Research Article: Integer programming for improving radiotherapy treatment efficiency

Date Published: July 10, 2017

Publisher: Public Library of Science

Author(s): Ming Lv, Yi Li, Bo Kou, Zhili Zhou, Jian Jian Li.


Patients received by radiotherapy departments are diverse and may be diagnosed with different cancers. Therefore, they need different radiotherapy treatment plans and thus have different needs for medical resources. This research aims to explore the best method of scheduling the admission of patients receiving radiotherapy so as to reduce patient loss and maximize the usage efficiency of service resources.

A mix integer programming (MIP) model integrated with special features of radiotherapy is constructed. The data used here is based on the historical data collected and we propose an exact method to solve the MIP model.

Compared with the traditional First Come First Served (FCFS) method, the new method has boosted patient admission as well as the usage of linear accelerators (LINAC) and beds.

The integer programming model can be used to describe the complex problem of scheduling radio-receiving patients, to identify the bottleneck resources that hinder patient admission, and to obtain the optimal LINAC-bed radio under the current data conditions. Different management strategies can be implemented by adjusting the settings of the MIP model. The computational results can serve as a reference for the policy-makers in decision making.

Partial Text

Normally, there is a period between a patient’s first-time consultation and the beginning of the radiotherapy [1]. Research suggests that the waiting time is relatively long [2–4]. The admission of patients receiving radiotherapy is an admission scheduling problem (ASP). It means that the patients are notified of whether and when they can be admitted by the oncology centers several days before their admission [5]. In China, because oncology centers concentrate in middle-size and large-size cities, famous oncology centers are usually overcrowded with patients. Naturally, some patients may not be able to be admitted within a certain period of time. In that case, they can either choose to wait or to go to another oncology center. Whatever choice they make, the treatment is delayed more or less (Some studies show that there is a correlation between the length of waiting time and outcomes of treatment for radio-receiving patients [6–8]). Here is the question for the oncology centers: What should be done to admit more patients in a specific period?

We made statistics of patients admitted by the oncology center of the First Affiliated Hospital of Xi’an JiaoTong University from August 31th to September 27th, 2015 (four consecutive weeks) by retrieving the admission record, and sending personnel to oncology center for data collection. As part of the data is missing and does not meet the assumptions, we re-sort the data, based on which we construct calculation examples needed in computational experiments.

Computational experiments are carried out on a server with Intel Xeon E5 (3.5 GHz, 12 threads) processor and 16GB RAM running Windows 7 Professional operating system. The solver is IBM ILOG 12.5. Computational results are reported in Tables 3 and 4.

We first compare the MIP method and the traditional FCFS method, that is, the first and the second calculation examples of each group. By comparing the results in Table 2, we find that compared with manual scheduling of patients, the MIP method is able to significantly increase the admission rate and thus increase the LINAC usage and bed occupancy. In all calculation examples, the solutions obtained by using the MIP method are far better than those obtained by manually scheduling patients. Hence, we come to the conclusion that the MIP method is superior over the manual scheduling method. In fact, this is in accordance with expectation. Because the solution obtained by using the MIP method is a global optimum. In contrast, the FCFS method is similar to the greedy algorithm and gives no consideration to global optimization. So, the solution obtained by using the FCFS method cannot be better than that obtained by using the MIP method.

This paper first studies the problem of scheduling patients at the radiotherapy department and constructs a mixed integer programming model for solving this problem. Computational results suggest that compared with the FCFS method, our proposed MIP method is able to significantly increase patient admission and thus boost the usage efficiency of medical service resources (LINAC and bed) by a wide margin.




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