Hospital number source supply adjustment method, device and system based on benders decomposition

Abstract

The present application relates to the field of hospital number source supply adjustment, in particular to a kind of hospital number source supply adjustment method, device and system based on Benders decomposition, wherein the hospital number source supply adjustment method based on Benders decomposition includes the following steps: S1: obtaining data;S2: scene generation;S3: model construction;S4: model fusion;S5: model decomposition and solution;And S6: output and execution.The hospital number source supply adjustment method based on Benders decomposition proposed in the present application faces the actual operation pain point of hospital medical skill examination number source allocation, combines the industry characteristics that patient demand random fluctuation, multi-period cross-period overflow scheduling, efficiency and fairness coexist, constructs two-stage stochastic integer programming model fusing multiple heterogeneous patients, for the large-scale solution problem of model, design single-cut, multi-cut and mixed-cut three kinds of Benders decomposition algorithm, effectively improve the solving efficiency.

Description

Technical Field

[0001] This invention relates to the field of hospital appointment supply adjustment, and in particular to a method, apparatus and system for adjusting hospital appointment supply based on Benders decomposition. Background Technology

[0002] With the continuous improvement of China's medical system, increased awareness of health checkups among residents, and the accelerating aging of the population, patient demand for medical examination services such as CT scans, MRI, and ultrasound is showing a year-on-year growth trend. As an essential part of clinical diagnosis, preoperative assessment, and chronic disease follow-up, the efficiency of medical examinations directly determines the overall efficiency of the treatment process. However, many large hospitals generally face a contradiction between the rigid supply of appointment slots and the random fluctuations in demand. Departments have fixed daily limits on resources such as examination equipment and medical staff, and the total number of appointment slots cannot be flexibly adjusted according to demand. At the same time, there is significant heterogeneity in the arrival patterns, urgency, and service needs of various patient groups, including emergency patients, general outpatients, chronic disease follow-up patients, and those undergoing physical examinations. This leads to excessively long waiting times for patient appointments, restricting treatment efficiency and reducing patient satisfaction. How to scientifically allocate limited examination slots to meet the randomly arriving patient demand, improve resource utilization efficiency, and ensure fairness among different patient groups is an important practical problem in hospital operation and management research.

[0003] In actual operation, hospitals typically pre-allocate appointment slots 1-7 days in advance, while actual patient demand arrives randomly, easily leading to a supply-demand mismatch. When there are insufficient pre-allocated slots on a given day, surplus patients cannot receive immediate examinations, and hospitals generally use cross-period appointments for scheduling. While this model alleviates same-day congestion, it incurs waiting costs for patients. If there are excess pre-allocated slots, due to the time-sensitive nature of examination services, idle slots cannot be carried over to later dates, resulting in a waste of medical resources. Meanwhile, the needs of different types of patients (such as emergency, general outpatient, and chronic disease follow-up) exhibit significant differences and randomness, and different types of patients have different requirements for service timeliness. This mismatch between the pre-allocation scheme and the subsequent fulfillment of demand makes the appointment allocation problem highly challenging in operational management.

[0004] More complexly, hospitals need to balance efficiency and fairness in the allocation of appointment slots. From an efficiency perspective, hospitals aim to maximize service utility (or minimize resource idleness and patient waiting costs). From a fairness perspective, the opportunity for different patient groups to obtain appointment slots should be commensurate with the scale of their demand and the urgency of their conditions. A long-term preference for high-utilization-coefficient or high-priority patient groups may impair the accessibility of patients with weaker needs or lower urgency. Furthermore, the cross-period scheduling of overflowing patients is a common and feasible practice. Unmet patients can be rescheduled for later available appointment dates, but this incurs additional waiting costs. This scheduling mechanism provides flexibility in alleviating supply-demand imbalances, but it also makes the decision-making process more complex over time. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies in which hospitals cannot simultaneously achieve both efficiency and fairness in the allocation of appointment slots, and to provide a method, apparatus and system for adjusting hospital appointment slot supply based on Benders decomposition.

[0006] In a first aspect, the present invention provides a method for adjusting hospital appointment supply based on Benders decomposition, characterized by comprising the following steps:

[0007] S1: Data Acquisition: Acquire current operational data, which includes at least the planning cycle, patient type, total daily appointment slots, total daily appointment slot demand for each type of patient, and average service utility coefficient, wherein the average service utility coefficient is determined by the clinical urgency, required consumables, and examination service duration for the same patient type. S2: Scene Generation: Using the sample mean approximation (SAA) method, Monte Carlo sampling is performed based on the acquired operational data to generate multiple independent demand scenarios, wherein each scenario includes a date with a length of the planning period, and the total daily appointment demand for each type of patient during the date period; S3: Model Construction: Based on the operational data and the demand scenario, construct a two-stage mixed integer programming model for patient scheduling, wherein, The first stage of decision-making determines the pre-allocated appointment slots for various patient types. The second stage of decision-making, based on the pre-allocated appointment slots, determines whether to reschedule unmet needs to subsequent planning cycles. A dual-objective optimization model is established based on the two-stage mixed integer programming model. The objective function of the dual-objective optimization model includes a first objective function for maximizing the expected service utility of the hospital and a second objective function for minimizing the expected waiting cost of patients. The constraints of the dual-objective optimization model include at least the following: daily appointment capacity constraint, daily service limit constraint, total demand constraint, inter-period scheduling capacity constraint, non-negativity and integer constraint of variables, and fairness constraint. S4: Model Fusion: The first objective function and the second objective function of the dual-objective optimization model are fused using a linear weighting method to construct a comprehensive single-objective function model; S5: Model Decomposition and Solution: The Benders decomposition algorithm is used to solve the integrated single-objective function model to obtain the optimal solution that satisfies the convergence condition; the solution process includes: The integrated single-objective function model is decomposed into a relaxed master problem corresponding to the first stage decision and a sub-problem corresponding to the second stage decision; Solve the main problem to obtain the initial pre-assignment decision, and input the initial pre-assignment decision into the sub-problem; The subproblem fixes the initial pre-allocation decision obtained from the main problem, solves the second stage decision in a single scenario, and generates Benders cut feedback to the main problem based on the solution results of the subproblem for iterative update until the difference between the objective values ​​of the main problem and the subproblem satisfies the preset convergence condition, thus obtaining the optimal solution scheme for the pre-allocated source quantity; S6: Output and Execution: Output the optimal solution for the pre-allocated number of appointment slots, and execute the adjustment of hospital appointment slot supply according to the optimal solution for the pre-allocated number of appointment slots.

[0008] Preferably, in step S4, the weights of the first objective function and the second objective function of the bi-objective optimization model are fused using the linear weighting method, which is given by the formula... The calculation shows that, among which For the first The proportion of demand from patients of this type The service utility coefficient per unit. Waiting cost per unit For the planning period, N represents the total number of patient types.

[0009] Preferably, in step S5, during the iterative update, a Benders optimal cut is constructed for each scenario, and the Benders optimal cut is added to the main problem.

[0010] Preferably, in step S5, during the iterative update, the aggregated dual variables of all the scenarios are calculated, the Benders optimal cut is constructed using the aggregated dual variables, and the Benders optimal cut is added to the main problem.

[0011] Preferably, in step S5, given an upper and lower bound gap threshold, in the iterative update, when the upper and lower bound gap is greater than the upper and lower bound gap threshold, a Benders optimal cut is constructed for each scenario and added to the main problem; when the upper and lower bound gap is less than or equal to the upper and lower bound gap threshold, the aggregated dual variables of all scenarios are calculated, a Benders optimal cut is constructed using the aggregated dual variables, and the Benders optimal cut is added to the main problem.

[0012] Preferably, in step S6, a hospital patient optimization scheduling strategy is generated based on the optimal solution of the pre-allocated appointment slots, and the daily examination appointment slots are actually allocated; and when actual demand occurs and the pre-allocated appointment slots are insufficient, the cross-period appointment scheduling operation for patients who have not been able to book an appointment is executed based on the pre-allocated appointment slots of the optimal solution.

[0013] Preferably, the patient types are four categories: newly diagnosed patients with severe chronic diseases, patients undergoing follow-up visits for severe chronic diseases, newly diagnosed patients without severe chronic diseases, and patients undergoing follow-up visits for severe non-chronic diseases.

[0014] In a second aspect, the present invention provides a data processing apparatus, characterized in that it is used to execute a hospital appointment supply adjustment method based on Benders decomposition, the apparatus comprising: The data acquisition module is used to acquire current operational data, which includes at least the planning cycle, patient type, total daily appointment slots, total daily appointment slot demand for each type of patient, and average service utility coefficient. The average service utility coefficient is determined by the clinical urgency, required consumables, and examination service duration for the same patient type. The scenario generation module is used to generate multiple independent demand scenarios by performing Monte Carlo sampling based on the acquired operational data using the sample mean approximation (SAA) method. Each scenario includes a date with a length equal to the planning period, and the total daily appointment demand for each type of patient during the date period. The model building module is used to construct a two-stage mixed integer programming model for patient scheduling based on the operational data and the demand scenario. The first stage of decision-making determines the pre-allocated appointment slots for various patient types. The second stage of decision-making, based on the pre-allocated appointment slots, determines whether to reschedule unmet needs to subsequent planning cycles. A dual-objective optimization model is established based on the two-stage mixed integer programming model. The objective function of the dual-objective optimization model includes a first objective function for maximizing the expected service utility of the hospital and a second objective function for minimizing the expected waiting cost of patients. The constraints of the dual-objective optimization model include at least the following: daily appointment capacity constraint, daily service limit constraint, total demand constraint, inter-period scheduling capacity constraint, non-negativity and integer constraint of variables, and fairness constraint. The model fusion module is used to fuse the first objective function and the second objective function of the dual-objective optimization model using a linear weighting method to construct a comprehensive single-objective function model; The model decomposition and solution module is used to solve the integrated single-objective function model using the Benders decomposition algorithm to obtain the optimal solution that satisfies the convergence condition; the solution process includes: The integrated single-objective function model is decomposed into a relaxed master problem corresponding to the first stage decision and a sub-problem corresponding to the second stage decision; Solve the main problem to obtain the initial pre-assignment decision, and input the initial pre-assignment decision into the sub-problem; The subproblem fixes the initial pre-allocation decision obtained from the main problem, solves the second stage decision in a single scenario, and generates Benders cut feedback to the main problem for iterative updates based on the solution results of the subproblem, until the difference between the objective values ​​of the main problem and the subproblem satisfies the preset convergence condition, and obtains the optimal solution scheme for the pre-allocated source quantity; The output and execution module is used to output the optimal solution for the pre-allocated number of appointment slots and to execute the adjustment of the hospital appointment slot supply according to the optimal solution for the pre-allocated number of appointment slots.

[0015] In a third aspect, the present invention provides a computer system comprising: a processor; and a memory storing a computer program, wherein when the computer program is executed by the processor, the processor performs the method as described in any of the first aspects.

[0016] This invention proposes a method, device, and system for adjusting hospital appointment supply based on Benders decomposition. Through a two-stage stochastic integer programming framework, it deeply aligns with the real-world operational scenario of "pre-allocation and post-event inter-period scheduling" in hospitals, effectively enhancing the resource allocation system's ability to withstand random fluctuations in demand and significantly reducing the idle rate of medical equipment and the rigid attrition rate of unmet patients. This method innovatively introduces fairness constraints, achieving a synergistic optimization of maximizing the overall service utility coefficient and minimizing the expected waiting cost for patients under a dual-objective evaluation system. At the core algorithm solution level, this invention combines multi-cut, single-cut, and hybrid-cut Benders decomposition algorithms, breaking through the computational bottleneck of large-scale, multi-scenario stochastic optimization problems. This enables the provision of efficient, highly flexible, and parameterized customized fine-grained operational decision support for different departments. Attached Figure Description

[0017] Figure 1 This is a flowchart of the hospital appointment supply adjustment method 100 based on Benders decomposition according to the present invention.

[0018] Figure 2 This is a flowchart of the Benders decomposition algorithm 200 with multiple cuts according to the present invention.

[0019] Figure 3 This is a flowchart of the Benders decomposition algorithm 300 including single cuts according to the present invention.

[0020] Figure 4 This is a flowchart of the Benders decomposition algorithm 400 including hybrid cut of the present invention.

[0021] Figure 5 This is a block diagram of the hospital appointment allocation optimization device 500 based on Benders decomposition according to the present invention.

[0022] Figure 6 A schematic block diagram illustrating a computer system 600 according to an embodiment of the present invention.

[0023] Marked in the image: 100 describes a hospital appointment supply adjustment method based on Benders decomposition, with S101~S106 representing its method steps. 200 represents the Benders decomposition algorithm involving multiple cuts, and S201~S206 are its method steps. 300 represents the Benders decomposition algorithm including single cuts, and S301~S306 are its method steps. 400 represents the Benders decomposition algorithm including hybrid cuts, and S401~S406 are its method steps. 500 is a hospital appointment allocation optimization device based on Benders decomposition; 501 is a data acquisition module; 502 is a scene generation module; 503 is a model building module; 504 is a model fusion module; 505 is a model decomposition and solution module; and 506 is an output and execution module. 600 is a computer system according to an embodiment of the present invention, 610 is a processor, and 620 is a memory. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0025] Unless otherwise specified, the use of terms such as "first," "second," and "third" in the description of specific embodiments of the present invention is merely for distinguishing descriptions of identical or similar components and should not be construed as emphasizing or implying the relative importance of a particular component.

[0026] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0027] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0028] Next, combine Figures 1 to 4 This invention specifically describes the hospital appointment supply adjustment method based on Benders decomposition proposed in the embodiments of the present invention. Figure 1 This is a flowchart of the hospital appointment supply adjustment method 100 based on Benders decomposition according to the present invention. Figure 2 This is a flowchart of the Benders decomposition algorithm 200 with multiple cuts according to the present invention. Figure 3 This is a flowchart of the Benders decomposition algorithm 300 including single cuts according to the present invention. Figure 4 This is a flowchart of the Benders decomposition algorithm 400 including hybrid cut of the present invention.

[0029] like Figure 1 As shown, this embodiment provides a hospital appointment supply adjustment method 100 based on Benders decomposition, including steps S101 to S106. Although the entire process of steps S101 to S106 is described in chronological order here, it should be noted that in actual implementation, steps S101 to S106 may not necessarily be performed in strict order.

[0030] exist Figure 1 Step S101, as shown, involves acquiring data. Specifically, this step acquires the current operational data of the hospital service system. This operational data includes at least the planning cycle length, the total number of appointment slots per day, patient types, the total daily appointment slot demand for each patient type, and the average service utility coefficient. The average service utility coefficient is determined by the clinical urgency (whether it's a severe chronic disease, whether it's a follow-up visit), required consumables, and examination service duration within the same patient category. For example, patients with severe chronic diseases requiring follow-up visits have a higher clinical urgency, necessitating more consumables and longer examination service times. In one embodiment, taking CT examination service operation practices and data statistics as an example, the CT examination appointment planning cycle length is... Heaven, service Patients with heterogeneity are categorized into four groups: newly diagnosed patients with severe chronic diseases, returning patients with severe chronic diseases, newly diagnosed patients without severe chronic diseases, and returning patients without severe chronic diseases. The hospital's daily testing equipment and medical staff service capacity are fixed, and the total number of available appointment slots per day is set at [a certain limit]. Person-times. Based on the survey data of CT examinations conducted at the surveyed hospitals from March 1 to August 31, 2024, the average daily number of examinations for the four types of patients on weekdays (i.e., the total daily demand for appointments) was as follows: 58 initial visits for patients with severe chronic diseases, 300 follow-up visits for patients with severe chronic diseases, 63 initial visits for patients without severe chronic diseases, and 206 follow-up visits for patients without severe chronic diseases. After weighting the clinical urgency (whether it is a severe chronic disease, whether it is a follow-up visit), required consumables, and examination service time within the same patient category, the average service utility coefficients for the four types of patients were as follows: 787.02 for initial visits for patients with severe chronic diseases, 886.48 for follow-up visits for patients with severe chronic diseases, 653.83 for initial visits for patients without severe chronic diseases, and 707.48 for follow-up visits for patients without severe chronic diseases.

[0031] exist Figure 1Step S102, as shown, involves scenario generation. Specifically, in this step, the Sample Mean Approximation (SAA) method is used to perform Monte Carlo sampling based on the acquired operational data to generate multiple independent demand scenarios. Each scenario includes a date within a planning period and the total daily appointment demand for each patient type within that planning period. Optionally, the information contained in a single scenario can be represented by a demand matrix, where each row of the demand matrix represents a patient type, each column represents a day within the planning period, and a specific position in the demand matrix represents the demand quantity for that patient type on that day. Where i represents the patient type and t represents the number of days. This represents a specific scenario. For example, in the embodiment described above, the demand matrix has a dimension of 4 rows and 14 columns, and each element of the demand matrix represents the length of the planning period. Under normal circumstances, the number of appointment slots needed for patients seeking initial diagnosis of severe chronic diseases, patients seeking follow-up diagnosis of severe chronic diseases, patients seeking initial diagnosis of non-severe chronic diseases, and patients seeking follow-up diagnosis of non-severe chronic diseases.

[0032] exist Figure 1 Step S103, as shown, involves model building. Specifically, in this step, a two-stage mixed integer programming model for patient scheduling is built based on operational data and demand scenarios.

[0033] The first phase of decision-making involves determining the pre-allocated appointment slots for various patient types. At the beginning of the planning cycle, managers utilize historical demand data and the algorithm proposed in this invention to generate the... The day was allocated to the first The initial number of appointment slots for this type of patient is counted as Once the decision is made, it will not be changed during the cycle. Each time a decision is accepted... For patients of this type, the system obtains a unit utility coefficient of: .

[0034] The second-stage decision-making process involves determining whether to schedule unmet needs to subsequent planning cycles based on the extent to which the pre-allocated number of available slots meets actual demand. To characterize the decision-making logic of this stage, this invention uses the demand scenarios defined above. As mentioned above, in the demand scenario... Below, on day t of the planning cycle. The examination needs of this type of patient are met. ( Furthermore, let the actual number of patients served on day t of the planning period for patient type i be... , No. Patients of this type in the planning cycle The number of unmet service demands is And in the planning cycle The first day of unsatisfactory service Patients of this type were dispatched to the first The number of patients per day was Decision-makers decide whether to reschedule unmet needs to subsequent planning cycles based on the extent to which the pre-allocated number of license plates meets actual demand: if the pre-allocated number of license plates is sufficient ( ): All needs on the same day can be met immediately, there are no overflow patients, and idle appointment slots cannot be carried over to the next day; if the pre-allocated appointment slots are insufficient ( Some patients can be examined on the same day; those with overflow will be subject to multi-cycle scheduling and can be rescheduled to any available date after the current day. Last day of the planning period Patients who overflow have no subsequent dates available for scheduling, so service is refused outright.

[0035] exist Figure 1 Step S103, as shown, further establishes a bi-objective optimization model for the established two-stage mixed integer programming model. The objective functions of the bi-objective optimization model include a first objective function for maximizing the expected service utility of the hospital, and a second objective function for minimizing the expected waiting cost of patients. In determining the first objective function, both immediate service patients and patients scheduled across timeframes can generate utility coefficients. This function takes the mathematical expectation of all random scenarios and is expressed by the following formula:

[0036] Where i represents the i-th type of patient, t represents the t-th day of the planning cycle, s represents any available date after the current day that can be rescheduled during multi-cycle inter-period scheduling, T represents the total number of days in the planning cycle, and N represents the total number of patient types. For the first The unit service utility coefficient for this type of patient for Scenario 1 Patients of this type in the planning cycle The actual number of patients served per day In scenario ω, the number of patients from the i-th type of patients who were not satisfied on day t of the planning period are scheduled to day s, where t+1≤s≤T.

[0037] Furthermore, the second objective function is used to minimize the patient's expected waiting cost, where the patient's waiting cost is related to the time interval of inter-period scheduling. Proportional to the expected value of the scenario, expressed by the following formula:

[0038] Where i represents the i-th type of patient, t represents the t-th day of the planning cycle, s represents any available date after the current day that can be rescheduled during multi-cycle inter-period scheduling, T represents the total number of days in the planning cycle, and N represents the total number of patient types. For the first The unit waiting cost for this type of patient In scenario ω, the number of patients from the i-th type of patients who were not satisfied on day t of the planning period are scheduled to day s, where t+1≤s≤T.

[0039] Optionally, It can be set to a specific percentage value of the unit service utility coefficient. For example, in the above embodiment using CT examination as an example, the unit service utility coefficient for each type of patient... The figures are as follows: 787.02 for initial visits of patients with severe chronic diseases, 886.48 for follow-up visits of patients with severe chronic diseases, 653.83 for initial visits of patients without severe chronic diseases, and 707.48 for follow-up visits of patients without severe chronic diseases. Based on the motivation to maximize utility through cross-period appointments and to avoid excessively long patient wait times, the unit waiting cost must be less than the unit service utility coefficient. The model sets the unit waiting cost for the four patient categories at 20% of the unit utility coefficient: 787.02 × 20% = 157.40 / person / day for initial visits of patients with severe chronic diseases, 886.48 × 20% = 177.30 / person / day for follow-up visits of patients with severe chronic diseases, 653.83 × 20% = 130.77 / person / day for initial visits of patients without severe chronic diseases, and 707.48 × 20% = 141.50 / person / day for follow-up visits of patients without severe chronic diseases.

[0040] In addition to determining the first and second objective functions, the optimization model obtained in step S103 also includes constraints. These constraints include at least: daily appointment capacity constraints, daily service limit constraints, total demand constraints, inter-period scheduling capacity constraints, non-negativity and integer constraints of variables, and fairness constraints. Each constraint is explained in detail below.

[0041] The daily appointment capacity constraint, limiting the sum of pre-allocated appointments for all patients to no more than the total daily capacity, is expressed by the following inequality:

[0042] Where, as mentioned above, i represents the i-th type of patient, t represents the t-th day of the planning period, N represents the total number of patient types, and T represents the total number of days in the planning period. For the first time within the planning period The day was allocated to the first The number of appointments available for this type of patient For the first time during the planning period The total daily appointment capacity. For example, in the embodiment above using CT scans as an example, the total daily available appointment capacity is set to... Number of people.

[0043] The daily service limit, restricting the number of patients of a single type to receive immediate service within the pre-allocated appointment slots, is expressed by the following inequality:

[0044] Where, as mentioned above, i represents the i-th type of patient, t represents the t-th day of the planning period, N represents the total number of patient types, and T represents the total number of days in the planning period. For the first time within the planning period The day was allocated to the first The number of appointments available for this type of patient for Scenario 1 Patients of this type in the planning cycle The actual number of patients served per day For the set of all scenarios with random requirements, .

[0045] The constraint on total demand, limiting the sum of the number of users providing immediate service on a given day and the number of users scheduled across periods to not exceed the actual demand on that day, can be expressed by the following inequality:

[0046] Where, as mentioned above, i represents the i-th type of patient, t represents the t-th day of the planning period, N represents the total number of patient types, and T represents the total number of days in the planning period. for Scenario 1 Patients of this type in the planning cycle The actual number of patients served per day For the first Patients with this type of disease Scenario 1 Daily demand In scenario ω, the number of patients from the i-th type who were not satisfied on day t of the planning period are scheduled to be reassigned to day s, where t+1≤s≤T. For the set of all scenarios with random requirements, .

[0047] On the last day of the appointment window Since the subsequent appointment window has not yet opened, and without considering the number of patients being transferred out, that is... Therefore, at the appointment window When, the constraint is:

[0048] For inter-period scheduling capacity constraints, the first... The sum of the total number of overflow patients received that day and the number of people served immediately that day shall not exceed [the number of patients who have already been admitted]. The total source capacity of the signal is expressed by the following inequality:

[0049] Where, as mentioned above, i represents the i-th type of patient, t represents the t-th day of the planning period, N represents the total number of patient types, and T represents the total number of days in the planning period. for Scenario 1 Patients of this type in the planning cycle The actual number of patients served per day In scenario ω, the number of patients from the i-th type who were not satisfied on day t of the planning period are scheduled to be reassigned to day s, where t+1≤s≤T. This represents the total signal source capacity on day s within the planning period. For the set of all scenarios with random requirements, .

[0050] For the constraint that variables are non-negative and integer, the number of people and the number source must be non-negative integers.

[0051]

[0052]

[0053] Regarding fairness constraints, in the healthcare industry, decision-makers need to consider service fairness when providing medical services to various patient groups. This invention uses vertical fairness as a standard, setting nominal appointment quotas based on the historical demand ratio of patients. It requires that the total absolute deviation (SAD) between the actual allocated appointments and the nominal quota for each patient group does not exceed a preset threshold, ensuring that the opportunity for different groups to obtain appointments matches their demand scale. This invention employs absolute deviation of demand ratios and quantified allocation fairness. Actual number of appointment slots and nominal quotas allocated to patients of this type throughout their entire treatment cycle ( The sum of absolute deviations of () shall not exceed the fairness threshold. This can be expressed by the following inequality:

[0054] in, For the first The proportion of patients with this type of need (which can be obtained by averaging the proportion of historical needs). Indicates the first Heavenly The nominal allocation capacity for patient categories (i.e., the category with the greatest demand should receive more appointment slots). For the first Heavenly The actual allocation capacity for patients of this type For the first Total absolute deviation of patients in this class during the planning period. A preset fairness threshold is set to ensure that the maximum total deviation between the actual allocation and the nominal allocation does not exceed an acceptable range across all patient categories, thereby ensuring consistency in the satisfaction rate of the needs of all patient categories.

[0055] For example, in the above embodiment using CT scans as an example, nominal appointment slots are allocated based on the proportion of patients served over the past six months, according to the standard of vertical fairness. The quota proportion is calculated based on the average daily number of examinations for four types of patients on weekdays (58 initial visits for patients with severe chronic diseases, 300 follow-up visits for patients with severe chronic diseases, 63 initial visits for patients with non-severe chronic diseases, and 206 follow-up visits for patients with non-severe chronic diseases). The breakdown is as follows: 9.15% for initial consultations of patients with severe chronic diseases, 48.06% for follow-up consultations of patients with severe chronic diseases, and 9.97% for initial consultations of patients without severe chronic diseases and 32.82% for follow-up consultations of patients without severe chronic diseases. The total absolute deviation threshold between the actual allocated appointment slots and the nominal quota for each patient category is set at [value missing]. This is to ensure that different groups have the opportunity to obtain appointment slots.

[0056] Since constraint (10) contains absolute value and maximum value operators, it is a nonlinear constraint and cannot be solved directly using a linear programming algorithm. Therefore, a nonnegative auxiliary decision variable is introduced. The constraint (10) is equivalently linearized into the following formulas (11)-(14).

[0057]

[0058]

[0059]

[0060]

[0061] Formulas (11)-(14) are completely equivalent to the original nonlinear fairness constraints, and all of them are linear constraints, ensuring that the model is solvable.

[0062] exist Figure 1 Step S104, as shown, involves a model fusion step. Specifically, in this step, a linear weighting method is used to fuse the first and second objective functions of the dual-objective optimization model to construct a comprehensive single-objective function. Specifically, the linear weighting formula is as follows: Weights are introduced. It indicates the degree to which managers attach importance to waiting costs.

[0063] For weights Optionally, the weight can be set manually based on preferences. The smaller the value, the less likely the manager is to control patient waiting costs; The model degenerates into a pure utility coefficient maximization model. Alternatively, weights... It can also be done through formulas The calculation shows that, among which For the first The proportion of demand from patients of this type The service utility coefficient per unit. Waiting cost per unit For the planning period, N represents the total number of patient types. For example, in the embodiment using CT scans described above, the trade-off coefficient between waiting costs and utility coefficients in the objective function is determined based on patient composition, service utility coefficient, and cost structure. The calculation formula is based entirely on the model's endogenous parameters. The formula calculates... The chosen value makes the utility coefficient term and the waiting cost term comparable in the objective function, while naturally reflecting the guiding role of high-demand, high-urgency patient groups in the direction of system optimization, which is in line with the hospital's public welfare and fairness orientation.

[0064] exist Figure 1 Step S105, as shown, involves model decomposition and solution. Specifically, in this step, the Benders decomposition algorithm is used to solve the comprehensive single-objective function model to obtain the optimal solution that satisfies the convergence condition. First, the main problem and subproblems are decomposed. Based on the model given in step S103, the first-stage pre-allocation decision corresponding to the main problem can be decomposed. With fairness constraints Introducing the expected utility coefficient as an auxiliary variable The expected utility coefficient of the subproblem is to be maximized. The objective and constraints of the relaxed main problem are as follows: max

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] Initially, the main problem has no cutting plane; during the iteration process, Benders optimal cuts are continuously added. The expression varies depending on whether a multi-cut Benders decomposition algorithm, a single-cut Benders decomposition algorithm, or a hybrid-cut Benders decomposition algorithm is used. The specific expression will be described later in relation to the multi-cut, single-cut, and hybrid-cut Benders algorithms.

[0072] Subproblems fix the first-stage variables Solve the second-stage decision problem in a single scenario. Based on the SAA model, the subproblem includes second-stage decision variables. and The objective is to maximize the average service utility coefficient. The sub-problems in different demand scenarios are independent and can be solved in parallel. In the scenario... The objectives and constraints of the relaxed subproblems are as follows:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] The dual problem of the relaxation subproblem is shown below:

[0081]

[0082]

[0083]

[0084]

[0085] in, These are the dual variables of the upper bound constraint, demand constraint, and capacity constraint, respectively.

[0086] By strong duality, for any fixed Scene Optimal value of the subproblem This equals the optimal value of the dual subproblem. Let the optimal value of the dual subproblem be... ,and For the optimal solution to the dual subproblem, we have:

[0087] in, .

[0088] Based on the optimal cut constraint of equation (15), a Benders decomposition algorithm with multiple cuts can be designed, with instance data as input. Convergence tolerance Where N is the total number of patient types and T is the total number of days in the planning period. For the set of all scenarios with random requirements, For the first time during the planning period Total signal source capacity of the day For the first The unit service utility coefficient for this type of patient For the first The unit waiting cost for this type of patient For the first The proportion of patients with this type of condition As a preset fairness threshold, The weights in the model fusion step are used to determine the optimal number source pre-allocation scheme. And the optimal target value.

[0089] like Figure 2 As shown, the Benders decomposition algorithm with multiple cuts consists of six steps.

[0090] First, in step S201, an initialization step is performed. The initialization step includes two sub-steps, one of which is to construct the relaxation master problem (RMP), which includes constraints (3), (11)-(14), and variables. , and auxiliary variables (No initial cut). The objective function of RMP is: Secondly, setting a global lower bound. Global upper bound Iteration counter .

[0091] Next, in step S202, the main problem is solved. Solving the main problem includes two sub-steps: the first is solving the current RMP to obtain the optimal solution. and target value The second is to update the global upper bound: .

[0092] Secondly, in step S203, sub-problem solving and lower bound updating are performed. This step includes two sub-steps. The first is for each scenario... ,fixed Solve the subproblem after linear relaxation. Due to its all-single-module nature, its integer constraints can be relaxed to linear constraints, and the optimal value of the subproblem is recorded. and dual optimal solution Secondly, we calculate the lower bound of the expectation: .

[0093] Then, in step S204, a convergence check is performed. If If the algorithm terminates, step S206 is executed, and the process returns. If the solution is optimal, proceed to step S205 to generate the cut.

[0094] Finally, in step S205, the process of generating multiple cuts is performed, which consists of three sub-steps. The first is for each scene... Construct the optimal cut: Secondly, multiple cuts are added to RMP (each scene corresponds to an independent cut). Thirdly, the k value is iterated to make... Then return to step S202.

[0095] If each scene The optimal objective function of the lower dual problem If the constructed optimal cut is provided to the relaxation master problem, then each iteration will return... The constraints are applied to the relaxation master problem. As iterations increase, the constraint size of the relaxation master problem will increase rapidly. To avoid the rapid increase in constraints slowing down the solution of the relaxation master problem, we can weight all independent scenarios, resulting in the inequality (Benders optimality cut):

[0096] in, , Thus, each iteration only requires providing one constraint to the relaxation master problem, greatly reducing the solution pressure. Based on the optimal cut constraint of equation (16), a Benders decomposition algorithm including a single cut is designed. Figure 3 As shown, the Benders decomposition algorithm, which includes single cuts, consists of six steps, with instance data as its input. Convergence tolerance Where N is the total number of patient types and T is the total number of days in the planning period. For the set of all scenarios with random requirements, For the first time during the planning period Total signal source capacity of the day For the first The unit service utility coefficient for this type of patient For the first The unit waiting cost for this type of patient For the first The proportion of patients with this type of condition As a preset fairness threshold, The weights in the model fusion step are used to determine the optimal number source pre-allocation scheme. And the optimal target value.

[0097] First, in step S301, an initialization step is performed. The initialization step includes two sub-steps, one of which is to construct the relaxation master problem (RMP), which includes constraints (3), (11)-(14), and variables. , and auxiliary variables (No initial cut). Secondly, set a global lower bound. Global upper bound Iteration counter .

[0098] Next, in step S302, the main problem is solved. Solving the main problem includes two sub-steps: the first is solving the current RMP to obtain the optimal solution. and target value The second is to update the global upper bound: .

[0099] Secondly, in step S303, sub-problem solving and lower bound updating are performed. This step includes two sub-steps. The first is for each scenario... ,fixed Solve the subproblem after linear relaxation. (Due to its all-single-module nature, its integer constraints can be relaxed to linear constraints), and the optimal value of the subproblem is recorded. and dual optimal solution Secondly, we calculate the lower bound of the expectation: .

[0100] Then, in step S304, a convergence check is performed. If... If the algorithm terminates, step S306 is executed, and the process returns. If the solution is optimal, proceed to step S305 to generate the cut.

[0101] Finally, in step S305, the process of generating a single cut is performed, which consists of four sub-steps. The first is calculating the aggregate dual variables: Secondly, constructing the Benders optimal cut. Thirdly, the new cut is added to RMP. Fourthly, the value of k is iterated so that... Then return to step S302.

[0102] Compared to returning in each iteration In the case of multiple cuts with constraints, the single optimal cut after aggregation is not the tightest. To combine the advantages of multiple cuts and single cuts, this invention further designs a hybrid cut strategy. Given a relative upper and lower bound gap threshold, during the iteration process, when the upper and lower bound gaps are greater than the threshold, the multiple cut strategy is used to quickly reduce the gap in the relaxation master problem; while when the upper and lower bound gaps are less than or equal to the threshold, the single cut strategy is used to control the expansion speed of the constraint size of the relaxation master problem while solving it quickly. Combining the optimal cut constraints of equations (15) and (16), this invention designs a Benders decomposition algorithm that simultaneously incorporates multiple cuts and single cuts. Figure 4 As shown, the Benders decomposition algorithm, which includes multi-cut and single-cut methods, consists of six steps, with instance data as input. Convergence tolerance Hybrid strategy switching threshold Where N is the total number of patient types and T is the total number of days in the planning period. For the set of all scenarios with random requirements, For the first time during the planning period Total signal source capacity of the day For the first The unit service utility coefficient for this type of patient For the first The unit waiting cost for this type of patient For the first The proportion of patients with this type of condition As a preset fairness threshold, The weights in the model fusion step are used to determine the optimal number source pre-allocation scheme. And the optimal target value.

[0103] First, in step S401, an initialization step is performed. The initialization step includes two sub-steps, one of which is to construct the relaxation master problem (RMP), which includes constraints (3), (11)-(14), and variables. , and auxiliary variables (No initial cut). The objective function of RMP is: Secondly, setting a global lower bound. Global upper bound Iteration counter Strategy pattern flag .

[0104] Next, in step S402, the main problem is solved. Solving the main problem includes two sub-steps, the first being... Solve the current RMP. If Solve the multi-cut form RMP to obtain the optimal solution. and target value ;like Solve the single-cut form RMP to obtain the optimal solution. and target value Secondly, updating the global upper bound: .

[0105] Secondly, in step S403, sub-problem solving and lower bound updating are performed. This step includes three sub-steps. The first is for each scenario... ,fixed Solve the subproblem after linear relaxation. (Due to its all-single-module nature, its integer constraints can be relaxed to linear constraints), and the optimal value of the subproblem is recorded. and dual optimal solution Secondly, we calculate the lower bound of the expectation: Thirdly, it calculates the current relative gap. .

[0106] Then, in step S404, a convergence check is performed. If... If the algorithm terminates, step S406 will be executed, and the process will return. If the solution is optimal, proceed to step S405 to generate the cut.

[0107] Finally, in step S405, the strategy switching and cut generation step is performed, which consists of three sub-steps. The first is the step of constructing the optimal cut: if Then according to Pattern, constructing optimal cut: ;like If at this time Then switch to single-cut mode: , and according to Pattern, calculating aggregate dual variables: Thus, the optimal cut is constructed: Secondly, the calculated cut is added to RMP. Thirdly, the k value is iterated to ensure that... Then return to step S402.

[0108] exist Figure 1 After the model decomposition and solution steps shown in step S105, finally, in Figure 1Step S106, as shown, involves executing the output and execution steps. Specifically, in this step, a hospital patient optimization scheduling strategy is generated based on the optimal solution for the pre-allocated appointment slots, and daily examination appointment slots are allocated. When actual demand occurs and the pre-allocated appointment slots are insufficient, the inter-period appointment scheduling operation for unmet patients is executed based on the calculated optimal solution. The optimal solution for the pre-allocated appointment slots refers to a set of best pre-allocation schemes calculated by the system under the premise of satisfying constraints such as daily appointment capacity, service limit, and fairness among different groups. In the above example of this invention, this means obtaining the optimal solution that satisfies the convergence condition by solving the comprehensive single-objective function model based on the Benders decomposition algorithm described above. Actual demand occurrence refers to a patient randomly arriving on a certain day within the planning period and generating a real examination need. The inter-period appointment scheduling operation refers to the management process of rescheduling overflow patients who could not receive immediate examinations to subsequent available dates within the planning period when the pre-allocated appointment slots for that day are insufficient to meet the aforementioned real demand.

[0109] The hospital appointment supply adjustment method based on Benders decomposition proposed in this invention addresses the practical operational pain points of hospital medical examination appointment allocation. Considering the industry characteristics of random fluctuations in patient demand, multi-period inter-period overflow scheduling, and the coexistence of efficiency and fairness objectives, a two-stage stochastic integer programming model integrating the heterogeneity of multiple patient types is constructed. Linearization techniques are used to handle nonlinear fairness constraints, and a sample averaging approximation method is employed to achieve deterministic transformation of the stochastic model. To address the challenge of large-scale model solving, three types of Benders decomposition algorithms—single-cut, multi-cut, and mixed-cut—are designed, effectively improving the solution efficiency.

[0110] Based on the same inventive concept, referring to Figure 5 This invention also provides a hospital appointment allocation optimization device 500 based on Benders decomposition. The hospital appointment allocation optimization device 500 based on Benders decomposition includes: a data acquisition module 501, a scene generation module 502, a model building module 503, a model fusion module 504, a model decomposition and solution module 505, and an output and execution module 506.

[0111] The data acquisition module 501 is used to acquire the current operational data of the hospital service system. The operational data includes at least the planning cycle length, patient type, the total number of appointments available daily for each patient type, the number of people examined daily, and the average service utility coefficient.

[0112] The scenario generation module 502 is used to sample and generate multiple independent demand scenarios based on the acquired operational data. Each scenario includes a date with a planning period length and the total daily appointment demand for each type of patient within that date.

[0113] Model building module 503 is used for model building. Based on operational data and demand scenarios, it constructs a two-stage mixed integer programming model for patient scheduling. The first stage decision determines the pre-allocated appointment slots for various patient types. The second stage decision determines whether to schedule unmet needs to subsequent planning cycles based on the degree to which the pre-allocated slots meet actual demand. Furthermore, a bi-objective optimization model is established for the two-stage mixed integer programming model. The objective functions of this bi-objective optimization model include a first objective function to maximize the hospital's expected service utility coefficient and a second objective function to minimize the patient's expected waiting cost. The constraints of this optimization model include at least: daily appointment slot capacity constraint, daily service limit constraint, total demand constraint, inter-period scheduling capacity constraint, variable non-negativity and integer constraint, and fairness constraint.

[0114] The model fusion module 504 is used to fuse the first objective function and the second objective function of the bi-objective optimization model using a linear weighting method to construct a comprehensive single objective function.

[0115] The model decomposition and solution module 505 is used to solve the comprehensive single-objective function model using the Benders decomposition algorithm to obtain the optimal solution that satisfies the convergence condition. The solution process includes: decomposing the comprehensive single-objective model into a relaxed master problem corresponding to the first-stage decision and a sub-problem corresponding to the second-stage decision; solving the master problem to obtain the initial pre-assignment decision and inputting the initial pre-assignment decision into the sub-problem; fixing the initial pre-assignment decision obtained from the master problem in the sub-problem, solving the second-stage decision in a single scenario, and generating a Benders cut based on the solution results of the sub-problem and feeding it back to the master problem for iterative updates until the difference between the objective values ​​of the master problem and the sub-problem satisfies the preset convergence condition, thus obtaining the optimal solution pre-assignment source quantity scheme.

[0116] The output and execution module 506 is used to output the optimal solution for the pre-allocated number of appointment slots and to execute the adjustment of the hospital appointment slot supply according to the optimal solution for the pre-allocated number of appointment slots.

[0117] Optionally, in the model fusion module 504, the weights of the first objective function and the second objective function of the bi-objective optimization model fused by the linear weighting method are given by the formula... The calculation shows that, among which For the first The proportion of demand from patients of this type The service utility coefficient per unit. Waiting cost per unit For the planning period, N represents the total number of patient types.

[0118] Optionally, in the model decomposition and solution module 505, during the iterative update, a Benders optimal cut is constructed for each scenario, and the Benders optimal cut is added to the main problem.

[0119] Optionally, in the model decomposition and solution module 505, during the iterative update, the aggregated dual variables of all scenarios are calculated, the Benders optimal cut is constructed using the aggregated dual variables, and the Benders optimal cut is added to the main problem.

[0120] Optionally, in the model decomposition and solution module 505, given the upper and lower bound gap thresholds, during the iterative update, when the upper and lower bound gaps are greater than the upper and lower bound gap thresholds, a Benders optimal cut is constructed for each scenario and added to the main problem. When the upper and lower bound gaps are less than or equal to the upper and lower bound gap thresholds, the aggregated dual variables of all scenarios are calculated, a Benders optimal cut is constructed using the aggregated dual variables, and the Benders optimal cut is added to the main problem.

[0121] Optionally, in the data acquisition module 501, the acquired patient types are four categories: newly diagnosed patients with severe chronic diseases, patients returning for follow-up visits with severe chronic diseases, newly diagnosed patients without severe chronic diseases, and patients returning for follow-up visits with severe non-chronic diseases, and the planning period length is 14 days.

[0122] The implementation methods and specific examples of the hospital appointment supply adjustment method based on Benders decomposition in the foregoing embodiments are also applicable to... Figure 5 The apparatus, through the foregoing detailed description of the hospital appointment supply adjustment method based on Benders decomposition, will be clearly understood by those skilled in the art. Figure 5 The implementation methods of the data processing methods in this document are not detailed here for the sake of brevity.

[0123] According to another aspect of the present invention, a computer system is also provided, comprising: a processor; and a memory storing a computer program, which, when executed by the processor, performs a hospital appointment supply adjustment method based on Benders decomposition according to an embodiment of the present invention.

[0124] Figure 6 This is a schematic block diagram illustrating a computer system for performing an embodiment of the present invention.

[0125] like Figure 6 As shown, a computer system 600 for executing a computer program contained in a computer-readable medium according to embodiments of the present invention may include a processor 610 and a memory 620. The memory 620 stores the computer program.

[0126] Processor 610 is any processing device, such as a microprocessor, that operates according to a computer program installed / stored in memory 620. Memory 620 is any volatile or non-volatile storage element, such as a hard disk, solid-state drive, ROM, or RAM. The program executed by processor 610, etc., is stored in memory 620. Figure 6 The computer system 600 shown can be used to implement a hospital appointment supply adjustment method based on Benders decomposition according to an embodiment of the present invention.

[0127] The hardware computing device or its components described in this invention can be implemented by various suitable hardware means, including but not limited to FPGA, ASIC, SoC, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The devices, apparatuses, methods, and systems involved in this invention are not limited to any specific hardware architecture or configuration. Components in the disclosed devices, apparatuses, and systems may be discrete or integrated, and may be combined in different ways and / or replaced or supplemented by other components. It should be understood that the teachings of this invention can be implemented in various forms, including hardware, software, firmware, dedicated processors, or combinations thereof.

[0128] The block diagrams of the devices, equipment, methods, systems, etc., involved in this invention are merely exemplary and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these circuits, devices, equipment, and systems can be connected, arranged, and configured in any manner that achieves the desired purpose.

[0129] In the foregoing description, the present invention has been described based on embodiments. The various embodiments described above are merely illustrative, and those skilled in the art should understand that the combination of constituent elements and processes of these embodiments can be modified in various ways, and such modifications are also within the scope of the present invention.

Claims

1. A method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition, characterized in that, Includes the following steps: S1: Data Acquisition: Acquire current operational data, which includes at least the planning cycle, patient type, total daily appointment slots, total daily appointment slot demand for each type of patient, and average service utility coefficient. The average service utility coefficient is calculated by weighting the clinical urgency, required consumables, and examination service duration for the same patient type. The clinical urgency is determined by whether the patient has a chronic disease and whether the patient is a follow-up visit. S2: Scenario Generation: Using the sample mean approximation (SAA) method, Monte Carlo sampling is performed based on the acquired operational data to generate multiple independent demand scenarios, wherein each scenario includes a date with a length of the planning period, and the total daily appointment demand for each type of patient during the date period; S3: Model Construction: Based on the operational data and the demand scenario, construct a two-stage mixed integer programming model for patient scheduling, wherein, The first stage of decision-making determines the pre-allocated appointment slots for various patient types. The second stage of decision-making, based on the pre-allocated appointment slots, determines whether to reschedule unmet needs to subsequent planning cycles. A bi-objective optimization model is established based on the two-stage mixed integer programming model. The objective function of the bi-objective optimization model includes a first objective function for maximizing the expected service utility of the hospital and a second objective function for minimizing the expected waiting cost of patients. The constraints of the bi-objective optimization model include at least: daily appointment capacity constraint, daily service limit constraint, total demand constraint, inter-period scheduling capacity constraint, variable non-negativity and integer constraint, and fairness constraint. The fairness constraint requires that the maximum value of the sum of the absolute deviations between the actual allocated appointments and the nominal quota for each type of patient within the planning period does not exceed a preset fairness threshold. S4: Model Fusion: The first objective function and the second objective function of the dual-objective optimization model are fused using a linear weighting method to construct a comprehensive single-objective function model; S5: Model Decomposition and Solution: The Benders decomposition algorithm is used to solve the integrated single-objective function model to obtain the optimal solution that satisfies the convergence condition; the solution process includes: The integrated single-objective function model is decomposed into a relaxed master problem corresponding to the first stage decision and a sub-problem corresponding to the second stage decision; Solve the main problem to obtain the initial pre-assignment decision, and input the initial pre-assignment decision into the sub-problem; The subproblem fixes the initial pre-allocation decision obtained from the main problem, solves the second-stage decision under a single scenario after linear relaxation, and constructs a Benders optimality cut based on the dual optimal solution of the subproblem, feeding it back to the main problem for iterative updates. Specifically, the Benders optimality cut is a multi-cut constructed for each scenario, or a single cut constructed using the aggregated dual variables of all scenarios, or a hybrid cut that switches between the multi-cut and the single cut based on a hybrid strategy switching threshold, until the difference between the global upper bound and the global lower bound is less than or equal to the convergence tolerance. The global upper bound is updated by the optimal objective value of the main problem, and the global lower bound is updated by the expected lower bound of the optimal value of the subproblem under all scenarios, thereby obtaining the optimal solution scheme for the pre-allocated number of sources. S6: Output and Execution: Output the optimal solution for the pre-allocated number of appointment slots, and execute the adjustment of the hospital's medical examination appointment slot supply according to the optimal solution for the pre-allocated number of appointment slots.

2. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, In step S4, the weights of the first objective function and the second objective function of the bi-objective optimization model are fused using the linear weighting method, which is given by the formula... The calculation shows that, among which For the first The proportion of demand from patients of this type The service utility coefficient per unit. Waiting cost per unit For the planning period, N is the total number of patient types.

3. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, The Benders optimal cut adopts a multi-cut approach, specifically: in the iterative update, a Benders optimal cut is constructed for each scenario, and the Benders optimal cut is added to the main problem.

4. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, The Benders optimal cut adopts a single cut approach, specifically: in the iterative update, the aggregated dual variables of all demand scenarios are calculated, the aggregated dual variables are used to construct the Benders optimal cut, and the Benders optimal cut is added to the main problem.

5. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, The Benders optimality cut adopts a hybrid cut approach, specifically: given a hybrid strategy switching threshold. ,and In the iterative update, the current relative gap is calculated. When the current relative gap is greater than the hybrid strategy switching threshold, a Benders optimal cut is constructed for each scenario and added to the main problem. When the current relative gap is less than or equal to the hybrid strategy switching threshold, the aggregated dual variables of all scenarios are calculated, a Benders optimal cut is constructed using the aggregated dual variables, and the Benders optimal cut is added to the main problem.

6. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, In step S6, a hospital patient optimization scheduling strategy is generated based on the optimal solution of the pre-allocated appointment slots, and the daily examination appointment slots are actually allocated. When actual demand occurs and the pre-allocated appointment slots are insufficient, the system will perform cross-period appointment scheduling operations for patients who have not been able to book an appointment slot, based on the optimal solution of the pre-allocated appointment slots.

7. The method for adjusting the supply of hospital medical examination appointment slots based on Benders decomposition according to claim 1, characterized in that, The patients are categorized into four types: newly diagnosed patients with severe chronic diseases, patients undergoing follow-up treatment for severe chronic diseases, newly diagnosed patients without severe chronic diseases, and patients undergoing follow-up treatment for severe non-chronic diseases.

8. A data processing apparatus for executing the hospital medical examination appointment supply adjustment method based on Benders decomposition as described in any one of claims 1-7, characterized in that, The device includes: The data acquisition module is used to acquire current operational data. The operational data includes at least the planning cycle, patient type, total number of appointments per day, total daily appointment demand for each type of patient, and average service utility coefficient. The average service utility coefficient is calculated by weighting the clinical urgency, required consumables, and examination service duration for the same patient type. The clinical urgency is determined by whether the patient has a chronic disease and whether the patient is a follow-up visit. The scenario generation module is used to generate multiple independent demand scenarios by performing Monte Carlo sampling based on the acquired operational data using the sample mean approximation (SAA) method. Each scenario includes a date with a length equal to the planning period, and the total daily appointment demand for each type of patient during the date period. The model building module is used to construct a two-stage mixed integer programming model for patient scheduling based on the operational data and the demand scenario. The first stage of decision-making determines the pre-allocated appointment slots for various patient types. The second stage of decision-making, based on the pre-allocated appointment slots, determines whether to reschedule unmet needs to subsequent planning cycles. A bi-objective optimization model is established based on the two-stage mixed integer programming model. The objective function of the bi-objective optimization model includes a first objective function for maximizing the expected service utility of the hospital and a second objective function for minimizing the expected waiting cost of patients. The constraints of the bi-objective optimization model include at least: daily appointment capacity constraint, daily service limit constraint, total demand constraint, inter-period scheduling capacity constraint, variable non-negativity and integer constraint, and fairness constraint. The fairness constraint requires that the maximum value of the sum of the absolute deviations between the actual allocated appointments and the nominal quota for each type of patient within the planning period does not exceed a preset fairness threshold. The model fusion module is used to fuse the first objective function and the second objective function of the dual-objective optimization model using a linear weighting method to construct a comprehensive single-objective function model; The model decomposition and solution module is used to solve the integrated single-objective function model using the Benders decomposition algorithm to obtain the optimal solution that satisfies the convergence condition; the solution process includes: The integrated single-objective function model is decomposed into a relaxed master problem corresponding to the first stage decision and a sub-problem corresponding to the second stage decision; Solve the main problem to obtain the initial pre-assignment decision, and input the initial pre-assignment decision into the sub-problem; The subproblem fixes the initial pre-allocation decision obtained from the main problem, solves the second-stage decision under a single scenario after linear relaxation, and constructs a Benders optimality cut based on the dual optimal solution of the subproblem, feeding it back to the main problem for iterative updates. Specifically, the Benders optimality cut is a multi-cut constructed for each scenario, or a single cut constructed using the aggregated dual variables of all scenarios, or a hybrid cut that switches between the multi-cut and the single cut based on a hybrid strategy switching threshold, until the difference between the global upper bound and the global lower bound is less than or equal to the convergence tolerance. The global upper bound is updated by the optimal objective value of the main problem, and the global lower bound is updated by the expected lower bound of the optimal value of the subproblem under all scenarios, thereby obtaining the optimal solution scheme for the pre-allocated number of sources. The output and execution module is used to output the optimal solution for the pre-allocated number of appointment slots and to adjust the supply of hospital medical examination appointment slots according to the optimal solution for the pre-allocated number of appointment slots.

9. A computer system, characterized in that, include: processor; as well as A memory storing a computer program, which, when executed by the processor, performs the method as described in any one of claims 1-7.

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