Multiresource Allocation Scheduling in Dynamic Environments

Motivated by service capacity-management problems in healthcare contexts, we consider a multiresource allocation problem with two classes of jobs (elective and emergency) in a dynamic and nonstationary environment. Emergency jobs need to be served immediately, whereas elective jobs can wait. Distributional information about demand and resource availability is continually updated, and we allow jobs to renege. We prove that our formulation is convex, and the optimal amount of capacity reserved for emergency jobs in each period decreases with the number of elective jobs waiting for service. However, the optimal policy is difficult to compute exactly. We develop the idea of a limit policy starting at a particular time, and use this policy to obtain upper and lower bounds on the decisions of an optimal policy in each period, and also to develop several computationally efficient policies. We show in computational experiments that our best policy performs within 1.8% of an optimal policy on average.