Staff Planning for Hospitals with Implicit Cost Estimation and Stochastic Optimization

We consider the anesthesiologist staff planning problem for operating services departments in large multi‐specialty hospitals without limit on anesthesiologist supply, where the planner makes monthly and daily decisions to minimize total costs. Each month the staff planner decides the number of anesthesiologists on regular duty and an on‐call consideration list for each day of the following month. In addition, each day, the staff planner decides how many on‐call anesthesiologists to call for the following day. Total costs consist of explicit and implicit costs. Explicit costs include the costs of calling an anesthesiologist and overtime costs. These costs are specified by the organization. Implicit costs encompass costs of not calling an on‐call anesthesiologist and under‐utilizing an anesthesiologist, and these have to be deduced from past decisions. We model the staff planning problem as a two‐stage integer stochastic dynamic program. We develop structural properties of this model and use them in a sample average approximation algorithm constructed to solve this problem. We also develop a procedure to estimate the implicit costs, which are included in this model. Using data from the operating services department at the UCLA Ronald Reagan Medical Center, our model shows the potential to reduce overall costs by 16%. We provide managerial insights related to the relative scale of these costs, hiring decisions by service, sensitivity to cost parameters, and improvements in the prediction of the booked time durations.