Robust doctor–patient assignment with endogenous service duration uncertainty and no-show behavior

In practice, patient’s service duration might be influenced by the workload of doctors who need to provide healthcare service. However, most existing studies have overlooked this correlation when scheduling patients and doctors. Motivated by this context, we incorporate the endogenous (decision-dependent) uncertain service duration, the presence of uncertainty dependent on assignment decisions, into the doctor–patient assignment problem with patient no-show behavior and propose a novel modeling framework. Specifically, we employ the distributionally robust optimization (DRO) approach that uses decision-dependent moment information to construct the ambiguity set of the service duration distribution. A novel decision-dependent DRO (DDRO) model is proposed for the doctor–patient assignment problem. The goal is to minimize the sum of the doctor’s assignment cost and penalty cost and the worst-case expected cost of overtime and cancellation cost. To solve this model, we propose an effective nested column-and-constraint generation (C&CG) solution scheme. This approach involves decomposing the model into an outer-level problem and an inner-level problem, both of which can be solved using the C&CG algorithm. This nested scheme enables us to efficiently solve the model and obtain optimal solutions. Numerical results show that the algorithm can solve most realistic-sized problem instances optimally within the two-hour time limit. In addition, to show the effectiveness of our new modeling framework, we also propose the classical DRO and stochastic programming (SP) models as the benchmark models in our out-of-sample test. The extensive numerical results show that when there exists variability in service duration and robustness in the ambiguity set, our DDRO model outperforms the DRO and SP approaches. In addition, when there are relatively enough doctors, the DDRO method is the best option for decision-makers to make assignment plans. We also show that the no-show behavior factor has a large effect on each model, and the decision-maker cannot ignore the factor, especially when the no-show rate is high. Overall, the numerical results demonstrate the importance of taking decision-dependent service duration uncertainty into account for the doctor–patient assignment problem and also provide an alternative modeling tool for healthcare managers to make assignment plans in scenarios where the service duration is influenced by doctors’ assignments.