

2011

Computers & Operations Research

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a b s t r a c tThe vendor location problem is the problem of locating a given number of vendors and determining the number of vehicles and the service zones necessary for each vendor to achieve at least a given profit. We consider two versions of the problem with different objectives: maximizing the total profit and maximizing the demand covered. The demand and profit generated by a demand point are functions of the distance to the vendor. We propose integer programming models for both versions of the vendor location problem. We then prove that both are strongly NP-hard and we derive several families of valid inequalities to strengthen our formulations. We report the outcomes of a computational study where we investigate the effect of valid inequalities in reducing the duality gaps and the solution times for the vendor location problem.

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“…Constraints (6) ensure that each vendor makes a profit of at least r min units. Constraints (7)- (9) state that the variables are binary.…”

Section: Formulations and Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The vendor location problem

Çınar

Yaman

2011

Computers & Operations Research

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“…The algorithm is deterministic and based on the primal-dual technique. Bumb (2001) presented a 0.47-approximation algorithm for the maximization version of the two level uncapacitated facility location problem. For the analysis of this algorithm the assumption that there are only two levels of facilities is essential.…”

Section: Solving Algorithms For Hierarchical Location Problemmentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

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“…Several methods have been proposed for solving multi-level facility location problems, based on polyhedral theory [1,2,9,20], Lagrangian relaxation [4,23,27,28], linear programming (LP) relaxation and approximation algorithms [5,8,10,33,34], greedy algorithms and metaheuristics [3,9,13,21,25,26,32].…”

Section: Introductionmentioning

confidence: 99%