Optimal spatiotemporal resource allocation in public health and renewable energy

Optimizing the spatiotemporal allocation and distribution of a limited number of critical resources is a pervasive problem, concerning both government agencies and private companies. This challenge is complicated by mismatches between supply and demand over time and also by uncertainty in demand and/or supply. We study such problems in public health and in renewable energy. Public health resources, such as antiviral medications and vaccines, are often in limited availability at the start of an influenza pandemic. Government agencies need to make balanced policy decisions, accounting for regional equity while maintaining an efficient distribution to mitigate spread of the influenza virus. In the absence of good initial information regarding the demand, resource allocation decisions need to encompass a variety of demand scenarios. On the renewable energy side, we seek to provide a fixed supply of energy from a system which includes a highly variable renewable source, such as wind power. Here, we must commit to a decision before the stochastic supply is realized. When bidding into the electricity market to buy or sell energy, an added difficulty concerning the prices of energy arises. We study five specific problems in these contexts.