An exact algorithm for the capacitated vertex p-center problem
Computers and Operations Research
Solving haplotyping inference parsimony problem using a new basic polynomial formulation
Computers & Mathematics with Applications
A memetic genetic algorithm for the vertex p-center problem
Evolutionary Computation
Computers and Operations Research
A flexible model and efficient solution strategies for discrete location problems
Discrete Applied Mathematics
An exact algorithm for the capacitated vertex p-center problem
Computers and Operations Research
Solving the constrained coverage problem
Applied Soft Computing
Solving the constrained p-center problem using heuristic algorithms
Applied Soft Computing
Solving Large p-Median Problems with a Radius Formulation
INFORMS Journal on Computing
Double bound method for solving the p-center location problem
Computers and Operations Research
A dual bounding scheme for a territory design problem
Computers and Operations Research
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Thep-center problem consists of choosingp facilities among a set ofM possible locations and assigningN clients to them in order to minimize the maximum distance between a client and the facility to which it is allocated. We present a new integer linear programming formulation for this min-max problem with a polynomial number of variables and constraints, and show that its LP relaxation provides a lower bound tighter than the classical one. Moreover, we show that an even better lower boundLB*, obtained by keeping the integrality restrictions on a subset of the variables, can be computed in polynomial time by solving at mostO(log 2( NM)) linear programs, each havingN rows andM columns. We also show that, when the distances satisfy triangle inequalities,LB* is at least one third of the optimal value. Finally, we useLB* in an exact solution method and report extensive computational results on test problems from the literature. For instances where the triangle inequalities are satisfied, our method outperforms the running time of other recent exact methods by an order of magnitude. Moreover, it is the first one to solve large instances of size up toN =M = 1,817.