Capacity Allocation And Patient Scheduling For The Key Resource In Radiotherapy Process

Healthcare service plays an essential role in nationals’ livelihoods.It is one of the core issues in social well-beings.Along with ageing population becomes more and more prominent,the number of diagnoses and referrals increases quickly.Correspondingly,healthcare expenses exploded.However,a severe shortage of medical resources is still faced by the Chinese government.In addition to implementing the Medical System Reformation and introducing more medical resources,we should apply advanced operations research(OR)models and efficient management approaches to help hospital managers meet the increasing medical requirements with the limited medical resources,so as to make quality-efficiency trade-offs.According to the report of the National Health and Family Planning Commission of China(NHFPC),there is at least one in 4-5 deaths caused by cancer in the past 20 years.Radiotherapy is one of the most effective treatment approaches for cancer patients.The needs of radiotherapy are increasing with the technology becomes more and more advanced so that the number of cancer diagnoses and referrals increases.Based on the field observation in the Shanghai Ruijin Hospital,we find there is 60% to 70% of cancer patients need to receive radiotherapy.However,LINACs are very expensive,and are usually the bottleneck of the radiotherapy process.Long waiting times are observed worldwide due to the shortage of LINACs.Long waiting times bring negative impact on the treatment outcome,cause patients anxiety,deteriorate quality of life,and even cause local recurrence increases.Various Waiting Time Targets(WTTs)are recommended worldwide to keep tumors at a lower growth rate.Radiotherapy uses various types of rays(e.g.,,,, rays,etc.),emitted from various Linear Accelerators(LINACs),directly irradiate on tumors to suppress the growth of tumors.According to cancer site,tumor size,urgent degree and tumor type,different patient types need to receive treatment on different LINACs.At the same time,to avoid harming the healthy cells around tumors during irradiation,the total needed dosage of a patient is segmented into multiple equal fractions.Once a patient starts the treatment,a fraction is delivered every day from the same LINAC.Therefore,compared to other medical processes,the radiotherapy treatment process is characterized by its long-term,multi-stage,re-entrance,and multiple patient types involved.Thus,the existing OR models and solutions proposed for other applications cannot be used directly in radiotherapy scheduling.The complexity of the radiotherapy process makes the operations control and patient scheduling in radiotherapy treatment process very challenging.To meet the challenge,considering the uncertainty of patient arrivals and heterogeneous WTT requirements,in this thesis,we have developed a novel queueing perspective to model patients’ treatment process on LINACs,based on which framework,we have solved various interesting problems for radiotherapy.Firstly,motivated by the long access time of patients(the waiting time between the “ready-to-treat” date to the first treatment date),this thesis studies the capacity allocation problem of LINACs considering multi-type radiotherapy patients that have various treatment protocols and service level requirements.This problem is solved at the med-long term level,which considers the uncertainty in patient arrivals.To evaluate the capacity of LINACs needed to meet the WTT requirement of each patient type,this thesis first proposed an innovative queueing framework which allows for nice modelling of the re-entrance behaviors of multi-type patients.It greatly simplified the mathematical formulation of the LINAC capacity planning problems.To improve the utilization of LINACs,pooling multiple patient types into patient groups is considered.Based on this framework,the capacity allocation problem is solved in the following three steps.1)An integer mathematical programming is proposed to solve the patient pooling problem,which is proved to be an NP-hard problem.Therefore,a nice structured pairwise merging heuristic is developed to deal with the practical-scale situation.2)Based on the pooling results,mixed-integer programming is provided to obtain the optimal capacity allocation solution.The goal was minimizing the total capacity needed to meet the given service level requirements.In the objective function,we also considered the fairness of utilization between LINACs.3)When the required capacity is more than the given amount,except for the allocation solution,we also offered the optimal static accept rate for each patient type by solving a Case-Mix optimization problem so that the revenue is maximized subject to all service level requirements.The numerical results showed that the total capacity needed can be saved by 12%after pooling patient types to groups.Diverse sensitivity analyses are also conducted to see how the solution changed with different parameters.Secondly,given the allocated capacity in each patient group,this thesis studies the patient admission control problem to reduce patient access time further.This problem is solved at the scheduling level.Note that the problem is also based on “slot-server” perspective and can be described in the following way: when a patient becomes “ready-to-treat”,if there is a time slot available on the LINAC,the patient will be directly scheduled to start his/her treatment;if all time slots are occupied,the patient will wait in the corresponding queue(i.e.,each queue is corresponding to a patient type).Once a time slot becomes available,the radiotherapy scheduler needs to decide which patient to treat next among all patients waiting in the queues.In specific,this thesis proposes an efficient and easy-to-use Waiting Index(WI)based policy which is called the Highest Waiting Index First(HWIF)policy,which updates the WI of each queue(i.e.,patient type)based on its current waiting status.The WI is the sum of the waiting time of the first patient in the queue(i.e.,the longest waiting time in the queue)and a certain priority factor that is calculated by a simulation-based optimization approach.The goal is minimizing the maximal tardiness time among all patient types.In this way,the service level of various patient types is balanced.A fairness ratio is proposed to evaluate the fairness among patient types.It is defined as the gap between the maximal tardiness and the minimal tardiness divided by the average tardiness.Numerical results showed that the proposed policy outperformed seven benchmark policies in various scenarios.Moreover,compared to a Markov decision process(MDP)based approach for radiotherapy patient scheduling that was proposed in 2012,our policy can reach the same performance with lower slot servers.This thesis also considers non-constant arrival rates.In most of the existing literature,patient arrival rates are considered constant.However,a number of events can cause arrival rates changes,for example,changes in treatment,and the opening or closing of competing centers in the neighborhood,introducing more capacity,and so on.Note that arrival rates usually have unforeseen changing patterns.Therefore,this thesis proposes a variant of the HWIF policy,which adaptively adjusts the WI,so that compensates for the impact caused by the change of arrival rates.Specifically,every day,the average service level of each patient type in the past days is re-estimated based on which the priority factor of the patient type with the worst performance will be adjusted by ?.All the related parameters are again decided by simulation.The improvement of using the adaptive policy other than the original HWIF policy is considerate in our numerical experiments.Lastly,given the patients scheduled on a LINAC every day,this thesis studies the appointment scheduling problem considering patient unpunctuality and uncertain session duration.This problem has barely explicitly studied in radiotherapy operations research for the following reasons: patient arrive time on the treatment day and session duration are often considered deterministic in the literature so that patients’ appointments are just planned according to the estimated average session duration.In reality,the fluctuation in session duration is unavoidable.Any unexpected events can cause randomness.Moreover,along with the development of radiotherapy,there are new LINACs with a CT scanner embedded,which update the image of the tumor in every treatment session followed with a short discussion on the current treatment protocol.Meanwhile,patient unpunctuality is also observed in radiotherapy departments,e.g.,cancer patients usually tend to arrive earlier.However,due to different patient types,unpunctual behaviors are not identical.For example,patients tend to have a higher chance to arrive earlier on the first-treatment-day,and urgent patients are more unpunctual or even no-show due to uncertain tumor situation.The distribution of the session duration and the unpunctuality are assumed already known(i.e.,can be fit according to the historical data)in the thesis.To understand the impact of unpunctuality behaviours on the system performance,we developed an exact analytical approach to evaluate various performance measurements(e.g.,the expected waiting time and its distribution per patient,the idle time of the server,etc.).The analysis was first given under the assumption of exponential treatment times,then was extended to consider a more general distribution to fit radiotherapy process.Then we propose an innovative mathematical programming model which has constraints on the expected waiting time of each scheduled patient and minimize the idle time of LINACs.Numerical experiments showed that making appointment schedules without considering patients’ unpunctuality can lead to underestimation of both the waiting time and the idle time.The impact is bigger when the treatment time distribution has relatively low variance.The proposed intra-day scheduling policy offers much better performance than the commonly used fixed-interval scheduling policy and shows its robustness under various sequence of patients scheduled.This thesis deeply studies the operations control problems in the medical process having the “re-entrance” behaviors.The proposed solutions,which provide theoretical guidance and decision-making basis for operational management in radiotherapy scheduling,help to improve the fairness of radiotherapy services,increase the utilization of the key medical resources,reduce both patients’ waiting time(the access time until the first radiotherapy treatment date and the direct waiting time within the treatment day),eventually improve patient satisfaction.Our work may also have important implications for managers in other service systems sharing similar characteristics such as bed resource allocation,call center scheduling.