Patient appointment scheduling at hemodialysis centers: An exact branch and price approach

Scheduling patient appointments at a hemodialysis center presents a unique setting. Unlike other appointment scheduling problems in healthcare systems, patients are scheduled for a series of dialysis treatment appointments instead of a single appointment. In this study, we formulate this multiple-appointment system as a set-partitioning problem that allows partial schedules to be feasible. We employ a Branch and Price (BP) algorithm to solve the problem, however, the pricing sub-problem proves to be exceedingly challenging for state-of-the-art dynamic programming algorithms. Therefore, we propose a novel decomposition of the sub-problem and design an efficient embedded Column Generation (CG) algorithm to find the optimal solution. We further design a greedy heuristic that enhances the computational efficiency of the BP algorithm. Our proposed BP algorithms efficiently solve challenging instances that are simulated based on the data from a collaborating hemodialysis center. Specifically, the Enhanced CG-embedded BP algorithm accelerates the CPU time on average by 78% compared to the Base BP algorithm (32% and 59% compared to the Enhanced and the CG-embedded BP algorithms, respectively). We also compare the optimal results with the current scheduling policy at the center. Our proposed Enhanced CG-embedded BP algorithm improves the percentage of leftover appointments by 98% on average and the hours of deviations per patient by 46% on average, compared to the current policy.