In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor’s decision problem where the interdiction plan is either pre-committed or adapts … Read more
We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem … Read more
We present a new complexity result on solving the Markov decision problem (MDP) with $n$ states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that, when the discount factor $\theta$ is strictly less than $1$, the problem can be solved in … Read more
We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more