Resource Allocation under Stochastic Demands using Shrinking Horizon Optimization

We consider the problem of optimally allocating a limited number of resources across time to maximize revenue under stochastic demands. This formulation is relevant in various areas of control, such as supply chain, ticket revenue maximization, healthcare operations, and energy allocation in power grids. We propose a bisection method to solve the static optimization problem and extend our approach to a shrinking horizon algorithm for the sequential problem. The shrinking horizon algorithm computes future allocations after updating the distribution of future demands by conditioning on the observed values of demand. We illustrate the method on a simple synthetic example with jointly log-normal demands, showing that it achieves performance close to a bound obtained by solving the prescient problem.