Approximate Dynamic Programming Methods for Dynamic Resource Allocation Problems in Health Care

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Waitlists and wait times are among the most significant problems in health care. These are a consequence not only of an imbalance between capacity and demand but also a result of inefficient resource allocation practices. Demand for health care services has increased dramatically in the past decade. Capacity, on the other hand, has failed to keep up with demand and limited attention has been paid to identifying efficient resource allocation strategies. The latter mainly due to the complexity introduced by a wide variety of services, different types of patients, resource heterogeneity, and the presence of patient-resource interactions. Many resource allocation problems in health care, such as patient scheduling problems, can be modelled as sequential decision-making problems. The determination of optimal decision strategies for such problems typically requires consideration of an extremely large number of scenarios and alternative courses of action. Dynamic programming is a method that offers a mathematical formalization of the trade-off between the immediate and the future impact of alternative actions for such problems. It is well known that for most real-world dynamic resource allocation problems in health care the computational requirements of dynamic programming are overwhelming. Sophisticated methods for dealing with this issue, called approximate dynamic programming (ADP), have been developed in the last two decades. A common approach in these methods consists of using an approximation architecture in the dynamic programming model to represent the future performance of the system for different scenarios. Most approximation architectures found in the literature are either affine in the variables that represent the state of the system or defined as an affine combination of a low-dimensional set of basis functions in such variables. However, the future performance of the system for problems with complex dynamics can be better represented by non-linear functional forms in these variables. The proposed research seeks to develop and use alternative approximation architectures, together with novel linear programming and simulation-based approaches, to obtain improved strategies for dynamic resource allocation problems, particularly for patient scheduling. It will also focus on extending existing models and solution approaches to consider multiple resources, patient-resource interactions, and factors such as stochastic service times and follow-ups. The long-term objectives of this research will thus be to advance ADP techniques and theory and to develop new, implementable methods for this type of problems. The proposed research is targeted primarily at the Operations Research (OR) community, but it is intended to impact practice as well. I expect its outcome to generate new research areas for the OR community and hopefully impact health care policy and patient care.