Remote consultation appointment scheduling optimization method and system in uncertain environment

Abstract

The invention relates to the technical field of remote medical treatment, and provides a remote consultation appointment scheduling optimization method and system in an uncertain environment. In the optimization method, the non-punctuality of experts in a superior hospital and the randomness of consultation service time are combined, the non-punctuality condition of the experts is analyzed, non-punctuality constraint conditions of the experts and a remote consultation appointment scheduling model based on stochastic programming are constructed, and meanwhile, uncertain factors in the scheduling distribution process are combined, so that the remote consultation appointment scheduling of the experts in the superior hospital is optimized. The method comprises the following steps of: linearizing an unpunctuality constraint condition, converting a random type remote consultation appointment scheduling model into a determined type mixed integer programming model by combining a sample average approximation method, and further solving the determined type mixed integer programming model based on input parameters of different subjects, so as to obtain an appointment scheduling result. And determining a globally optimal consultation scheduling distribution scheme of the remote consultation application.

Description

Technical Field

[0001] The present application relates to the field of telemedicine technology, and in particular to a method and system for optimizing remote consultation appointment scheduling in an uncertain environment. Background Art

[0002] With policy guidance and the development of communication technology, telemedicine has developed rapidly. As an emerging medical model in the "Internet +" era, telemedicine has played its own advantages, enabling patients to receive precise remote guidance for diagnosis and treatment, and effectively improving the diagnosis and treatment rate in areas with relatively backward medical resources.

[0003] As the coverage of telemedicine services gradually expands, the service model becomes more mature, and the service volume increases, good operation management has become a favorable guarantee for the high-quality development of telemedicine. Remote consultation is the main service form in telemedicine. Grassroots doctors and patients, as the applicants, apply to the telemedicine center for remote consultation services. The telemedicine center formulates a scheduling plan based on the arrangements of expert doctors. As the number of applications continues to expand, formulating a reasonable remote consultation appointment scheduling plan has become the key to improving resource utilization and patient satisfaction for telemedicine centers. Summary of the invention

[0004] The purpose of the present application is to provide a remote consultation appointment scheduling optimization method and system in an uncertain environment to solve or alleviate the problems existing in the above-mentioned prior art.

[0005] In order to achieve the above objectives, this application provides the following technical solutions:

[0006] The present application provides a remote consultation appointment scheduling optimization method in an uncertain environment. Based on the unpunctuality of experts in superior hospitals, the remote medical center schedules and allocates the remote consultation applications submitted by the grassroots hospitals, including: step S101, determining the unpunctuality of experts according to the relationship between the appointment consultation start time, the actual consultation service start time, the actual consultation service end time, and the actual arrival time of experts of two adjacent patients, and constructing the unpunctuality constraint of experts; step S102, constructing a remote consultation appointment scheduling model based on random programming according to the unpunctuality of experts; step S103, linearizing the unpunctuality constraint, and converting the random programming remote consultation appointment scheduling model into a mixed integer programming model based on the sample average approximation method according to the linearized unpunctuality constraint; step S104, according to the total number of consultation departments N determined by the remote medical center, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n corresponding to the appointment allocation time slot j n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the specialist for the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the ith patient determined by the grassroots hospital and the total number of patients I, and based on the mixed integer programming model, determine the consultation scheduling allocation plan for the remote consultation application submitted by the grassroots hospital.

[0007] Preferably, in step S101, the expert's unpunctuality constraint is constructed:

[0008]

[0009] In the formula, s j+1 The idle time of the consultation room after the consultation service of the patient assigned to the appointment time slot j+1 is completed; a j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The time interval of k; among them, the patient with the scheduled allocation time slot j and the patient with the scheduled allocation time slot j+1 are two adjacent remote consultation patients; j The scheduled consultation start time A of the patient assigned time slot j for the appointment j The actual consultation service start time B j The time interval; j The actual consultation service time of the patient assigned time slot j for the appointment; k j+1 The scheduled consultation start time A of the patient assigned time slot j+1 for the appointment j+1 The actual consultation service start time B j+1 The time interval; μ j The scheduled consultation start time A of the patient assigned time slot j for the appointment j Arrival time with experts R j The time interval; w j The arrival time R of the expert who assigns time slot j to the appointment j The actual consultation service end time E j The time interval v j+1 The scheduled consultation start time A of the patient assigned time slot j+1 to the appointment j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

[0010] Preferably, in step S102, the remote consultation appointment scheduling model of random planning is:

[0011]

[0012] Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, and J is the total number of the appointment allocation time slots; The penalty cost coefficient for not assigning a consultation to the patient who requested the i-th remote consultation; x i Assign the result of the remote consultation to the i-th patient, x, a, and ξ are the patient’s allocation result, the allocated appointment service duration, and the actual consultation service time, respectively; The waiting cost coefficient for the patient who requested the i-th remote consultation; l ij Indicates whether the patient who requested the i-th remote consultation is assigned to the appointment allocation time slot j; k j (ω) is the actual waiting time of the patient assigned to the appointment time slot j under the unpunctual situation ω; The waiting cost coefficient of the expert who allocates time slot j for the appointment; w j (ω) is the actual waiting time of the expert assigned to the appointment time slot j under the unpunctual situation ω; c o is the expert's overtime cost coefficient; O(ω) is the consultation service overtime time within the consultation scheduling cycle under the unpunctual situation ω; c s is the idle cost coefficient of the consultation room; s j (ω) is the idle time of the consultation room after the patient service of the appointment allocated time slot j is completed in the said unpunctual situation ω.

[0013] Preferably, the conditional constraints of the remote consultation appointment scheduling model of random planning include: decision constraints, the unpunctuality constraints and time slot constraints; wherein the decision constraints are:

[0014]

[0015] Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, J is the total number of the appointment allocation time slots; a i The appointment service time allocated to the patient who applied for the remote consultation, D is the total service time in the consultation scheduling cycle, l ij Whether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j, x i The remote consultation allocation result for the patient who applied for the remote consultation, a j The appointment service duration of the patient assigned time slot j for the appointment; θ n (j) the minimum guaranteed service duration of department n corresponding to the appointment allocation time slot j determined by the telemedicine center;

[0016] The time slot constraints are:

[0017]

[0018] Where O(ω) is the consultation service timeout time within the consultation scheduling cycle under the unpunctual situation ω; v J+1 (ω) is the waiting time of the patient and the expert in the appointment allocation time slot J+1 without considering the expert's unpunctuality; w1(ω) is the actual waiting time of the expert in the first appointment allocation time slot under the unpunctual situation ω; μ1(ω) is the unpunctuality time of the expert in the first appointment allocation time slot under the unpunctual situation ω; k1(ω) is the actual waiting time of the patient in the first appointment allocation time slot under the unpunctual situation ω; v1(ω) is the waiting time of the patient and the expert in the first appointment allocation time slot under the unpunctual situation ω without considering the expert's unpunctuality; s j (ω) is the idle time of the consultation room after the patient service of the appointment time slot j is completed under the unpunctual situation ω, k j (ω) is the actual waiting time of the patient with the appointment allocated time slot j under the unpunctual situation ω, w j (ω) is the actual waiting time of the expert assigned to the appointment time slot j under the unpunctual situation ω; v j (ω) is the waiting time of the patient and the specialist for the appointment assigned to time slot j without considering the lateness in the lateness scenario ω.

[0019] Preferably, in step S103, the non-punctuality constraint condition is linearized to obtain a linear non-punctuality constraint condition; wherein the linear non-punctuality constraint condition is:

[0020]

[0021] Where i is the patient serial number of the remote consultation application, I is the total number of patients in the remote consultation application; s j+1 (ω) is the idle time of the consultation room after the consultation service of the patient with the appointment allocated time slot j+1 under the unpunctual situation ω is completed; a j The scheduled consultation start time A of the patient assigned time slot j for the appointment j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The time interval of the appointment allocation time slot j and the appointment allocation time slot j+1 are two adjacent remote consultation patients; k j+1 (v) is the scheduled consultation start time A of the patient whose scheduled time slot j+1 is assigned in the unpunctual situation ω j+1 The actual consultation service start time B j+1 The time interval k j(ε) The scheduled consultation start time A of the patient assigned time slot j to the appointment j The actual consultation service start time B j The time interval; ij Indicates whether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j; ξ i (ω) is the actual consultation service time of the patient who applied for the i-th remote consultation under the said unpunctual situation ω; w j (ω) is the expert arrival time R of the patient assigned to the appointment time slot j under the unpunctual situation ω j The actual consultation service end time E j The time interval; μ j (ω) is the scheduled consultation start time A of the patient assigned time slot j under the unpunctual situation ω j Arrival time with experts R j The time interval v j+1 (ω) is the scheduled consultation start time A of the patient in the scheduled allocation time slot j+1 under the unpunctual situation ω j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

[0022] Preferably, the teleconsultation sample data of the telemedicine center is sampled by Monte Carlo simulation; according to the sampling results and the linear non-time-keeping constraints, the remote consultation appointment scheduling model of random programming is converted into a mixed integer programming model based on the sample average approximation method.

[0023] Preferably, the mixed integer programming model is:

[0024]

[0025] Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, and J is the total number of the appointment allocation time slots; is the unassigned penalty cost coefficient for the patient who applied for the ith remote consultation; Z is the number of samples sampled in the Monte Carlo simulation, and z is the serial number of the sampled sample in the Monte Carlo simulation; The waiting cost coefficient of the patient who applied for the i-th remote consultation determined by the grassroots hospital; It is a constructed decision variable and has no practical significance; The waiting cost coefficient of the expert for the appointment allocation time slot j determined by the superior hospital c is the actual waiting time of the expert in the appointment allocation time slot j at the sampling time z;o is the expert’s overtime cost coefficient, c is the service timeout time of the reserved allocation time slot J+1 at the sampling time z; s is the idle cost coefficient of the clinic; The free time of the consultation room after the consultation service of the patient in the appointment allocation time slot j at the sampling sample z is completed.

[0026] Preferably, in step S104, according to the formula:

[0027]

[0028] Determine the total number of appointment time slots J; where D is the total service time in the consultation scheduling cycle, j is the appointment allocation time slot, θ n (j) is the minimum guaranteed service time of department n determined by the telemedicine center; based on the mixed integer programming model, according to the total number of appointment time slots J, the teleconsultation scheduling allocation plan for the teleconsultation application submitted by the grassroots hospital is determined by enumeration method and Benders decomposition algorithm.

[0029] The embodiment of the present application also provides a remote consultation appointment scheduling optimization system in an uncertain environment, in which the remote medical center schedules and allocates the remote consultation applications submitted by the grassroots hospitals based on the unpunctuality of the experts in the superior hospitals, including: a non-punctuality analysis unit, configured to determine the unpunctuality of the experts and construct the unpunctuality constraint conditions of the experts according to the relationship between the appointment consultation start time, the actual consultation service start time, the actual consultation service end time, and the actual arrival time of the experts of two adjacent patients; a random model unit, configured to construct a remote consultation appointment scheduling model based on random planning according to the unpunctuality of the experts; a model conversion unit, configured to linearize the unpunctuality constraint conditions, and based on the linearized unpunctuality constraint conditions, convert the remote consultation appointment scheduling model of random planning into a mixed integer programming model based on the sample average approximation method; a scheduling allocation unit, configured to calculate the total number of consultation departments N, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n in the appointment allocation time slot j determined by the remote medical center. n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the expert in the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the ith patient determined by the grassroots hospital and the total number of patients I, and based on the mixed integer programming model, determine the consultation scheduling allocation plan for the remote consultation application submitted by the grassroots hospital.

[0030] Beneficial effects:

[0031] The embodiment of the present application provides a remote consultation appointment scheduling optimization method under an uncertain environment. Based on the unpunctuality of experts in superior hospitals, the remote medical center schedules and allocates the remote consultation applications submitted by grassroots hospitals. First, according to the relationship between the appointment consultation start time, the actual consultation service start time, the actual consultation service end time, and the actual arrival time of the experts of two adjacent patients, the unpunctuality of the experts is determined, and the unpunctuality constraint of the experts is constructed; and, according to the unpunctuality constraint of the experts, a remote conference appointment scheduling model based on random programming is constructed; then, the unpunctuality constraint is linearized, and according to the linearized unpunctuality constraint, the random programming remote consultation appointment scheduling model is converted into a mixed integer programming model based on the sample average approximation method; finally, according to the total number of consultation departments N determined by the remote medical center, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n in the appointment allocation time slot j n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the specialist in the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the i-th patient determined by the grassroots hospital As well as the total number of patients I, based on the mixed integer programming model, the consultation scheduling allocation plan for remote consultation applications submitted by grassroots hospitals is determined.

[0032] Therefore, combining the unpunctuality of experts in superior hospitals and the randomness of consultation service time, the unpunctuality of experts is analyzed, and the unpunctuality constraints of experts and the remote consultation appointment scheduling model based on random programming are constructed. At the same time, combined with the uncertain factors in the scheduling allocation process, the unpunctuality constraints are linearized, and combined with the sample average approximation method, the random remote consultation appointment scheduling model is transformed into a deterministic mixed integer programming model. Then, based on the input parameters of different subjects, the deterministic mixed integer programming model is solved to determine the globally optimal consultation scheduling allocation plan for remote consultation applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings constituting part of the present application are used to provide a further understanding of the present application. The exemplary embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. Among them:

[0034] Figure 1 A flowchart of a remote consultation appointment scheduling optimization method in an uncertain environment provided according to some embodiments of the present application;

[0035] Figure 2 A schematic diagram of a remote consultation process provided according to some embodiments of the present application;

[0036] Figure 3 A schematic diagram of a non-punctual time window provided according to some embodiments of the present application;

[0037] Figure 4 A schematic diagram of analyzing a situation of being late according to some embodiments of the present application;

[0038] Figure 5 Optimal cost and appointment allocation service duration for different numbers of patients provided according to specific embodiments of the present application;

[0039] Figure 6 Total costs and scheduling solutions under different expert waiting cost coefficients provided according to a specific embodiment of the present application;

[0040] Figure 7 This is a schematic diagram of the structure of a remote consultation appointment scheduling optimization system in an uncertain environment provided according to some embodiments of the present application. DETAILED DESCRIPTION

[0041] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present application and does not limit the present application. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present application without departing from the scope or spirit of the present application. For example, a feature shown or described as a part of an embodiment may be used in another embodiment to produce yet another embodiment. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the embodiments of the present invention should belong to the scope of protection of the embodiments of the present invention.

[0042] In remote consultation, existing research mainly focuses on appointment scheduling issues in outpatient or operating room scenarios, such as considering random service times, patient lateness, or patient cancellation. There is a lack of research on appointment scheduling for remote consultation operation scenarios in uncertain environments.

[0043] The uncertainty factors in the remote consultation operation scenario are the key and difficult points of the medical system appointment scheduling problem, and are important factors affecting the optimization of remote consultation appointment scheduling. They are mainly manifested in the uncertainty of doctor's behavior and the uncertainty of service time. Among them, the uncertainty of doctor's behavior is mainly manifested in the unpunctuality of doctors from superior hospitals during remote consultation. Doctors and patients from grassroots hospitals, as the parties seeking help, often arrive in advance and wait, and will not be unpunctual.

[0044] Based on this, this application proposes a remote consultation appointment scheduling optimization method under an uncertain environment. According to the actual operation scenario of remote consultation, the random arrival time and random service duration of expert doctors in the remote consultation process are considered. The goal is to minimize the unallocated cost of consultation applications, the waiting cost of doctors in primary hospitals, the waiting cost of experts in superior hospitals, the idle cost of remote consultation clinics, and the overtime cost of experts. A two-stage random planning remote consultation appointment scheduling model is established and solved to determine the number of consultation application allocations, appointment order, and appointment interval. At the theoretical level, it expands the research on remote consultation appointment scheduling issues in the field of medical system operation and management, and at the practical level, it provides theoretical support and decision-making references for telemedicine center staff, thereby improving the efficiency of telemedicine operations.

[0045] The optimization method for remote consultation appointment scheduling in this uncertain environment is based on the fact that experts from higher-level hospitals are not punctual. The telemedicine center schedules and allocates the remote consultation applications submitted by grassroots hospitals, such as Figure 1 As shown, the method includes:

[0046] Step S101, according to the relationship between the scheduled consultation start time, the actual consultation service start time, the actual consultation service end time and the actual arrival time of the expert of two adjacent patients, determine the expert's unpunctuality situation and construct the expert's unpunctuality constraint condition.

[0047] Different from the outpatient and operating room scheduling problems in traditional medical operation management, telemedicine consultation requires the collaboration of expert doctors from higher-level hospitals, doctors from grassroots hospitals, and telemedicine center platforms. Figure 2 As shown, the doctor of the grassroots hospital first submits a remote consultation application on the system and uploads the patient's case information. The doctor of the grassroots hospital proposes the required department of the superior hospital. After receiving the remote consultation application, the telemedicine center platform schedules and arranges the remote consultation application submitted by the grassroots hospital based on the current resource allocation of the superior hospital.

[0048] On the day of the teleconsultation, doctors at primary hospitals and experts at higher-level hospitals conduct teleconsultation via communication equipment and medical auxiliary equipment in the teleconsultation clinics of their respective hospitals. After the consultation, experts at higher-level hospitals fill out a written diagnosis and upload it to the telemedicine center platform, and doctors at primary hospitals view the consultation report through the telemedicine center platform.

[0049] In this application, I is defined as the total number of patients applying for remote consultation, and D is defined as the total service time within each consultation scheduling cycle. The staff of the telemedicine center completes the scheduling arrangements before each consultation cycle. All remote consultations are conducted in the same remote consultation clinic. Experts from higher-level hospitals need to arrive at the remote consultation clinic for consultation from their current positions (outpatient clinic, inpatient rounds, surgery, etc.) at the appointment time. Since there is a great deal of uncertainty in the end of the current work of the experts, it is inevitable that the experts will not be punctual in arriving at the remote consultation clinic; and the grassroots hospitals, as the party seeking assistance, will prepare for the consultation in advance at the appointment time.

[0050] Due to the limitation of daily opening hours of teleconsultation clinics, the Telemedicine Center needs to decide whether to arrange teleconsultation for each patient. If the patient chooses not to arrange it, the patient can continue to make an appointment for the next consultation cycle. If the patient chooses to arrange it, the patient's specific consultation time and scheduled consultation duration will be arranged, and all patients who choose to arrange it will be sorted.

[0051] In this application, J is defined as the total number of all time slots after sorting. Each patient is scheduled for one time slot. Obviously, the total number of patients I is greater than or equal to the total number of appointment allocation time slots J. Definition A j is the appointment start time of the patient (and specialist) scheduled to the appointment allocation time slot j, R j The actual arrival time of the expert assigned to time slot j for the appointment.

[0052] After sorting all the patients who choose to be scheduled, the patient who is assigned to the time slot j will arrive on time as the help-seeking party. The unpunctuality of the expert in the superior hospital is defined as the actual arrival time R of the expert j The appointment consultation starts at A j The difference is denoted as: μ j =R j -A j That is, μ j is the random variable for the expert's lateness in the appointment allocation time slot j. If the expert arrives earlier than the appointment time, then μ j <0, if the expert is late for the appointment, then μ j >0. Here, μ is defined j and are the early arrival time and late arrival time of the expert who is assigned to the appointment time slot j in the unpunctual time window, such as Figure 3 shown.

[0053] In this application, we define w j The actual waiting time of the expert assigned to the appointment time slot j is the arrival time R of the expert assigned to the appointment time slot j. j The actual consultation service end time E j time interval; define kj The actual waiting time for patients assigned to time slot j is the start time of the appointment consultation for patients assigned to time slot j. j The actual consultation service start time B j The time interval; define s j The idle time of the consultation room after the service of the patient assigned to the appointment time slot j is completed; define v j+1 is the waiting time of the patient and the expert for the appointment slot j+1 without considering the expert's lateness (when not considering lateness, the waiting time of the patient and the expert is the same), that is, the appointment consultation start time A of the patient for the appointment slot j+1 j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j Then, the decision variables are described as follows:

[0054]

[0055] According to the patient's actual consultation service end time E j 、The patient's scheduled consultation start time A j and the actual arrival time of the expert R j The different sequences of waiting time and idle time are divided into 6 different types of unpunctuality, such as Figure 4 shown.

[0056] The first unpunctual situation (i.e., situation 1) describes the service end time E of the patient whose appointment is assigned time slot j. j The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1 and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 , and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1 , that is, E j >R j+1 >A j+1 In the first case of non-punctuality, the relationship between the decision variables is:

[0057]

[0058] In the formula, a j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The patient with the scheduled time slot j and the patient with the scheduled time slot j+1 are two adjacent remote consultation patients. j+1The actual waiting time for the patient assigned to time slot j+1 is the start time of the appointment consultation for the patient assigned to time slot j+1. j+1 The actual consultation service start time B j+1 The time interval; j The actual consultation service time for the patient assigned time slot j for the appointment; w j+1 The actual waiting time of the expert assigned to the appointment time slot j+1, that is, the arrival time R of the expert assigned to the appointment time slot j+1 j+1 The actual consultation service end time E j+1 time interval; The late arrival time in the unpunctual time window of the expert assigned to the appointment time slot j+1; s j+1 The idle time of the consultation room after the consultation service of the patient with appointment time slot j+1 is completed. The actual consultation service time of the patient with appointment time slot j is:

[0059]

[0060] In the formula, l ij Indicates whether the patient applying for remote consultation i is assigned to the appointment allocation time slot j, ξ i The actual teleconsultation service time for the patient who requested the i-th teleconsultation.

[0061] The second unpunctuality scenario (i.e., scenario 2) describes the service end time E of the patient whose scheduled allocation time slot j is j The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1 and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 , and the actual arrival time R of the expert assigned to time slot j+1 j+1 The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 , that is, E j >A j+1 >R j+1 In the second case of non-punctuality, the relationship between the decision variables is:

[0062]

[0063] In the formula, μ j+1 The early arrival time in the unpunctual time window of the expert who is assigned time slot j+1 for the appointment.

[0064] The third unpunctual situation (i.e., situation 3) describes the service end time E of the patient whose appointment is assigned time slot j. j The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1, and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 The service end time E of the patient who is later than the appointment allocation time slot j j and the appointment start time A of the patient whose appointment is assigned to time slot j+1 j+1 , that is, R j+1 >E j >A j+1 In the third case of non-punctuality, the relationship between the decision variables is:

[0065]

[0066] The fourth unpunctuality scenario (i.e., scenario 4) describes the service end time E of the patient whose appointment is assigned time slot j. j The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 , and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 , that is, A j+1 >R j+1 >E j In the fourth case of lateness, the relationship between the decision variables is:

[0067]

[0068] The fifth unpunctuality scenario (i.e., scenario 5) describes the service end time E of the patient whose appointment is assigned time slot j. j The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 , and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1 , that is, R j+1 >A j+1 >E j In the fifth case of non-punctuality, the relationship between the decision variables is:

[0069]

[0070] The sixth unpunctuality scenario (i.e., scenario 6) describes the service end time E of the patient whose appointment is assigned time slot j. j The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 , and the actual arrival time R of the expert who reserved the allocation time slot j+1 j+1 The service end time E of the patient who is earlier than the appointment allocation time slot j jand the appointment start time A of the patient whose appointment is assigned to time slot j+1 j+1 , that is, A j+1 >E j >R j+1 In the sixth case of non-punctuality, the relationship between the decision variables is:

[0071]

[0072] It can be seen that in cases 1 to 3, the service end time E of the patient with scheduled time slot j is j The appointment start time A of the patient who is later than the appointment allocation time slot j+1 j+1 , in cases 4 to 6, the service end time E of the patient whose appointment is assigned to time slot j j The appointment start time A of the patient who is earlier than the appointment allocation time slot j+1 j+1 Based on the above analysis of the expert's unpunctuality, the expert's unpunctuality constraints are constructed:

[0073]

[0074] In the formula, s j+1 The idle time of the consultation room after the consultation service of the patient assigned to the appointment time slot j+1 is completed; a j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The time interval of k; among them, the patient with the scheduled allocation time slot j and the patient with the scheduled allocation time slot j+1 are two adjacent remote consultation patients; j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The actual consultation service start time B j The time interval; j The actual consultation service time for the patient assigned time slot j for the appointment; k j+1 The appointment start time A of the patient assigned to the appointment slot j+1 j+1 The actual consultation service start time B j+1 The time interval; μ j The scheduled consultation start time A for the patient assigned to the appointment time slot j j Arrival time with experts R j The time interval; w j The arrival time R of the expert who assigns the appointment to time slot j j The actual consultation service end time E j The time interval v j+1 The appointment start time A of the patient assigned to the appointment slot j+1 j+1The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

[0075] Step S102: According to the expert's unpunctuality, a remote consultation appointment scheduling model based on stochastic planning is constructed.

[0076] By analyzing the experts' unpunctuality, we know that the scheduled consultation start time A of the patient with scheduled time slot j is j The actual consultation service start time B j The time interval k j represents the waiting time of the patient in the appointment allocation time slot j before receiving the consultation service; the arrival time R of the expert in the appointment allocation time slot j j The actual consultation service end time E j The time interval w j The waiting time before the expert with appointment time slot j provides consultation services to the patient with appointment time slot j; the appointment start time A of the patient with appointment time slot j+1 j+1 That is, the appointment end time of the patient assigned to time slot j. If the actual consultation service end time E of the last remote consultation (i.e., the patient assigned to time slot J) is J If it is later than the appointment end time, a timeout will occur. For this, the following definitions are made:

[0077] O=(E J -A J+1 ) + =v J+1

[0078] In the formula, A J+1 The appointment start time for the patient assigned to the appointment slot J+1, v J+1 The waiting time of the patient and the expert in the appointment allocation time slot J+1 without considering the expert's lateness, that is, the appointment consultation start time A of the patient in the appointment allocation time slot J+1 J+1 The actual consultation service end time E of the patient with the appointment allocation time slot J J It should be noted that the appointment allocation time slot J+1 is virtual data that does not actually exist, representing the time period after the last patient's remote appointment consultation ends, which is later than the appointment end time. Here, the timeout time period is equivalently expressed as the time that the patient in the virtual appointment allocation time slot J+1 needs to wait.

[0079] Establish a remote consultation appointment scheduling model based on two-stage stochastic programming:

[0080]

[0081] Where i is the serial number of the patient applying for remote consultation, I is the total number of patients applying for remote consultation; j is the appointment allocation time slot, and J is the total number of appointment allocation time slots; The penalty cost coefficient for not being assigned a consultation for the patient who requested the i-th remote consultation; x i Assign the result of the remote consultation to the i-th patient, x, a, and ξ are the patient’s allocation result, the allocated appointment service duration, and the actual consultation service time, respectively; The waiting cost coefficient for the patient who requested the i-th remote consultation; l ij Indicates whether the patient who requested the i-th remote consultation is assigned to the appointment allocation time slot j; k j (ω) is the actual waiting time for patients with appointments assigned to time slot j under the unpunctuality scenario ω; The waiting cost coefficient of the expert who allocates time slot j to the appointment; w j (ω) is the actual waiting time of the expert who makes an appointment for time slot j under the unpunctual situation ω; c o is the expert's overtime cost coefficient; O(ω) is the consultation service overtime time within the consultation scheduling cycle under the condition of non-punctuality; c s is the idle cost coefficient of the consultation room; s j (ω) is the idle time of the consultation room after the patient with appointment assigned to time slot j is served in the case of non-punctuality.

[0082] In this application, first, the first stage decides whether each patient is scheduled, the duration of the consultation appointment scheduled for each patient, and the order of the patients (i.e., the patient's consultation location or consultation time slot), which represents the comprehensive cost of minimizing the unallocated penalty cost and the expected cost of the second stage decision. Then, the second stage decides the waiting time of the expert, the waiting time of the patient, the idle time of the clinic, and the overtime time under different circumstances, which represents the sum of minimizing the waiting cost of the expert, the waiting cost of the patient, the idle cost of the clinic, and the overtime cost of the expert.

[0083] Here, the first stage of the random planning remote consultation appointment scheduling model is limited by decision constraints to determine the patient's consultation allocation result (allocated or not allocated), the allocated consultation appointment duration, and the consultation time slot. Specifically, the decision constraints are:

[0084]

[0085] Where i is the serial number of the patient applying for remote consultation, I is the total number of patients applying for remote consultation; j is the appointment allocation time slot, J is the total number of appointment allocation time slots; a i The appointment service time allocated to the patient who applied for the i-th remote consultation, D is the total service time in the consultation scheduling cycle, l ijWhether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j, x i The remote consultation allocation result for the patient who requested the i-th remote consultation, a j The appointment service time of the patient assigned to the appointment time slot j. Among them, constraint (1) indicates that the sum of the appointment allocation time is equal to the total service time in the consultation cycle; constraint (2) indicates that each constraint time slot is allowed to schedule at most one patient; constraint (3) indicates that each patient is allowed to schedule at most one appointment time slot; constraint (4) indicates that the sum of all allocation numbers (i.e., the data of all patients assigned to the appointment allocation time slot) is equal to the number of determined allocations; constraint (5) ensures that the appointment allocation time of each case cannot be less than the minimum service time limit of the corresponding department, thereby ensuring the service quality of each remote consultation; constraints (6) and constraints (7) indicate that their corresponding decision variables are binary variables.

[0086] The second stage of the random planning remote consultation appointment scheduling model is limited by the expert's unpunctuality constraint and time slot constraint to determine the optimal patient consultation allocation plan. Specifically, the time slot constraint is:

[0087]

[0088] Where O(ω) is the consultation service timeout time within the consultation scheduling cycle under the non-punctuality condition ω; v J+1 (ω) is the waiting time of the patient and the specialist in the appointment allocation time slot J+1 without considering the specialist's lateness. It should be noted that the appointment allocation time slot J+1 here is virtual data that does not actually exist.

[0089] w1(ω) is the actual waiting time of the specialist in the first appointment allocation time slot under the unpunctual situation ω; μ1(ω) is the unpunctual time of the specialist in the first appointment allocation time slot under the unpunctual situation ω; k1(ω) is the actual waiting time of the patient in the first appointment allocation time slot under the unpunctual situation ω; v1(ω) is the waiting time of the patient and specialist in the first appointment allocation time slot under the unpunctual situation ω without considering the unpunctuality of the specialist; s j (ω) is the idle time of the consultation room after the patient with appointment slot j is served in the case of non-punctuality, k j (ω) is the actual waiting time of the patient assigned to time slot j under the unpunctual situation ω, w j (ω) is the actual waiting time of the expert who makes an appointment for time slot j under the unpunctual situation ω; v j (ω) is the waiting time of patients and specialists assigned to time slot j in the latent scenario ω without considering latent schedule.

[0090] Among them, the expert's unpunctuality constraint and constraint (8) are the constraint relationships among the expert's waiting time, patient's waiting time, waiting time without considering unpunctuality, clinic idle time and overtime time obtained based on the analysis of unpunctuality. Constraint (9) indicates that if the patient of the first appointment allocation time slot has a waiting time, his waiting time shall not be less than his early arrival time; constraint (10) indicates that if the patient of the first appointment allocation time slot has a waiting time, his waiting time shall not be less than the expert's late arrival time; constraint (11) indicates that the waiting time of the expert and patient of the first appointment allocation time slot without considering the expert's unpunctuality is 0; constraint (12) restricts all decision variables to be non-negative.

[0091] Since patients are heterogeneous, when applying for remote consultation, they will request experts from different departments according to their needs, and the allocated time will also be limited to different minimum service time limits due to the different departments applied for. That is:

[0092]

[0093] In the formula, θ n (j) is the minimum guaranteed service time of department n corresponding to the appointment allocation time slot j determined by the telemedicine center; N is the total number of departments.

[0094] Step S103: linearize the unpunctuality constraint condition, and according to the linearized unpunctuality constraint condition, based on the sample average approximation method, transform the random programming remote consultation appointment scheduling model into a mixed integer programming model.

[0095] In this application, the two uncertain factors of the expert's unpunctual arrival and the random service time are combined, and the remote consultation appointment scheduling model directly through random planning is relatively complicated. In order to transform the remote consultation appointment scheduling model of random planning into a mixed integer linear programming problem, the two-stage model is linearized here. First, the unpunctuality constraint condition is linearized to obtain a linear unpunctuality constraint condition. Specifically, the linear unpunctuality constraint condition is:

[0096]

[0097] In the formula, i is the serial number of the patient applying for remote consultation, I is the total number of patients applying for remote consultation; s j+1 (ω) is the idle time of the consultation room after the consultation service of the patient with appointment allocation time slot j+1 under the unpunctual situation ω is completed; a j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1The time interval of k; among them, the patient with the scheduled allocation time slot j and the patient with the scheduled allocation time slot j+1 are two adjacent remote consultation patients; j+1 (ω) is the scheduled consultation start time A of the patient with scheduled time slot j+1 in the unpunctual case ω j+1 The actual consultation service start time B j+1 The time interval k j (ω) is the scheduled consultation start time A of the patient assigned to time slot j j The actual consultation service start time B j The time interval; ij Indicates whether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j; ξ i (ω) is the actual consultation service time of the patient who applied for the i-th remote consultation under the unpunctual situation ω; w j (ω) is the expert arrival time R of the patient with appointment allocation time slot j under the unpunctual situation ω j The actual consultation service end time E j The time interval; μ j (ω) is the appointment consultation start time A of the patient assigned time slot j in the unpunctual case ω j Arrival time with experts R j The time interval v j+1 (ω) is the scheduled consultation start time A of the patient with scheduled time slot j+1 in the unpunctual case ω j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

[0098] At the same time, construct the decision variable y ij ,use Alternative And add constraints:

[0099]

[0100] Among them, M is a very large positive number. ij (ω) has no actual meaning and is a decision variable constructed to linearize the objective function.

[0101] Then, based on the Sample Average Approximation (SAA) method, sample scenarios are extracted from the probability distribution of uncertain parameters to approximate the expected value of the objective function, so that the stochastic programming problem of the remote consultation appointment scheduling model is reformulated as a deterministic problem.

[0102] Specifically, the remote consultation sample data of the telemedicine center is sampled through Monte Carlo simulation; according to the sampling results and linear non-punctuality constraints, the random planning remote consultation appointment scheduling model is converted into a mixed integer programming model based on the sample average approximation method. Among them, the mixed integer programming model is:

[0103]

[0104] Where i is the serial number of the patient applying for remote consultation, I is the total number of patients applying for remote consultation; j is the appointment allocation time slot, and J is the total number of appointment allocation time slots; is the penalty cost coefficient for the unassigned patient for the i-th remote consultation application; Z is the number of sampling samples for Monte Carlo simulation, and z is the serial number of the sampling samples for Monte Carlo simulation; The waiting cost coefficient of the patient who applied for the i-th teleconsultation determined by the primary hospital; The waiting cost coefficient of the expert in the appointment allocation time slot j determined by the superior hospital; c o is the expert's overtime cost coefficient; c s is the idle cost coefficient of the clinic; It is a constructed decision variable and has no practical significance; The actual waiting time of the expert who made an appointment for time slot j when sampling sample z; The service timeout time for the reserved allocation time slot J+1 for the sample z; The idle time of the consultation room after the consultation service of the patient who made an appointment at time slot j for sample z is completed.

[0105] Step S104: according to the total number of consultation departments N determined by the telemedicine center, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n corresponding to the appointment allocation time slot j n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the specialist in the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the i-th patient determined by the grassroots hospital As well as the total number of patients I, based on the mixed integer programming model, the consultation scheduling allocation plan for remote consultation applications submitted by grassroots hospitals is determined.

[0106] In this application, the goal of consultation scheduling allocation is to minimize the sum of unallocated penalty cost, expert waiting time cost, patient waiting time cost, clinic space time cost and overtime cost.

[0107] First, follow the formula:

[0108]

[0109] Determine the total number of reservation time slots J. Where, represents the integer downward, D is the total service time in the consultation scheduling cycle, j is the appointment allocation time slot, θ n (j) the minimum guaranteed service hours for department n determined by the telemedicine center.

[0110] Then, by enumeration, the total number of appointment time slots J is reduced one by one, and the solution is repeatedly solved to minimize the sum of the unassigned penalty cost, the expert waiting time cost, the patient waiting time cost, the clinic space time cost and the overtime cost. When the sum of costs When it is minimum, the corresponding decision variable is optimal. Among them, the first-stage decision variables are whether each patient is scheduled, the duration of the consultation appointment scheduled for each patient, and the patient ranking (i.e., the patient's consultation location or consultation time slot), which represents the comprehensive cost of minimizing the unallocated penalty cost and the expected cost of the second-stage decision. The decision variables of the second-stage decision are the waiting time of the expert, the waiting time of the patient, the idle time of the clinic, and the overtime time under different circumstances, which represents the sum of minimizing the expert waiting cost, the patient waiting cost, the idle cost of the clinic, and the expert overtime cost.

[0111] In this application, when the scale of the mixed integer programming problem is large, the solution speed is slow. Here, the Benders decomposition algorithm is used to solve the mixed integer programming model to speed up the solution of the model. Specifically, the binary variable l ij As a complex variable, the mixed integer programming model is divided into the main problem and sub-problems:

[0112]

[0113] Among them, there are constraints for the main problem (M-MILP):

[0114]

[0115] For the subproblem (S-MILP), there are constraints:

[0116]

[0117] Introduce the dual variable α corresponding to the constraint of the subproblem (S-MILP), μ j , τ z , z ,Furthermore, the dual subproblem (DS-MILP) can be expressed as:

[0118]

[0119] The dual subproblem (DS-MILP) has constraints:

[0120]

[0121] When solving, first, initialize the effective upper bound UB of the original problem to positive infinity, the effective lower bound LB to negative infinity, solve the relaxed main problem (M-MILP), and obtain the initial feasible solution Then, the initial feasible solution Substitute the objective function of the dual subproblem (DS-MILP) and solve the dual subproblem. If the solution to the dual subproblem is unbounded, record the extreme direction set of the dual subproblem constraint Add feasible splits:

[0122]

[0123] Enter the constraints of the main problem (M-MILP), solve the main problem (M-MILP) containing all feasible partitions, and obtain a feasible solution At this time, the optimal goal of the relaxed main problem provides a new effective lower bound LB for the original problem; when the effective upper bound UB is equal to the effective lower bound LB or the difference is very small, the iteration stops and the optimal solution is obtained.

[0124] If the dual subproblem has an optimal solution, the extreme point set of the dual subproblem constraint is Add the optimal cut:

[0125]

[0126] Enter the constraints of the main problem (M-MILP), solve the main problem (M-MILP) containing all feasible partitions and optimal cuts, and obtain a feasible solution At this time, the optimal goal of the relaxed main problem provides a new effective lower bound LB for the original problem; when the effective upper bound UB is equal to the effective lower bound LB or the difference is very small, the iteration stops and the optimal solution is obtained.

[0127] Therefore, combining the unpunctuality of experts in superior hospitals and the randomness of consultation service time, the unpunctuality of experts is analyzed, and the unpunctuality constraints of experts and the remote consultation appointment scheduling model based on random programming are constructed. At the same time, combined with the uncertain factors in the scheduling allocation process, the unpunctuality constraints are linearized, and combined with the sample average approximation method, the random remote consultation appointment scheduling model is transformed into a deterministic mixed integer programming model. Then, based on the input parameters of different subjects, the deterministic mixed integer programming model is solved to determine the globally optimal consultation scheduling allocation plan for remote consultation applications.

[0128] In a specific example, taking the one-year remote consultation history data of a medical center as an example, each case of remote consultation history data contains complete fields such as consultation appointment time, actual consultation start time, actual consultation end time, and consultation expert. In the remote consultation history data, there are 57 departments providing remote consultation services. In order to reduce the amount of calculation, the 57 consultation departments are divided into five types of medical departments (N=5): Internal Medicine Department, Surgery Department, Women's and Children's Medicine Department, General Medicine Department, and Medical Technology Department. The number of consultations, proportion, average service time, and standard deviation information of each type of medical department after re-division are shown in Table 1. Table 1 is as follows:

[0129] Table 1 Statistics of teleconsultation in each medical department

[0130]

[0131] The teleconsultation working hours are 9:00-12:00 in the morning and 15:00-18:00 in the afternoon, for a total of 6 hours. In order to allow patients who apply in the morning to arrange consultations in the afternoon, half a day is used as a scheduling cycle. The total service time in each scheduling cycle is D = 3 hours, and scheduling is performed twice a day. Minimum consultation time for each consultation θ n =1 / 6h, The waiting time of the superior hospital experts, the idle cost of the clinic and the overtime cost are equivalent to the loss of the experts' working time. c s =40, c o =40; the patient's waiting time cost The unallocated cost of consultation request is the loss of revenue of telemedicine center, and the unallocated penalty cost coefficient of patient is The number of scenarios Z = 100. Then, the optimal scheduling results under different numbers of arriving patients are obtained, as shown in Table 2.

[0132] Table 2 Optimal scheduling results under different numbers of arriving patients

[0133]

[0134] Among them, the scheduling scheme represents the position of the original arrival order after sorting. It can be observed that as the number of patients increases from 7 to 11, all patients are assigned under different patient numbers, the patient waiting time increases by 140%, the idle time decreases by 234%, and the timeout time increases by 264%.

[0135] like Figure 5As shown in the figure, the optimal cost and appointment scheduling scheme for different numbers of patients are shown, where the application sequence represents the sorted sequence. From the total cost graph, it can be found that the total cost reaches the lowest point when the number of patients is 10. After that, as the number of patients increases, the waiting time and overtime will increase rapidly, thereby greatly increasing the total cost. From the allocation time graph, it can be found that the allocation time for different numbers of patients is relatively stable and has small fluctuations. Since the random service time sample uses historical samples with greater randomness, rather than samples assumed to be evenly distributed, the overall scheduling scheme presents a sawtooth shape rather than a dome shape.

[0136] like Figure 6 As shown in the figure, the total cost under different expert waiting cost coefficients and the scheduling scheme with 7 arriving patients is selected. The higher the expert waiting cost coefficient, the higher the expert level. From the total cost graph, it can be seen that as the expert waiting cost coefficient decreases, the total cost shows an overall downward trend under different numbers of arriving patients. From the scheduling scheme, it can be seen that the higher the expert waiting cost coefficient, the smoother the allocation time. Figure 6 It can be concluded that the higher the level of the experts arranged, the lower the degree of differentiated services, but the overall cost will increase. The staff of the telemedicine center needs to weigh the balance between cost and service to make the most appropriate scheduling plan.

[0137] like Figure 7 As shown, the embodiment of the present application also provides a remote consultation appointment scheduling optimization system in an uncertain environment. Based on the unpunctuality of experts in the superior hospital, the remote medical center schedules and allocates the remote consultation applications submitted by the grassroots hospitals. The system includes: an unpunctuality analysis unit 701, which is configured to determine the unpunctuality of the expert according to the relationship between the appointment consultation start time, the actual consultation service start time, the actual consultation service end time, and the actual arrival time of the expert of two adjacent patients, and construct the unpunctuality constraint of the expert; a random model unit 702, which is configured to construct a remote consultation appointment scheduling model based on random planning according to the unpunctuality of the expert; a model conversion unit 703, which is configured to linearize the unpunctuality constraint, and according to the linearized unpunctuality constraint, based on the sample average approximation method, convert the random planning remote consultation appointment scheduling model into a mixed integer programming model; a scheduling allocation unit 704, which is configured to calculate the total number of consultation departments N determined by the remote medical center, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n in the appointment allocation time slot j n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the specialist in the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o; The waiting cost coefficient of the i-th patient determined by the grassroots hospital As well as the total number of patients I, based on the mixed integer programming model, the consultation scheduling allocation plan for remote consultation applications submitted by grassroots hospitals is determined.

[0138] The remote consultation appointment scheduling optimization system under uncertain environment provided by the embodiment of the present application can implement the steps and processes of the remote consultation appointment scheduling optimization method under uncertain environment of any of the above embodiments, and achieve the same technical effects, which will not be repeated here one by one.

[0139] In the description of the present invention, the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0140] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A remote consultation appointment scheduling optimization method under uncertain environment, characterized in that: In case of unpunctuality of experts from higher-level hospitals, the Telemedicine Center will dispatch and allocate the teleconsultation applications submitted by grassroots hospitals, including: Step S101: Determine the expert's unpunctuality according to the relationship between the scheduled consultation start time, the actual consultation service start time, the actual consultation service end time, and the expert's actual arrival time of two adjacent patients, and construct the expert's unpunctuality constraint condition; Step S102: construct a remote consultation appointment scheduling model based on stochastic planning according to the expert's unpunctuality; Step S103, linearizing the unpunctuality constraint condition, and according to the linearized unpunctuality constraint condition, based on the sample average approximation method, converting the remote consultation appointment scheduling model of random programming into a mixed integer programming model; Step S104: according to the total number of consultation departments N determined by the telemedicine center, the total service time D in the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n corresponding to the appointment allocation time slot j n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the specialist for the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the ith patient determined by the grassroots hospital and the total number of patients I, and based on the mixed integer programming model, determine the consultation scheduling allocation plan for the remote consultation application submitted by the grassroots hospital.

2. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 1 is characterized in that: In step S101. Construct the expert's unpunctuality constraint: In the formula, s j+1 The idle time of the consultation room after the consultation service of the patient assigned to the appointment time slot j+1 is completed; a j The scheduled consultation start time A for the patient assigned to the appointment time slot j j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The time interval of ; wherein the patient with the scheduled allocation time slot j and the patient with the scheduled allocation time slot j+1 are two adjacent remote consultation patients; k j The scheduled consultation start time A of the patient assigned time slot j for the appointment j The actual consultation service start time B j The time interval; j The actual consultation service time of the patient assigned time slot j for the appointment; k j+1 The scheduled consultation start time A of the patient assigned time slot j+1 to the appointment j+1 The actual consultation service start time B j+1 The time interval of j The scheduled consultation start time A of the patient assigned time slot j for the appointment j Arrival time with experts R j The time interval; w j The arrival time R of the expert who assigns time slot j to the appointment j The actual consultation service end time E j The time interval v j+1 The scheduled consultation start time A of the patient assigned time slot j+1 to the appointment j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

3. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 1 is characterized in that: In step S102, the remote consultation appointment scheduling model of random planning is: Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, and J is the total number of the appointment allocation time slots; The penalty cost coefficient for not assigning a consultation to the patient who requested the i-th remote consultation; x i Assign the result of the remote consultation to the i-th patient, x, a, and ξ are the patient’s allocation result, the allocated appointment service duration, and the actual consultation service time, respectively; The waiting cost coefficient for the patient who requested the i-th remote consultation; l ij Indicates whether the patient who requested the i-th remote consultation is assigned to the appointment allocation time slot j; k j (ω) is the actual waiting time of the patient assigned to the appointment time slot j under the unpunctual situation ω; the waiting cost coefficient of the expert who allocates time slot j for the appointment; w j (ω) is the actual waiting time of the expert assigned to the appointment time slot j under the unpunctual situation ω; c o is the expert's overtime cost coefficient; O(ω) is the consultation service overtime time within the consultation scheduling cycle under the unpunctual situation ω; c s is the idle cost coefficient of the consultation room; s j (ω) is the idle time of the consultation room after the patient service of the appointment allocated time slot j is completed in the said unpunctual situation ω.

4. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 3 is characterized in that: The conditional constraints of the remote consultation appointment scheduling model of random programming include: decision constraints, the unpunctuality constraints and time slot constraints; The decision constraints are: Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, J is the total number of the appointment allocation time slots; a i The appointment service time allocated to the patient who applied for the remote consultation, D is the total service time in the consultation scheduling cycle, l ij Whether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j, x i The remote consultation allocation result for the patient who applied for the remote consultation, a j The appointment service duration of the patient assigned time slot j for the appointment; θ n (j) the minimum guaranteed service duration of department n corresponding to the appointment allocation time slot j determined by the telemedicine center; The time slot constraints are: Where O(ω) is the consultation service timeout time within the consultation scheduling cycle under the unpunctual situation ω; v J+1 (ω) is the waiting time of patients and specialists for the appointment allocation time slot J+1 without considering the specialist’s unpunctuality; w1(ω) is the actual waiting time of the expert in the first time slot assigned to the appointment under the unpunctual situation ω; μ1(ω) is the unpunctual time of the expert in the first time slot assigned to the appointment under the unpunctual situation ω; k1(ω) is the actual waiting time of the patient in the first time slot assigned to the appointment under the unpunctual situation ω; v1(ω) is the waiting time of the patient and expert in the first time slot assigned to the appointment under the unpunctual situation ω without considering the unpunctuality of the expert; s j (ω) is the idle time of the consultation room after the patient service of the appointment time slot j is completed under the unpunctual situation ω, k j (ω) is the actual waiting time of the patient with the appointment allocated time slot j under the unpunctual situation ω, w j (ω) is the actual waiting time of the expert assigned to the appointment time slot j under the unpunctual situation ω; v j (ω) is the waiting time of the patient and the specialist for the appointment assigned to time slot j without considering the lateness in the lateness scenario ω.

5. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 1 is characterized in that: In step S103. The non-punctuality constraint condition is linearized to obtain a linear non-punctuality constraint condition; wherein the linear non-punctuality constraint condition is: Where i is the patient serial number of the remote consultation application, I is the total number of patients; s j+1 (ω) is the idle time of the consultation room after the consultation service of the patient with the appointment allocated time slot j+1 under the unpunctual situation ω is completed; a j The scheduled consultation start time A of the patient assigned time slot j for the appointment j The scheduled consultation start time A of the patient with scheduled allocation time slot j+1 j+1 The time interval of the appointment allocation time slot j and the appointment allocation time slot j+1 are two adjacent remote consultation patients; k j+1 (ω) is the scheduled consultation start time A of the patient in the scheduled allocation time slot j+1 under the unpunctual situation ω j+1 The actual consultation service start time B j+1 The time interval k j (ω) The scheduled consultation start time A of the patient assigned time slot j to the appointment j The actual consultation service start time B j The time interval; ij Indicates whether the patient who applied for the i-th remote consultation is assigned to the appointment allocation time slot j; ξ i (ω) is the actual consultation service time of the patient who applied for the i-th remote consultation under the said unpunctual situation ω; w j (ω) is the expert arrival time R of the patient assigned to the appointment time slot j under the unpunctual situation ω j The actual consultation service end time E j The time interval of j (ω) is the scheduled consultation start time A of the patient assigned time slot j under the unpunctual situation ω j Arrival time with experts R j The time interval v j+1 (ω) is the scheduled consultation start time A of the patient in the scheduled allocation time slot j+1 under the unpunctual situation ω j+1 The actual consultation service end time E of the patient assigned to the appointment time slot j j time interval.

6. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 5 is characterized in that: The teleconsultation sample data of the telemedicine center are sampled by Monte Carlo simulation; According to the sampling results and the linear non-punctuality constraint conditions, based on the sample average approximation method, the remote consultation appointment scheduling model of random programming is converted into a mixed integer programming model.

7. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 6 is characterized in that: The mixed integer programming model is: Wherein, i is the patient serial number of the remote consultation application, I is the total number of patients of the remote consultation application; j is the appointment allocation time slot, and J is the total number of the appointment allocation time slots; is the unassigned penalty cost coefficient for the patient who applied for the ith remote consultation; Z is the number of samples sampled in the Monte Carlo simulation, and z is the serial number of the sampled sample in the Monte Carlo simulation; The waiting cost coefficient of the patient who applied for the i-th remote consultation determined by the grassroots hospital; It is a constructed decision variable and has no practical significance; The waiting cost coefficient of the expert for the appointment allocation time slot j determined by the superior hospital c is the actual waiting time of the expert in the appointment allocation time slot j at the sampling time z; o is the expert’s overtime cost coefficient, c is the service timeout time of the reserved allocation time slot J+1 at the sampling time z; s is the idle cost coefficient of the clinic; The free time of the consultation room after the consultation service of the patient in the appointment allocation time slot j at the sampling sample z is completed.

8. The remote consultation appointment scheduling optimization method under uncertain environment according to claim 1 is characterized in that: In step S104. According to the formula: Determine the total number of reservation time slots J; Where D is the total service time in the consultation scheduling cycle, j is the appointment allocation time slot, θ n (j) the minimum guaranteed service hours for department n determined for the telemedicine center; Based on the mixed integer programming model, according to the total number J of the appointment time slots, the remote consultation scheduling allocation plan for the remote consultation application submitted by the grassroots hospital is determined through enumeration method and Benders decomposition algorithm.

9. A remote consultation appointment scheduling optimization system under uncertain environment, characterized in that: In case of unpunctuality of experts from higher-level hospitals, the Telemedicine Center will dispatch and allocate the teleconsultation applications submitted by grassroots hospitals, including: The unpunctuality analysis unit is configured to determine the unpunctuality of the expert according to the relationship between the scheduled consultation start time, the actual consultation service start time, the actual consultation service end time, and the actual arrival time of the expert between two adjacent patients, and to construct the unpunctuality constraint condition of the expert; A stochastic model unit is configured to construct a remote consultation appointment scheduling model based on stochastic programming according to the unpunctuality of the experts; A model conversion unit is configured to linearize the unpunctuality constraint condition, and according to the linearized unpunctuality constraint condition, based on a sample average approximation method, convert the remote consultation appointment scheduling model of random programming into a mixed integer programming model; The scheduling allocation unit is configured to calculate the total number of consultation departments N determined by the telemedicine center, the total service time D within the consultation scheduling cycle, and the minimum guaranteed service time θ of the consultation department n for the appointment allocation time slot j. n (j) Penalty cost coefficient for the i-th patient not assigned a consultation The waiting cost coefficient of the expert in the appointment allocation time slot j determined by the superior hospital The expert's overtime cost coefficient c o ; The waiting cost coefficient of the ith patient determined by the grassroots hospital and the total number of patients I, and based on the mixed integer programming model, determine the consultation scheduling allocation plan for the remote consultation application submitted by the grassroots hospital.

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