Modeling Uncertainty in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. This study introduces a novel numerical method to solve large-scale dynamic stochastic natural resource allocation problems that cannot be addressed by conventional methods. The method is illustrated with an application focusing on the allocation of global land resource use under stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters, the range of land conversion is considerably smaller for the dynamic stochastic model as compared to deterministic scenario analysis. The scenario analysis can thus significantly overstate the magnitude of expected land conversion under uncertain crop yields

Parallel ADMM for robust quadratic optimal resource allocation problems

An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation of the solver on a graphics processing unit (GPU) using a bespoke quartic function minimizer. An application to robust optimal energy management in hybrid electric vehicles is described, and the results of numerical simulations comparing the computation times of the parallel GPU implementation with those of an equivalent serial implementation are presented

Exponential penalty function control of loss networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy--it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.Comment: Published at http://dx.doi.org/10.1214/105051604000000936 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org