Equitable anesthesiologist scheduling under demand uncertainty using multiobjective programming

This work addresses the practical anesthesiologist scheduling (AS) problem motivated by the needs of an academic anesthesiology department. The AS problem requires the department to plan and deploy providers to adequately meet clinical demand and institutional protocols of various clinical units over a planning horizon of up to several weeks. A data‐driven two‐step AS framework is developed by exploiting the historical demand data of anesthesia cases. The first step is a shift design which obtains the optimal shifts considering clinical demand under uncertainty using conditional value‐at‐risk constraints, and the second step is provider assignments that generate the schedule considering optimal and equitable workload distribution and provider availability using multiobjective mixed‐integer programming models. Moreover, the AS framework incorporates the provider specialties, and clinical and lifestyle preferences and aligns with the existing scheduling practices. An ɛ‐constraint solution method is applied for multiobjective optimization, and an iterative solution method is developed to improve solution quality for workload equity in clinical applications. Computational experiments are performed to evaluate the performance of three alternative forms of the workload equity objective function, and the results show that the minimization of the sum of the absolute deviations of provider workloads best balances solution runtime and quality. In the concerned academic anesthesiology department, two clinical problems, the budget and hiring planning and the monthly scheduling, are addressed via the application of the proposed AS framework. For budget and hiring, decision‐makers can make trade‐offs based on their preference using the nondominated frontiers obtained via the ɛ‐constraint method. For monthly scheduling, the iterative solution method can accommodate preassigned shifts capturing institutional requirements while improving workload equity. The workload variance has been substantially reduced from 2.92 to 1.39 after the implementation based on the historical schedule data. The provider schedule satisfaction is improved from 3.13/5 to 3.44/5, and at least 82% of scheduling burden on department leaders is relieved. The developed AS framework is generic and can be extended to the scheduling of other types of care providers, including nurses and residents.