Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
L-shaped decomposition of two-stage stochastic programs with integer recourse
Mathematical Programming: Series A and B
Journal of Global Optimization
Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse
SIAM Journal on Optimization
The Million-Variable "March" for Stochastic Combinatorial Optimization
Journal of Global Optimization
Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
On a stochastic sequencing and scheduling problem
Computers and Operations Research
Introduction to Stochastic Programming
Introduction to Stochastic Programming
Dual decomposition in stochastic integer programming
Operations Research Letters
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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.