Radiation Queue: Meeting Patient Waiting Time Targets

This article proposes a queueing and patient pooling approach for radiotherapy capacity allocation with heterogeneous treatment machines called linear accelerators (LINACs), different waiting time targets (WTTs), and treatment protocols. We first propose a novel queueing framework with LINAC time slots as servers. This framework leads to simple single-class queues for the evaluation of WTT satisfaction that would, otherwise, require an analysis of complicated multiclass queues with reentrance. Mixed-integer programming models are proposed for capacity allocation and case-mix optimization under WTT constraints. We then extend the queueing framework by pooling the basic patient types into groups sharing the same slot servers. A mathematical programming model and a pairwise merging heuristic are proposed for patient pooling optimization to minimize the overall LINAC capacity needed to meet all WTT requirements. Extended numerical experiments are conducted to assess the efficiency of our approach and to show the properties of optimal capacity allocation and patient pooling.