Locating mobile servers on a network with markovian properties

Oded Berman · Amedeo R. Odoni

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Optimization and Search Problems

Abstract

Abstract The median problem has been generalized to the case in which facilities (“servers”) can be moved, at a cost, on the network in response to changes in the state of the network. Such changes are brought about by changes in travel times on the links of the network due to the occurrence of probabilistic events. For the case examined here, transitions among states of the network are assumed to be Markovian. The problem is examined for an objective which is a weighted function of demand travel times and of server relocation costs. It is shown that when these latter costs are a concave function of the time to travel from the current server location to the new server location, an optimal set of server locations exists solely on the nodes of the network. The location‐relocation problem can be formulated as an integer programming problem. The problem of locating a single server on a network which is a tree is shown to have a simple solution. A heuristic algorithm for the single server on a general network is also described. The paper develops simple bounds for the general multifacility, multistate problem and concludes with the description of a relaxed version of this model and with a discussion of the model's applicability.

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References

1964Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph 1970Central Facilities Location 1977Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms 1974A hypercube queuing model for facility location and redistricting in urban emergency services 1971Optimal Center Location in Simple Networks 1974An Algorithm for the Dynamic Relocation of Fire Companies 1972Response Areas for Two Emergency Units 1979Locations of Medians on Stochastic Networks

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2017Optimization of competitive facility location for chain stores 1999Location Models in Transportation 2012The maximum covering problem with travel time uncertainty 2011Resource Location and Relocation Models with Rolling Horizon Forecasting for Wildland Fire Planning 1984Location-Relocation of Mobile Facilities on a Stochastic Network 1987Single Facility Location on Networks

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