Stochastic Dynamic Programming

This paper proposes an operational policy for long-term hydropower scheduling based on deterministic nonlinear
optimization and annual inflow forecasting models using an
open-loop feedback control framework. The optimization model precisely represents hydropower generation by taking into consideration water head as a nonlinear function of storage, discharge and spillage. The inflow is made available by a forecasting model based on a fuzzy inference system that captures the nonlinear correlation of consecutive inflows on an annual basis, then disaggregating it on a monthly basis. In order
to focus on the ability of the approach to handle the stochastic
nature of the problem, a case study with a single-reservoir system is considered. The performance of the proposed approach is evaluated by simulation over the historical inflow records and compared to that of the stochastic dynamic programming approach. The results show that the proposed approach leads to a better operational performance of the plant, providing lower spillages and higher average hydropower efficiency and generation.

Over the last decade, geological uncertainty and its effects on long-term or strategic mine planning and methods for related risk management have been studied. However, the combined effect of geological and commodity price uncertainty has received relatively less attention in the technical literature. A research experiment that addresses both these sources of uncertainty is presented herein and accounts for their differences. In particular, while the current commodity price is known at the beginning of every new mining period, the geology, including the mineral grades, metal content, material types and so on, remain uncertain, even when additional information becomes available. The proposed method first uses a two-stage model to manage the geological uncertainty that leads to a scenario-independent extraction sequence. Based on different metal production targets, a pool of subsets of mining blocks is also precomputed for every period. Then, a stochastic dynamic programming algorithm is developed and employed to define the best policy in terms of metal production targets to follow, depending on the evolution of the related commodity price. This policy follows the scenario tree of the commodity price, as it is scenario-dependent (price only) with non-anticipativity constraints, which is similar to an operator that adapts to a fluctuating market. This new approach is tested through a case study that reveals the counter-intuitive combined effects of both sources of uncertainty. For instance, based on the previous evolution of the commodity price, the obtained policy suggests adaptations of the metal production target that go against common practices of mining operators.

We study a multi-location inventory problem with a so-called quick response warehouse. In case of a stock-out at a local warehouse, the demand might be satised by a stock transfer from the quick response warehouse. We derive the optimal policy for when to accept and when to reject such a demand at the quick response warehouse. We also derive conditions under which it is always optimal to accept these demands. Furthermore, we conduct a numerical study and consider model variations.

Published in: Operations Research Letters, Volume 41, Issue 3, May 2013, Pages 305–310, see doi:10.1016/j.orl.2013.03.002