Location Science

doi:10.1007/978-3-319-13111-5

Cited by 131 publications

(18 citation statements)

References 555 publications

(852 reference statements)

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“…Uncapacitated facility location problem with matroid constraints. Numerous algorithms have been developed for the UFLP [31,Section 3.4]. Yet in practice, the required solutions are often subject to additional side constraints [31], which make algorithms for the pure UFLP inapplicable.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

Bevern

Tsidulko

Zschoche

2019

Lecture Notes in Computer Science

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We consider a variant of the matroid median problem introduced by Krishnaswamy et al. [SODA 2011]: an uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids. We show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids. To this end, we derive fixed-parameter algorithms for computing representative families for matroid intersections and maximum-weight set packings with multiple matroid constraints. To illustrate the modeling capabilities of the new problem, we use it to obtain algorithms for a problem in social network analysis. We complement our tractability results by lower bounds.Keywords: matroid set packing · matroid parity · matroid median · representative families · social network analysis · strong triadic closure 4 The State Register of Waste Disposal Facilities of the Russian Federation lists 18 dumps for municipal solid waste in Moscow region-the largest city of Europe.

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Section: Introductionmentioning

confidence: 99%

Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

Bevern

Tsidulko

Zschoche

2019

Lecture Notes in Computer Science

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“…To solve location problems, which are formulated in different settings, a variety of analytical approaches and computational techniques exists, including methods of linear and mixed-integer linear programming, methods of discrete, combinatorial and graph optimization [29,17,9,7,26]. Another approach, which finds increasing application in solving some classes of optimization problems, is to use models and methods of tropical mathematics.…”

Section: Introductionmentioning

confidence: 99%

“…In [23,18,24,25,21], an approach based on idempotent algebra is applied to solve unweighted unconstrained and constrained location problems. Further results on both unweighted and weighted location problems can be found in the survey papers [11,1,28,2,3], as well as in the books [29,17,9,7,26].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Solution of Weighted Minimax Single-Facility Constrained Location Problems

Krivulin

2018

Relational and Algebraic Methods in Computer Science

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We consider location problems to find the optimal sites of placement of a new facility, which minimize the maximum weighted Chebyshev or rectilinear distance to existing facilities under constraints on a feasible location domain. We examine Chebyshev location problems in multidimensional space to represent and solve the problems in the framework of tropical (idempotent) algebra, which deals with the theory and applications of semirings and semifields with idempotent addition. The solution approach involves formulating the problem as a tropical optimization problem, introducing a parameter that represents the minimum value of the objective function in the problem, and reducing the problem to a system of parametrized inequalities. The necessary and sufficient conditions for the existence of a solution to the system serve to evaluate the minimum, whereas all corresponding solutions of the system present a complete solution of the optimization problem. With this approach, we obtain direct, exact solutions represented in a compact closed form, which is appropriate for further analysis and straightforward computations with polynomial time complexity. The solutions of the Chebyshev problems are then used to solve location problems with rectilinear distance in the two-dimensional plane. The obtained solutions extend previous results on the Chebyshev and rectilinear location problems without weights and with less general constraints.Key-Words: tropical mathematics, idempotent semifield, constrained optimization problem, single-facility location problem, Chebyshev and rectilinear distances MSC (2010): 65K10, 15A80, 90B85, 90C47, 90C48

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“…The partitioning subproblem MPSTDP-P has been studied extensively in the districting literature (see, e.g., Kalcsics, 2015, for a survey of applications and solution methods). However, we believe that this is the first academic work to deal with the scheduling subproblem MPSTDP-S.…”

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confidence: 99%

“…Partitioning subproblem (MPSTDP-P): This subproblem corresponds to the well-known territory design or districting problem (see Kalcsics, 2015, for an overview of typical planning criteria). The set of customers must be partitioned into service territories with exactly one service provider being responsible for each service territory.…”

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confidence: 99%

The multi-period service territory design problem – An introduction, a model and a heuristic approach

Bender

Meyer

Kalcsics

et al. 2016

Transportation Research Part E: Logistics and Transportation Re

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In service territory design applications, a field service workforce is responsible for providing recurring services at their customers' sites. We introduce the associated planning problem, which consists of two subproblems:In the partitioning subproblem, customers must be grouped into service territories. In the scheduling subproblem, customer visits must be scheduled throughout the multi-period planning horizon. The emphasis of this paper is put on the scheduling subproblem. We propose a mixed integer programming model for this subproblem and present a location-allocation heuristic. The results of extensive experiments on real-world instances show that the proposed heuristic produces high-quality solutions.Keywords: territory design, multi-period planning horizon, mixed integer linear programming, location-allocation heuristic 2010 MSC: 90B06, 90B80, 90C59

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Location Science

Cited by 131 publications

References 555 publications

Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

Fixed-Parameter Algorithms for Maximum-Profit Facility Location Under Matroid Constraints

Algebraic Solution of Weighted Minimax Single-Facility Constrained Location Problems

The multi-period service territory design problem – An introduction, a model and a heuristic approach

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