A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty

A multi-period stochastic model and an algorithmic approach to location of prison facilities under uncertainty are presented and applied to the Chilean prison system. The problem consists of finding locations and sizes of a preset number of new jails and determining where and when to increase the ca...

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Veröffentlicht in:Computers & operations research Jg. 39; H. 9; S. 2232 - 2241
Hauptverfasser: Hernández, Patricio, Alonso-Ayuso, Antonio, Bravo, Fernanda, Escudero, Laureano F., Guignard, Monique, Marianov, Vladimir, Weintraub, Andrés
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier Ltd 01.09.2012
Elsevier
Pergamon Press Inc
Schlagworte:
Algorithms
Applied sciences
Branch & bound algorithms
Branch-and-fix coordination
Costs
Demand
Exact sciences and technology
Location analysis
Logistics
Marketing
Mathematical models
Mathematical programming
Multi-period scenario tree
Operational research and scientific management
Operational research. Management science
Position (location)
Prison facility location
Prisons
Stochastic integer programming
Stochastic models
Studies
Uncertainty
Chile
Prison facility location
Branch-and-fix coordination
Stochastic integer programming
Multi-period scenario tree
Stochastic model
Algorithmics
Modeling
Location problem
Optimization
Facility location
Uncertain system
Zero one programming
Branching
Lower bound
Script
Probabilistic approach
Coordination
Branch and bound method
Criminality
Average cost
Cluster
Scheduling
Scale model
Stochastic programming
Integer programming
Scaling law
Upper bound
Heuristic method
Large scale
ISSN:0305-0548, 1873-765X, 0305-0548
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Zusammenfassung:A multi-period stochastic model and an algorithmic approach to location of prison facilities under uncertainty are presented and applied to the Chilean prison system. The problem consists of finding locations and sizes of a preset number of new jails and determining where and when to increase the capacity of both new and existing facilities over a time horizon, while minimizing the expected costs of the prison system. Constraints include maximum inmate transfer distances, upper and lower bounds for facility capacities, and scheduling of facility openings and expansion, among others. The uncertainty lies in the future demand for capacity, because of the long time horizon under study and because of the changes in criminal laws, which could strongly modify the historical tendencies of penal population growth. Uncertainty comes from the effects of penal reform in the capacity demand. It is represented in the model through probabilistic scenarios, and the large-scale model is solved via a heuristic mixture of branch-and-fix coordination and branch-and-bound schemes to satisfy the constraints in all scenarios, the so-called branch-and-cluster coordination scheme. We discuss computational experience and compare the results obtained for the minimum expected cost and average scenario strategies. Our results demonstrate that the minimum expected cost solution leads to better solutions than does the average scenario approach. Additionally, the results show that the stochastic algorithmic approach that we propose outperforms the plain use of a state-of-the-art optimization engine, at least for the three versions of the real-life case that have been tested by us.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2011.11.006