The low operational efficiency in the field of medical and health care has become a serious problem in China; the long time that the patients have to wait for is the main phenomenon of difficult medical service. Medical industry is service-oriented and its main purpose is to make profits, so the benefits and competitiveness of a hospital depend on patient satisfaction. This paper makes a survey on a large hospital in Harbin of China and collects relevant data and then uses the prospect theory to analyze patients’ and doctors’ behavioral characteristics and the model of patient satisfaction is established based on fuzzy theory with a triplet
With the improvement of living standards, people tend to pursue a higher quality of life, and the limitation of treatment level in secondary hospitals and community hospitals leads to a serious problem of registered queue in high-level hospitals. There are usually three types of registration in hospitals, namely, general-clinic, specialist-clinic, and emergency-clinic. How to allocate the number of doctor outpatient departments for every type of registration is very essential for operational efficiency in hospital and has a close relationship with patient satisfaction at the same time. Because of the different-type registrations, this paper makes optimal scheduling for the number of doctor outpatient departments considering the patient behavioral characteristics in order to minimize patient waiting time and increase their satisfaction and reduce operating costs.
The main goal of current researches in hospital is lowering costs and running better. Many papers achieved these goals from the perspective of the effective utilization of resource. The resource can be divided into human resource and material resource. Researchers used different methods to optimize the material resource such as Operating Room (OR), multihospital network, and limited number of wards [
In many literatures, patients’ waiting time is a major factor to be considered because it is closely linked with the quality of hospital operation. Now the hospital aims to deliver the highest quality of care, so reducing waiting time of patient is important [
Queuing theory is always being used to deal with the problem of minimum waiting time. Lakshmi and Iyer [
Our research applies prospect theory and membership functions of patient satisfaction to build a model, taking into account the patient behavioral characteristics. Xuping et al. [
It is worth noting that the optimization of service industries is different from manufacturing industries; the former one is always accompanied by the participation of people, and usually it will be affected by people’s behavior and subjective emotion, so the hospital should focus on patient satisfaction. Combined with prospect theory and fuzzy theory and taking into account the patient behavioral characteristics at the same time, we have the research of the optimal scheduling for doctor outpatient departments in one high-level hospital of Harbin. And the starting point matches the urgent social medical problems in China.
The remainder of this paper is organized as follows. In Section
The types of hospital registration always include general-clinic, specialist-clinic, and emergency-clinic. Under normal circumstances, the fee of these three types of registrations increases in turn. In general, the number of emergency-clinics is much less than the former two. The difference between general-clinic and specialist-clinic is that doctors’ experience and technology are relatively richer in specialist-clinics and the registration’s fee is higher. Usually, if the patient’s situation is not too serious, he will choose general-clinic; if the patient needs comprehensive thorough check, he will choose specialist-clinic; if there is urgent situation, the patient will choose emergency-clinic. Patients can select the appropriate type of registrations according to their own conditions and actual demands. Due to the needs of doctor outpatient departments are different in each type of registration; this paper makes optimal scheduling under actual situations. The following is description of registration categories: general-clinic A: suitable for the milder clinical symptoms of patients; specialist-clinic B: suitable for the heavy condition and needs a thorough examination of patients; emergency-clinic C: suitable for the emergency condition of patients.
The emphasis of this article is on the lean staffing of doctor outpatient departments according to different needs of patients under the varied registration. That is, how much doctors should be arranged for each type of registrations in order to minimize patient waiting time and increase their satisfaction and reduce operating costs.
In general, different patients in a hospital have different expected waiting time when they are queuing and here are several factors affecting it. First, people with different personality have different expectation of waiting time. Character is the factor that influences patients’ emotion themselves. The expected waiting time of patients who have urgent character is much shorter than the patients who have slow character. Second, it depends on patients’ different conditions. Usually, the expected waiting time of patients who have serious illness is much shorter than the patients whose illness is lighter. But it does not adapt to all patients absolutely and the length of expected waiting time is different from person to person. If patients’ actual waiting time exceeds the length of expected waiting time, the patients will produce bad emotion such as anxiety and discontent. So we divide patient satisfaction degree into three levels: satisfaction (the value is equal to 1), dissatisfaction, and very dissatisfaction (the value is equal to 0). We make survey of the patients in a high-level hospital in Harbin and collect data through the way of interview and questionnaire. And then arrange the data to draw the figure of patient waiting time distribution in the same satisfaction degree, as shown in Figures
The distribution of waiting time under satisfaction level.
The distribution of waiting time under dissatisfaction level.
The distribution of waiting time under very dissatisfaction level.
About patients’ satisfaction level, the following points should be noted. The hospital is a special service agency; its service system is different from dining hall or bank and its process is more complicated. Patients can choose any type of registration for treatment, so after receiving the first service from one doctor outpatient department, the patients are likely to go to other service systems such as pharmacy and radiology and, then through the queuing, wait to receive service again and finally they may leave or go back to the first queuing system. In this paper, the satisfaction level of patients we study only refers to the fact that patients produce negative emotions when they get into queuing system for the first time. In the whole process of treatment, patients not only have to queue for many times, but also through a number of staff positions in hospital. So the factors that influence patient satisfaction degree not only contain the length of waiting time at the first time entering into queuing system, but also will be affected by other aspects of service quality. This paper highlights the number of doctor outpatient departments for every type of registration ignoring other factors and only considers the influence that the length of waiting time brings to patient satisfaction for the first time of queuing.
If the number of doctor outpatient departments has irrational allocation for every type of registration, it will not only make patients wait long time, but also affect the doctor work’s efficiency and accuracy. On one hand, if more doctor outpatient departments are opened, it will greatly shorten the waiting time of patients, but it increases operating costs of the hospital and causes the waste of doctor resources. On the other hand, if setting up the low cost as the center goal of hospital and reducing the number of doctor outpatient departments, it will lead to serious queuing phenomenon of patients and increase the doctors’ workload. As a result, it will let the misdiagnosis rate rise because of no time to rest for doctors and ultimately affect patient satisfaction. What is more, it can make the relationship between doctor and patient become more nervous.
The major research of customer satisfaction is the relationship between their psychological characteristics and activities; thus human behavior characteristics should be mainly considered to improve the customer satisfaction. There are many valuable researches about human behavior. Zhihong et al. [
The environment of hospitals, staff service attitude, and the length of waiting time can affect patient satisfaction. This paper analyzes patient and doctor behavior characteristics by using the theory of behavior science and then establishes patient satisfaction function of waiting time.
People’s perception of behavior and satisfaction is fuzzy and uncertain. The prospect theory has great advantage to describe people behavior characteristics; we can accurately build descriptive model through analyzing patient satisfaction degree based on this theory. However, the prospect theory lacks mathematical theory to support. Fuzzy theory has good mathematical theory basis, but it cannot accurately describe patient behavior characteristics. So we combined the two methods effectively to establish patient satisfaction function.
Prospect theory combines psychology with economics effectively and uses the value function to represent policymakers’ subjective value. Its core is the selection of reference point. The evaluation of effectiveness about prospect theory is based on the reference point
The value function diagram.
When patient’s actual waiting time is longer than expected waiting time (reference point
The value function transports the surface value into decision value. This paper treats the expected waiting time of patient as a reference point because patients pay more attention to the value of difference between expected waiting time and actual waiting time rather than the result itself. According to the prospect theory which Kahneman and Tversky [
As the patient’s perception of events is fuzzy and uncertain and the prospect theory can only describe this uncertainty qualitatively, it cannot make decision accurately. So this paper uses the membership function of fuzzy theory to obfuscate objective function. The specific steps are as follows.
In the end, the satisfaction membership function can be established, as in the following formula. Figure
The satisfaction membership function diagram of patient
According to formula (
Hospital managers need to adjust the number of doctor outpatient departments according to patients’ number and their registration type in order to improve patient satisfaction and reduce operating costs. Hospital belongs to service-oriented industry, and its highest goal is patient satisfaction. Thus, the problem can be described as maximizing patient satisfaction for the main goal and minimizing operating costs for the secondary goal. So it is a multiobjective scheduling problem. We can use a triple
Patients can choose different types of registration according to their own conditions and demands. The service level is different under each type of registration (usually, the doctors of specialist-clinic have higher qualification and rich experience). As this paper focuses on solving the optimal scheduling problem of doctor outpatient departments, we make the following description.
The treatment process diagram of patient
A, B, and C respectively represent general-clinic, specialist-clinic, and emergency-clinic.
Each patient should choose the appropriate registration type according to their own actual situation to accept service in doctor outpatient departments, so there is constraint of using different registration types. Let
The hospital’s ultimate target is to make profit as a service-oriented institution. For hospitals, the goal is to reduce operating costs as far as possible, but it is not a major one. The service quality is directly related to performance of hospital. If patients produce bad emotion because of long waiting time, it will influence the revenue of hospital. So improving patient satisfaction is the most important. Patient satisfaction is affected by many factors, but this article focuses on the waiting time that patient enters into the queuing system at first time, ignoring the interference of other factors. The first goal is to maximize patient satisfaction and we use the formula
Each patient must select only one doctor outpatient department to get service.
Do not consider the case that the patients go back to the queuing system for the second time.
The patients will leave when waiting time exceeds a certain range.
Each type of registration follows the principle of FCFS and the patients cannot change the queue when they selected.
Treating doctor outpatient departments scheduling problem as parallel machine scheduling problem with different speed, we establish the following models:
The corresponding mathematical models are as follows:
In this model, formula (
Since this problem about optimal scheduling of doctor outpatient departments belongs to the multiobjective combinatorial optimization. The number of combinations has an exponential relationship with the number of patients, so using the traversal method to search results is not feasible. In our article, the plant growth simulation algorithm (PGSA) is used to solve this problem. PGSA is the algorithm which applies the rules of plant phototropism into solving optimal scheduling problem. This algorithm compares the feasible region of optimal problem to plant growth environment and it compares global optimum solution to light which the plant requires to grow. So it can simulate the plant phototropism growth rules and then build growth model of tree trunks and branches under the action of different morphactins. In recent years, many scholars put PGSA into different research areas and have received satisfactory results. Such as Xuping et al. [
Firstly, we number the patients and then encode them according to the way of real number. An array shows a treatment plan and the length of array is
The coding example.
3 | 4 | −1 | 6 | 8 | −2 | 7 | 10 | 2 | 5 | −3 | 1 | 9 |
We assume the growth process of plant including roots, trunks, and branches. The initial feasible solution
In the formulas,
A survey has been carried out in a high-level hospital in Harbin, China, and the goal is to make the optimal scheduling of doctor outpatient departments for the peak attendance period (8:00–10:00). The total number of doctor outpatient departments is 10, and the general-clinic’s number is 4, the specialist-clinic’s number is 3, and the emergency-clinic’s number is 3. The average service time of general-clinic is 10 minutes and the service rate is 6 persons per hour; the average service time of specialist-clinic is 20 minutes and the service rate is 3 persons per hour and the average service time of emergency-clinic is 8 minutes and the service rate is 7.5 persons per hour. The total number of patients under this period is 112. The arrival rate of patients is
Optimization results.
Category | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
General-clinic | Specialist-clinic | Emergency-clinic | ||||||||
Number | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 1 | 2 | 3 |
State | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
The number of patients | 21 | 21 | 20 | 0 | 12 | 12 | 13 | 13 | 0 | 0 |
The row of “State” represents whether the doctor outpatient department is open. “1” indicates that it is open and “0” indicates that it is closed.
In order to analyze the performance of PGSA, we compare results in Table
The comparative analysis results of PGSA and GA.
Algorithm | The number of general-clinics | The number of specialist-clinics | The number of emergency-clinics | Satisfaction degree | Running time of CPU |
---|---|---|---|---|---|
GA | 3 | 2 | 2 | 0.88 | 75 |
PGSA | 3 | 3 | 1 | 0.92 | 68 |
The optimal solution of convergence.
The results’ simulation shows that setting appropriate number of doctor outpatient departments under different types of clinics can improve patient satisfaction effectively and reduce hospital operating costs at the same time and then achieve excellent management. Thus, adjusting the doctor outpatient departments’ quantity under different types of clinics according to dynamic periods is very necessary choice in hospital.
Patients are main part of hospital, so it is very significant to improve patients’ satisfaction. In this paper, an optimal scheduling strategy has been designed for the problem of patients queuing in the hospital. Firstly, the patient behavioral characteristics are analyzed, and then the patient membership functions and basic model are built to make optimal scheduling for doctor outpatient departments. Secondly, PGSA is used to solve this problem. Comparing with traditional algorithm GA, it takes less time to find the optimal solution which has better stability. The PGSA can solve optimal scheduling of doctor outpatient departments effectively in order to increase patient satisfaction and at the same time reduce operating costs in hospital. Finally, the simulation results of an example have proved the correctness and validity of the model and PGSA we designed. The paper focuses on different types of registrations without considering the different types of doctor outpatient departments. In the future, different types of doctor outpatient departments as a variable will be added in order to make the research of this problem close to reality greatly.
The authors declare that they have no competing interests.
This work is supported by the National Nature Science Foundation of China (71371061) and Postdoctoral Foundation of Heilongjiang Province (LBH-Z15108).