IEEE Robotics & Automation Magazine - June 2015 - 63
Table 15. The patient grouping versus
scheduling policies.
Policy
Slots
Patient Groups
NPP
110
{1,2,3,4,5,7,8,9,10,11,12,13,15,16,17,18
(93)}, {6,14(17)}
FIFO
110
{1,2,3,7(4)}, {4,5,8,9,10,11,12,13,15,16,17,
18(88)}, {6,14(18)}
heterogeneous LINACs for multiple patient types with different treatment protocols and WTTs. The main contribution is
a queueing and patient pooling approach for LINAC capacity
allocation. A queueing framework was proposed by considering the time slots of LINACs as servers. This original queueing
perspective allows for a nice modeling of the treatment protocols with single-class queueing models that, otherwise, would
lead to complicated multiclass queueing systems with reentrance. It greatly simplifies the mathematical formulation of
the LINAC capacity planning problems. Mixed-integer programming models are provided for the capacity allocation and
CMOPs. The queueing framework was extended to pool
patient types into groups served by the same slot servers to
efficiently reduce the total number of slot servers. A mathematical programming model and a pairwise merging heuristic
were proposed for patient pooling optimization.
This research can be extended in several directions. The
BP evaluation of a multiclass, multiserver queue with multiple WTTs is a challenging open issue, but it is important to
speed up our approach. Joint patient pooling and case-mix
optimization is highly combinatorial and requires efficient
solution techniques. The joint optimization of the service
level and case mix is another interesting direction. Finally,
the real-time patient admission control of multiple patient
types with heterogeneous WTTs is the next step to improving radiotherapy operations.
Acknowledgments
We are grateful to the physicians and nurses of the Radiotherapy Unit headed by C. Xu of the Ruijin Hospital, Shanghai,
China, for their helpful discussions and information. This
work was supported by the Natural Science Foundation of
China (71131005, 71471113, 61104173), by the Specialized
Research Fund for the Doctoral Program of Higher Education
(20120073110040), and by the Agence Nationale de Recherche
(ANR-11-TECS-010-04).
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Siqiao Li, Shanghai Jiao Tong University, China. E-mail: aprilsiqiao@126.com.
Na Geng, Shanghai Jiao Tong University, China. E-mail:
gengna@sjtu.edu.cn.
Xiaolan Xie, École des Mines de Saint Etienne, Saint Etienne,
France, and Shanghai Jiao Tong University, China. E-mail:
xie@emse.fr.
JUNE 2015
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