Medical consumable operation type sleeve package optimization method

Abstract

The invention discloses a medical consumable operative kit optimization method, which realizes optimization of types and quantity of surgical consumables in a medical consumable operative kit by constructing a medical consumable operative kit optimization model, setting constraint conditions for the optimization model and solving the medical consumable operative kit optimization model based on the constraint conditions. According to the invention, the kit is optimized, and the optimized surgical kit is associated to a specific surgical style to be used by a doctor, so that the problem of consumable shortage or waste caused by unreasonable kit arrangement can be effectively solved.

Description

Technical Field

[0001] This invention relates to a method for managing medical consumables, and more specifically, a method for designing surgical kits for specific surgeries. Background Technology

[0002] Medical consumables are a crucial component of medical activities. They are not only numerous and diverse, but also present numerous challenges, including difficulty in traceability, frequent intraoperative use, and high regulatory complexity. Traditional consumable management largely involves the head nurse requisitioning a certain amount of consumables based on past usage and storing them in the department. Nurses then submit usage requests to the department's warehouse to collect the consumables, and return the usage list and any remaining consumables to the warehouse after treatment. This model has several problems: First, consumable requests may not match demand, increasing procurement and storage costs; second, requests are made by medical staff, which can be influenced by their personal habits; and finally, the lack of effective end-to-end management of medical consumables can lead to waste and leakage. Against this backdrop, establishing a rational and effective consumable management model for hospitals and improving operational efficiency has become an urgent technical challenge.

[0003] Patent application CN118762811A discloses a method and system for managing medical consumables, focusing on inventory early warning, expiration date management, and automated usage records. Patent application CN118507006B discloses a traceability management method and system for medical consumables, using blockchain technology to record the entire process of consumable production, distribution, and use, ensuring compliance and anti-counterfeiting. However, these solutions do not bind consumable combinations to specific surgical types, failing to achieve intelligent management of "pre-configured kits by surgical procedure." Patent application CN118262886B discloses an intelligent monitoring and traceability management system for operating room SPD (Supply-Process-Distribution) medical consumables, combining the SPD model with real-time monitoring of consumable usage status via IoT devices to optimize delivery efficiency. However, this technology only monitors, replenishes, and delivers pre-configured kits. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a method for optimizing surgical kits for medical consumables. By optimizing the kits, the problem of consumable shortages or waste caused by unreasonable kit settings is solved, and the optimized surgical kits are associated with specific surgical procedures for doctors to use.

[0005] The present invention adopts the following technical solution to solve the technical problem: The characteristic of the medical consumable surgical kit optimization method of the present invention is that it constructs an optimization model of the medical consumable surgical kit, sets various constraints for the optimization model, and solves the optimization model of the medical consumable surgical kit based on the constraints, thereby optimizing the types and quantities of surgical consumables in the medical consumable surgical kit.

[0006] The characteristic of the optimized method for surgical kits of medical consumables of the present invention is that the optimization method is carried out according to the following steps: Step 1: Construct an optimization model for medical consumable surgical kits. The optimization model is the objective function of minimizing the sum of out-of-stock costs and replenishment costs, as represented by equation (1): In formula (1): by Indicates the first Consumables , This refers to the total number of different types of consumables. by Indicates the first Surgical procedures, , Total number of surgical types; by Indicates surgery medium consumables The amount of stock shortage, , It is a set of positive integers; by Indicating consumables in the operating room Inventory levels; This indicates the cost factors involved in replenishing consumables; by The decision variables of the model are respectively abbreviation; by Indicates the first Surgical kit, , Total number of surgical kit types; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; by Indicates allocation to surgery Consumables The amount of goods returned to inventory; Step 2: Set the constraints for the objective function described in equation (1), which are as follows: Constraint 1 is the surgical kit characterized by equation (2-1). Is it assigned to surgery? Value constraints: Equation (2-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 2 is the consumable characterized by equation (2-2). Assigned to package Constraints on the number of values: Equation (2-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 3 is the constraint on the values ​​of consumable shortage and return quantity, represented by equation (2-3): in, Let be the set of positive real numbers, and let equation (2-3) represent the operation. medium consumables Both the out-of-stock quantity and the number of items returned to inventory are positive real numbers; Constraint 4 is the surgical condition expressed by equation (2-4). medium consumables Inventory return quantity constraints: In equation (2-4): Indicates surgery medium consumables Usage; Constraint 5 is the surgical condition expressed by equation (2-5). medium consumables Stockout constraints: Constraint 6 is the level constraint on the reduction of the amount of goods returned to inventory, expressed by equation (2-6): In equation (2-6): Indicates consumables The current inventory return volume; Indicates the level of reduction in the amount of goods returned to inventory; Step 3: Based on the constraints in Step 2, solve the objective function in Step 1 to optimize the medical consumable surgical kit.

[0007] The characteristic of the medical consumable surgical kit optimization method of the present invention is that: based on a data-driven model decomposition method, the medical consumable surgical kit optimization model is decomposed into sub-model a and sub-model b. Sub-model a is an initial surgical kit constructed based on the correlation between consumables and surgery; sub-model b is a supplementary surgical kit based on the initial surgical kit and the consumable shortage situation. By solving sub-model a and sub-model b, the medical consumable surgical kit optimization model is solved, and the optimized medical consumable surgical kit scheme is obtained.

[0008] The characteristic of the medical consumable surgical kit optimization method of this invention is that the optimization model of the medical consumable surgical kit is solved according to the following method: Step 4.1: Construct sub-model a, and set the model objective function to minimize the sum of stockout cost and replenishment cost as shown in equation (2): In formula (2): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, ,in satisfy ; by This represents the total number of surgical kit types generated in step 4.1; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; Set model constraints such as constraint 3, and add constraint 7 to constraint 12; Constraint 7 is the surgical kit characterized by equation (3-1). Is it assigned to surgery? Value constraints: Equation (3-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 8 is the consumable characterized by equation (3-2). Assigned to package Constraints on the number of values: Equation (3-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 9 is the surgical condition expressed by equation (3-3). medium consumables Inventory return quantity constraints: Constraint 10 is the surgical condition expressed by equation (3-4). medium consumables Stockout constraints: Constraint 11 is the constraint on the level of reduction in the amount of goods returned to inventory, characterized by equation (3-5): In equation (3-5): This indicates the level of reduction in the amount of goods returned to inventory in sub-model a; [Settings] , For the subsequent step 4.2 constraint 18, the level of reduction in the amount of returned goods is more stringent than the final solution in the initial solution for surgical kits. Constraint 12 is the surgical consumables represented by equation (3-6). With surgery Association constraints: In equation (3-6): Surgical consumables With surgery The correlation coefficient threshold; Equation (3-6) stipulates that the initial kit allocated to the surgery can only contain consumables that are strongly correlated with the surgery, that is, the correlation coefficient between the consumables in the initial kit and the surgery must be greater than 1. ; Using the Gurobi commercial solver, sub-model a is solved to obtain the solution results for sub-model a, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; Step 4.2: Construct sub-model b, and set the model objective function to minimize the sum of stockout cost and replenishment cost as shown in equation (3). In formula (3): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, This refers to the surgical kit that needs optimization in step 4.2, starting from the coding. Start to Finish; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; Set model constraints as shown in constraint 3, and add constraints 13 through 18: Constraint 13 is the surgical kit characterized by equation (4-1). Is it assigned to surgery? Value constraints: Equation (4-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 14 is a nested condition characterized by equation (4-2). Consumables that need optimization Value constraints: Equation (4-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 15 is the surgical kit characterized by equations (4-3) and (4-4). Shortage of consumables in China and Africa Quantity constraints: In equation (4-3): This refers to a collection of consumables facing shortages. Equation (4-4) represents the allocation of surgical kits. Consumables The quantity is 0.

[0009] Constraint 16 is the surgical condition expressed by equation (4-5). medium consumables Inventory return quantity constraints: In equation (4-5): and The solution result from step 4.1 is kept constant in step 4.2 and is not optimized. Constraint 17 is the surgical condition expressed by equation (4-6). medium consumables Stockout constraints: Constraint 18 is the level constraint for reducing the amount of goods returned to inventory, expressed by equation (4-7): The sub-model b was solved using the Gurobi commercial solver, and the solution results for sub-model b were obtained, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; ultimately forming a group containing An optimized solution for surgical kits.

[0010] Compared with existing technologies, the beneficial effects of this invention are reflected in: 1. The present invention provides a joint optimization modeling method; it establishes a multi-objective optimization model to simultaneously optimize the category combination (i.e., category optimization) and configuration quantity (i.e., quantity optimization) of consumables in the surgical kit, thereby achieving the overall optimal configuration of consumables; 2. This invention features a hierarchical solution algorithm design. Addressing the challenge of solving the main model in polynomial time, a novel two-stage decomposition algorithm is proposed. The first stage primarily generates an initial surgical kit plan, while the second stage addresses and optimizes the missing consumables in the first stage plan, thereby achieving efficient solution to the optimization problem. Polynomial time is a crucial concept in computational complexity theory, describing the relationship between algorithm runtime and input size. An algorithm running in polynomial time means that its worst-case time complexity can be expressed as the input size. A polynomial function. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the model construction process in this invention; Figure 2 This is a schematic diagram of the surgical kit production process in this invention; Detailed Implementation

[0012] See Figure 1 and Figure 2 In specific implementation, the optimization method of medical consumable surgical kits is as follows: First, construct an optimization model for medical consumable surgical kits and set various constraints for the optimization model; then, solve the optimization model for medical consumable surgical kits based on the constraints, and finally optimize the types and quantities of surgical consumables in the medical consumable surgical kits.

[0013] In practice, the optimization method for medical consumable surgical kits is carried out according to the following steps: Step 1: Construct an optimization model for medical consumable surgical kits. The optimization model is represented by the objective function of minimizing the sum of out-of-stock costs and replenishment costs, as described by equation (1): In formula (1): by Indicates the first Consumables , This refers to the total number of different types of consumables. by Indicates the first Surgical procedures, , Total number of surgical types; by Indicates surgery medium consumables The amount of stock shortage, , It is a set of positive integers; by Indicating consumables in the operating room Inventory levels; This indicates the cost factors involved in replenishing consumables; by The decision variables of the model are respectively abbreviation; by Indicates the first Surgical kit, , Total number of surgical kit types; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; by Indicates allocation to surgery Consumables The amount of goods returned to inventory; In formula (1): express: ; The significance of step 1 lies in transforming the actual business problem into a mathematical optimization problem and clarifying the optimization objective; by minimizing the sum of out-of-stock costs and replenishment costs, the optimal surgical kit strategy is found to avoid excessive inventory or shortages in surgical consumables management.

[0014] Step 2: Set the constraints for the objective function shown in equation (1), which are as follows: Constraint 1 is the surgical kit characterized by equation (2-1). Is it assigned to surgery? Value constraints: Equation (2-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 2 is the consumable characterized by equation (2-2). Assigned to package Constraints on the number of values: Equation (2-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 3 is the constraint on the values ​​of consumable shortage and return quantity, represented by equation (2-3): in, Let be the set of positive real numbers, and let equation (2-3) represent the operation. medium consumables Both the out-of-stock quantity and the number of items returned to inventory are positive real numbers; Constraint 4 is the surgical condition expressed by equation (2-4). medium consumables Inventory return quantity constraints: In equation (2-4): Indicates surgery medium consumables Usage; Constraint 5 is the surgical condition expressed by equation (2-5). medium consumables Stockout constraints: Constraint 6 is the level constraint on the reduction of the amount of goods returned to inventory, expressed by equation (2-6): In equation (2-6): Indicates consumables The current inventory return volume; Indicates the level of reduction in the amount of goods returned to inventory; The significance of step 2 is to ensure that the optimization results conform to actual business rules and resource constraints.

[0015] Step 3: Based on the constraints in Step 2, solve the objective function represented by Equation (1) in Step 1 to optimize the medical consumables surgical kit. The significance of Step 3 is to select the solution algorithm according to the model properties and give the optimization result of the medical consumables surgical kit.

[0016] To solve the optimization model of medical consumable surgical kits, a data-driven model decomposition method is used. The optimization model is decomposed into sub-models a and b. Sub-model a is the initial surgical kit constructed based on the correlation between consumables and surgery. Sub-model b is a supplementary surgical kit based on the initial surgical kit and the situation of consumable shortages. By solving sub-models a and b, the optimization model of medical consumable surgical kits is solved, yielding an optimized solution. In this embodiment, the significance of model decomposition lies in addressing the difficulty of solving the main model in polynomial time due to its high complexity. By decomposing the original problem into two sub-problems solvable in polynomial time, the computational complexity is significantly reduced. Phased optimization ensures the feasibility of the initial solution and achieves the global optimization goal through local adjustments.

[0017] In practice, the optimization model for medical consumable surgical kits is solved using the following method: Step 4.1: Construct sub-model a and set the model objective function to minimize the sum of out-of-stock cost and replenishment cost as shown in equation (2). In formula (2): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, ,in satisfy ; by This represents the total number of surgical kit types generated in step 4.1; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; In formula (2): express: ; Set model constraints such as constraint 3, and add constraint 7 to constraint 12; Constraint 7 is the surgical kit characterized by equation (3-1). Is it assigned to surgery? Value constraints: Equation (3-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 8 is the consumable characterized by equation (3-2). Assigned to package Constraints on the number of values: Equation (3-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 9 is the surgical condition expressed by equation (3-3). medium consumables Inventory return quantity constraints: Constraint 10 is the surgical condition expressed by equation (3-4). medium consumables Stockout constraints: Constraint 11 is the constraint on the level of reduction in the amount of goods returned to inventory, characterized by equation (3-5): In equation (3-5): This indicates the level of reduction in the amount of goods returned to inventory in sub-model a; [Settings] , For the subsequent step 4.2 constraint 18, the level of reduction in the amount of returned goods is more stringent than the final solution in the initial solution for surgical kits. Constraint 12 is the surgical consumables represented by equation (3-6). With surgery Association constraints: In equation (3-6): Surgical consumables With surgery The correlation coefficient threshold; Equation (3-6) stipulates that the initial kit allocated to the surgery can only contain consumables that are strongly correlated with the surgery, that is, the correlation coefficient between the consumables in the initial kit and the surgery must be greater than 1. ; Using the Gurobi commercial solver, sub-model a is solved to obtain the solution results for sub-model a, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; The significance of step 4.1 lies in constructing an initial surgical kit plan based on historical data and utilizing the correlation between consumables and surgery, thereby reducing the scale of subsequent optimization variables by pre-generating highly correlated kits.

[0018] Step 4.2: Construct sub-model b, and set the model objective function to minimize the sum of stockout cost and replenishment cost as shown in equation (3). In formula (3): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, This refers to the surgical kit that needs optimization in step 4.2, starting from the coding. Start to Finish; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; In formula (3): express: ; Set model constraints as shown in constraint 3, and add constraints 13 through 18: Constraint 13 is the surgical kit characterized by equation (4-1). Is it assigned to surgery? Value constraints: Equation (4-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 14 is a nested condition characterized by equation (4-2). Consumables that need optimization Value constraints: Equation (4-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 15 is the surgical kit characterized by equations (4-3) and (4-4). Shortage of consumables in China and Africa Quantity constraints: In equation (4-3): This refers to a collection of consumables facing shortages. Equation (4-4) represents the allocation of surgical kits. Consumables The quantity is 0.

[0019] Constraint 16 is the surgical condition expressed by equation (4-5). medium consumables Inventory return quantity constraints: In equation (4-5): and The solution result from step 4.1 is kept constant in step 4.2 and is not optimized. Constraint 17 is the surgical condition expressed by equation (4-6). medium consumables Stockout constraints: Constraint 18 is the level constraint for reducing the amount of goods returned to inventory, expressed by equation (4-7): The sub-model b was solved using the Gurobi commercial solver, and the solution results for sub-model b were obtained, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; The significance of step 4.2 lies in dynamically replenishing and optimizing the consumables that are missing in the initial package generated in step 4.1. The optimization in step 4.2 is based on the optimization in step 4.1, which greatly reduces the complexity of the problem and solves the long-tail requirements that the initial package cannot cover.

[0020] The Gurobi solver is a high-performance mathematical programming solver specifically designed for solving optimization problems such as linear programming, mixed-integer linear programming, quadratic programming, and mixed-integer quadratic programming. The problem in this study, after defining variables, setting the objective function, and adding constraints, is transformed into a mixed-integer linear programming problem solvable using the Gurobi solver. Therefore, the Gurobi solver can be used for solving this problem. Compared to other existing mathematical programming solvers, the Gurobi solver has the advantages of being the fastest and supporting a wide range of problem types.

[0021] The final form includes An optimized solution for surgical kits. The surgical kit includes: the solution obtained from sub-model a The various packages, and the solution obtained from sub-model b Surgical kit; among them, the first The quantity of consumables corresponding to each type of surgical kit is , ;No. The quantity of consumables corresponding to each type of surgical kit is , The allocation rules for surgical kits are as follows: Surgical kit , No. Type of surgical kit corresponding .

[0022] Example: Assuming three types of surgeries require five types of surgical consumables, the consumables matrix used is as follows. Represented as: Correlation coefficient matrix between consumables and surgery for: Inventory levels of 5 types of consumables for: The return quantity V of the five types of consumables is: Assuming a threshold for the correlation coefficient between consumables and surgery The level of reduction in the amount of goods returned to the warehouse , Consumable replenishment costs This generates 2 initial surgical kits and 3 supplementary kits.

[0023] (1) The result obtained by solving sub-model a (initial surgical kit design) is: Package 1 contains Consumable 1 (1 piece), Consumable 2 (3 pieces), and Consumable 5 (3 pieces), and is allocated to Surgery 1; Package 2 contains Consumable 1 (1 piece), Consumable 2 (1 piece), and Consumable 4 (3 pieces), and is allocated to Surgery 2 and 3; Consumables 2, 3, and 5 are out of stock.

[0024] (2) Further solving sub-model b (supplementary surgical kit design) yields the following results: Package 3 contains two consumables 2 and one consumable 3, which are allocated to surgery 2; Package 5 contains one consumable 5, which is allocated to surgery 3; Package 4 does not contain any consumables and is not allocated.

[0025] Thus, the optimization of surgical consumable kits has been completed. This invention, through precise pre-preparation of consumable kits before surgery, can proactively reduce the preparation time of consumables during surgery, decrease the frequency of consumable searches by medical staff, and significantly improve the continuity and efficiency of the surgical procedure. This invention also aims to minimize stockouts and inter-operating room replenishment costs, while limiting the post-operative return of surgical consumables to the warehouse, effectively reducing the inventory and usage costs of medical consumables.

Claims

1. A method for optimizing surgical procedure kits for medical consumables, characterized in that: An optimization model for surgical consumable kits is constructed, and various constraints are set for the optimization model. The optimization model for surgical consumable kits is solved based on the constraints to optimize the types and quantities of surgical consumables in the surgical consumable kits.

2. The method for optimizing the surgical procedure package of medical consumables according to claim 1, characterized in that: The optimization method is carried out according to the following steps: Step 1: Construct an optimization model for medical consumable surgical kits. The optimization model is the objective function of minimizing the sum of out-of-stock costs and replenishment costs, as represented by equation (1): In formula (1): by Indicates the first Consumables , This refers to the total number of different types of consumables. by Indicates the first Surgical procedures, , Total number of surgical types; by Indicates surgery medium consumables The amount of stock shortage, , It is a set of positive integers; by Indicating consumables in the operating room Inventory levels; This indicates the cost factors involved in replenishing consumables; by The decision variables of the model are respectively abbreviation; by Indicates the first Surgical kit, , Total number of surgical kit types; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; by Indicates allocation to surgery Consumables The amount of goods returned to inventory; Step 2: Set the constraints for the objective function described in equation (1), which are as follows: Constraint 1 is the surgical kit characterized by equation (2-1). Is it assigned to surgery? Value constraints: Equation (2-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 2 is the consumable characterized by equation (2-2). Assigned to package Constraints on the number of values: Equation (2-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 3 is the constraint on the values ​​of consumable shortage and return quantity, represented by equation (2-3): in, Let be the set of positive real numbers, and let equation (2-3) represent the operation. medium consumables Both the out-of-stock quantity and the number of items returned to inventory are positive real numbers; Constraint 4 is the surgical condition expressed by equation (2-4). medium consumables Inventory return quantity constraints: In equation (2-4): Indicates surgery medium consumables Usage; Constraint 5 is the surgical condition expressed by equation (2-5). medium consumables Stockout constraints: Constraint 6 is the level constraint on the reduction of the amount of goods returned to inventory, expressed by equation (2-6): In equation (2-6): Indicates consumables The current inventory return volume; Indicates the level of reduction in the amount of goods returned to inventory; Step 3: Based on the constraints in Step 2, solve the objective function in Step 1 to optimize the medical consumable surgical kit.

3. The method for optimizing the surgical procedure kit for medical consumables according to claim 2, characterized in that: Based on a data-driven model decomposition method, the optimization model of the medical consumable surgical kit is decomposed into sub-model a and sub-model b. Sub-model a is an initial surgical kit constructed based on the correlation between consumables and surgery. Sub-model b is a supplementary surgical kit based on the initial surgical kit and the situation of consumable shortage. By solving sub-model a and sub-model b, the optimization model of the medical consumable surgical kit is solved, and the optimization scheme of the medical consumable surgical kit is obtained.

4. The method for optimizing the surgical procedure kit for medical consumables according to claim 3, characterized in that: The optimization model for medical consumable surgical kits can be solved using the following method: Step 4.1: Construct sub-model a and set the model objective function to minimize the sum of out-of-stock cost and replenishment cost as shown in equation (2). In formula (2): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, ,in satisfy ; by This represents the total number of surgical kit types generated in step 4.1; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; Set model constraints such as constraint 3, and add constraint 7 to constraint 12; Constraint 7 is the surgical kit characterized by equation (3-1). Is it assigned to surgery? Value constraints: Equation (3-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 8 is the consumable characterized by equation (3-2). Assigned to package Constraints on the number of values: Equation (3-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 9 is the surgical condition expressed by equation (3-3). medium consumables Inventory return quantity constraints: Constraint 10 is the surgical condition expressed by equation (3-4). medium consumables Stockout constraints: Constraint 11 is the constraint on the level of reduction in the amount of goods returned to inventory, characterized by equation (3-5): In equation (3-5): This indicates the level of reduction in the amount of goods returned to inventory in sub-model a; [Settings] , For the subsequent step 4.2 constraint 18, the level of reduction in the amount of returned goods is more stringent than the final solution in the initial solution for surgical kits. Constraint 12 is the surgical consumables represented by equation (3-6). With surgery Association constraints: In equation (3-6): Surgical consumables With surgery The correlation coefficient threshold; Equation (3-6) stipulates that the initial kit allocated to the surgery can only contain consumables that are strongly correlated with the surgery, that is, the correlation coefficient between the consumables in the initial kit and the surgery must be greater than 1. ; Using the Gurobi commercial solver, sub-model a is solved to obtain the solution results for sub-model a, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; Step 4.2: Construct sub-model b, and set the model objective function to minimize the sum of stockout cost and replenishment cost as shown in equation (3). In formula (3): by Represents a set of variables ; by Represents a set of variables ; by Indicates surgical kit, This refers to the surgical kit that needs optimization in step 4.2, starting from the coding. Start to Finish; by Indicates surgical kit Is it assigned to surgery? ; by Indicates consumables Assigned to package The number of items in; Set model constraints as shown in constraint 3, and add constraints 13 through 18: Constraint 13 is the surgical kit characterized by equation (4-1). Is it assigned to surgery? Value constraints: Equation (4-1) represents the package Assigned to surgery hour, ,otherwise ; Constraint 14 is a nested condition characterized by equation (4-2). Consumables that need optimization Value constraints: Equation (4-2) represents consumables Assigned to package The number of elements in the list is a positive integer; Constraint 15 is the surgical kit characterized by equations (4-3) and (4-4). Shortage of consumables in China and Africa Quantity constraints: In equation (4-3): This refers to a collection of consumables facing shortages. Equation (4-4) represents the allocation of surgical kits. Consumables The quantity is 0. Constraint 16 is the surgical condition expressed by equation (4-5). medium consumables Inventory return quantity constraints: In equation (4-5): and The solution result from step 4.1 is kept constant in step 4.2 and is not optimized. Constraint 17 is the surgical condition expressed by equation (4-6). medium consumables Stockout constraints: Constraint 18 is the level constraint for reducing the amount of goods returned to inventory, expressed by equation (4-7): The sub-model b was solved using the Gurobi commercial solver, and the solution results for sub-model b were obtained, including... and , respectively represent packages It contains consumables Quantity and packages Is it assigned to surgery? ; ultimately forming a group containing An optimized solution for surgical kits.

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