Large scale markov decision processes in healthcare management

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The purpose of this research is to develop a mathematical framework for solving large scale stochastic decision problems and capacity planning within healthcare management. Such decisions include the scheduling of patients to a specific resource and the daily decisions around hospital congestion and ward capacity. A shortage of resources in Canadian hospitals is a chronic and steadily worsening challenge. Thus, the efficient use of what resources are available is becoming increasingly critical. We seek to develop a model that will concurrently determine the optimal decision policy and the optimal capacity allocation. We will look to analyse the impact of available surge capacity (i.e. overtime) and determine the appropriate balance between surge and base capacity. Markov decision processes (MDPs) are an ideal method for solving stochastic decision problems but suffer from two deficiencies. First, MDPs generally solve the decision problem and the capacity planning problem in sequence rather than in parallel. This does not take into account the inter-related nature of these two problems. Second, MDPs are limited in the size of decision problem they can handle. We seek to apply and improve the methodologies of approximate dynamic programming (ADP) that allow the use of MDP theory for large scale stochastic decision problems. The overall contributions of this research are both in the practical applications to healthcare management (in improved resource utilization and evidence-based capacity planning) as well as the discovery of fundamental insights into the inter-related nature of decision policies and capacity planning and the improvement of ADP theory in solving large scale stochastic decision problems.