Dynamic decision making within spatially-explicit systems subject to environmental uncertainty

Dynamic decision making under uncertainty provides managers with tools to make better-informed decisions to improve objectives such as profits, throughput through networks, scheduling, and reducing the impact of extreme events. However, many systems can both impact and be impacted by their surrounding environment. Businesses and governments must therefore account for these factors. This necessitates the development of models that can account for ways to dynamically control systems over time while accounting for environmental effects. Dynamic programming (DP) is one popular method of finding optimal solutions to multi-stage decisions. It uses backward induction to recursively compute the effect of decisions at earlier stages on future outcomes and therefore the objective function. This principle has been extended to systems subject to uncertainty via ‘stochastic dynamic programming’ (SDP). SDP is similar to ‘stochastic programming’, in that it takes into account a range of possible future outcomes. In contrast to classical DP, SDP produces a decision policy rather than a fixed sequence of decisions over time. This allows decision makers to adapt optimally as uncertain variables are revealed. However, these approaches suffer from the ‘curse of dimensionality’ and can usually only tractably deal with systems that have a small number of states and controls. This limits their application in real-world scenarios. This is exacerbated by the fact that many environmental systems have spatial variability, further adding to the dimensionality of the problem. Techniques such as ‘approximate dynamic programming’ (ADP) have sought to address this problem by introducing policy approximations that map the current system state and possible decisions to expected outcomes (Powell, 2014). Notable progress has been made through various applications such as financial and real options, vehicle routing, and energy distribution. This thesis builds upon these developments to evaluate flexibi