Planning Radiation Treatment Capacity to Meet Patient Waiting Time Targets *

 Abstract—This paper proposes a queueing and patient pooling approach for radiotherapy capacity allocation with heterogeneous treatment machines called LINAC (Linear Accelerators), different waiting time targets (WTT) and treatment protocols. We first propose a novel queueing framework with LINAC time slots as servers. It leads simple single-class queues for evaluation of WTT satisfaction that would, otherwise, require analysis of complicated multi-class queues with re-entrance. Mixed integer programming models are given for capacity allocation and case-mix optimization under WTT constraints. We then extend the queueing framework by pooling 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 properties of optimal capacity allocation and patient pooling.