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This paper proposes a new formulation for the dynamic resource allocationproblem, which converts the traditional MDP model with known parameters and nocapacity constraints to a new model with uncertain parameters and a resourcecapacity constraint. Our motivating example comes from a medical resourceallocation problem: patients with multiple chronic diseases can be providedeither normal or special care, where the capacity of special care is limiteddue to financial or human resources. In such systems, it is difficult, if notimpossible, to generate good estimates for the evolution of health for eachpatient. We formulate the problem as a two-stage stochastic integer program.However, it becomes easily intractable in larger instances of the problem forwhich we propose and test a parallel approximate dynamic programming algorithm.We show that commercial solvers are not capable of solving the probleminstances with a large number of scenarios. Nevertheless, the proposedalgorithm provides a solution in seconds even for very large problem instances.In our computational experiments, it finds the optimal solution for $42.86\%$of the instances. On aggregate, it achieves $0.073\%$ mean gap value. Finally,we estimate the value of our contribution for different realizations of theparameters. Our findings show that there is a significant amount of additionalutility contributed by our model.

Modeling and Optimizing Resource Allocation Decisions through Multi-model Markov Decision Processes with Capacity Constraints