A tea product family association decision optimization method based on nested reinforcement cosine algorithm

Abstract

The present application relates to a tea product family association decision optimization method based on nested reinforcement cosine algorithm, belonging to the field of supply chain management and intelligent optimization technology. In view of the problems of independent game between manufacturers and suppliers, continuous raw material ratio and complex cost accounting in the tea industry supply chain, a Stackelberg master-slave associated double-layer optimization model is constructed to maximize the profits of manufacturers and suppliers, covering product ingredient selection, supplier selection, inventory setting and dynamic pricing decisions. A nested reinforcement cosine algorithm is designed for solution, discrete processing is realized through integer coding, and the non-smooth parameters of the cosine algorithm are adaptively adjusted by introducing Q-learning, and an optimization process of alternating iteration between upper and lower layers is established. The present application can output tea product family configuration, supplier quotation and inventory strategy, and provide quantitative basis for tea enterprise supply chain collaborative decision making.

Description

Technical Field

[0001] This invention belongs to the field of supply chain management and intelligent optimization technology, specifically involving a tea product family association decision optimization method based on nested reinforced sine and cosine algorithms. Background Technology

[0002] In recent years, the tea beverage market has continued to expand, and the pace of product iteration has accelerated. Product family configuration and supplier collaboration optimization within the tea beverage industry supply chain are core factors influencing the efficiency of enterprise production resource allocation and sustainable development. Currently, tea beverage companies tend to focus their decision-making on upstream aspects such as understanding end-market preferences, paying insufficient attention to the allocation of technical resources within the internal supply chain and the optimization of upstream and downstream collaboration. Traditional supply chain decision-making models often treat manufacturers as the sole core, viewing suppliers as passive fulfillers, failing to consider the autonomous game-playing behavior of suppliers as independent stakeholders. This makes it difficult to address the issues of independent game-playing between manufacturers and suppliers, continuous raw material proportioning, and complex cost accounting within the tea beverage industry supply chain.

[0003] Existing research on product family design and supplier collaborative optimization primarily focuses on general component manufacturing scenarios. In these scenarios, raw material selection follows discrete logic with simple proportioning rules, fundamentally differing from the characteristics of process-oriented prepared products like tea beverages. Tea beverage raw material proportioning involves continuous concentration adjustment, core ingredients are measured by weight or volume, and cost accounting requires dynamic conversion based on formula concentration and the proportion of main base ingredients. Existing collaborative decision-making models for discrete manufacturing cannot directly adapt to the cost structure and decision-making logic of the tea beverage industry. Furthermore, the aforementioned decision-making problem involving tea product families and suppliers is a two-layer discrete nonlinear NP-hard problem. Traditional mathematical programming methods struggle to handle complex constraints such as non-convexity and non-differentiability. Conventional intelligent optimization algorithms are highly sensitive to parameters and prone to getting trapped in local optima. Their efficiency and accuracy in solving two-layer discrete nonlinear NP-hard problems fail to meet the actual operational needs of enterprises, thus limiting the ability of computer systems to solve the technical resource allocation problem in the tea beverage supply chain. Summary of the Invention

[0004] The purpose of this invention is to address the problems of independent game between manufacturers and suppliers, continuous raw material ratio, and complex cost accounting in the tea beverage industry supply chain by providing a tea product family association decision optimization method based on nested reinforced sine and cosine algorithms.

[0005] To achieve the above objectives, the technical solution of this invention is: a tea product family association decision optimization method based on nested reinforced sine and cosine algorithms, applicable to resource allocation decisions in the tea beverage industry's process manufacturing supply chain, comprising:

[0006] Acquire basic configuration data and supply chain data for tea product families; wherein, the basic configuration data and supply chain data are technical parameters at the physical production level of the tea beverage supply chain.

[0007] A Stackelberg master-slave optimization model is constructed, which includes an upper-level manufacturer optimization sub-model and a lower-level supplier optimization sub-model. The upper-level manufacturer optimization sub-model aims to maximize the expected profit of the tea beverage manufacturer, and the decision variables include product ingredient category selection variables, supplier selection variables, product inventory quantity variables, and product retail price variables. The lower-level supplier optimization sub-model aims to maximize the expected profit of the supplier, and the decision variables include supplier order acceptance decision variables and supplier quotation variables.

[0008] A nested reinforced sine and cosine algorithm is used to iteratively solve the Stackelberg master-slave correlation optimization model, outputting the optimal decision results on the manufacturer's side and the optimal decision results on the supplier's side to guide the allocation of supply chain technical resources for tea beverage product families; in the nested reinforced sine and cosine algorithm, the position update parameters of the sine and cosine algorithm are... Through dynamic adjustment using Q-learning, the state space is defined as a stagnation level. Improved level 9 A 9-grid layout is used, with the reward function being the difference between the objective functions of adjacent generations. Furthermore, the upper-level manufacturer optimization sub-model and the lower-level supplier optimization sub-model share the same Q-table, achieving optimization through alternating iterations between the upper and lower layers. Cross-layer transmission.

[0009] Furthermore, in the upper-level manufacturer optimization sub-model, the tea beverage manufacturer's expected profit equals expected revenue minus expected cost, where:

[0010] Expected revenue is the sum of the products of the retail price of each product and the expected demand for the corresponding product;

[0011] The expected costs include the tea beverage manufacturer's reprocessing costs, raw material procurement costs, and inventory costs. The tea beverage manufacturer's reprocessing costs are the sum of the products of the reprocessing costs corresponding to the selected ingredient categories for each product and the expected demand for the corresponding product. The raw material procurement costs are the sum of the products of the suppliers' quotations for the supplied raw materials and the corresponding purchase quantities and expected demand for the product. The purchase quantities are determined by the product ingredient category selection variables and the supplier selection variables.

[0012] Furthermore, the expected demand for the product is determined by the following formula:

[0013]

[0014] in, for The expected market demand for each product Indicates the first The sensitivity coefficient of a product to its market selling price. For the first The potential market demand for each product For the first Retail price of each product This is the demand fluctuation term, reflecting the volatility caused by uncertainty in market demand. , This represents the total number of products.

[0015] The inventory cost is determined by the following formula:

[0016]

[0017] in, Total inventory cost For the first Unit holding cost of each product For the first Inventory quantity of each product To minimize demand, ; For remaining inventory, It is a probability density function used to describe the demand. Probability distribution of occurrence ,obey The upper mean is The variance is Distribution; Yes The points.

[0018] Furthermore, in the lower-level supplier optimization sub-model, the supplier's expected profit equals expected revenue minus expected cost, where:

[0019] Expected revenue is the sum of the products of the supplier's quoted price for the raw materials supplied and the corresponding purchase quantity and expected demand for the product;

[0020] The expected cost includes raw material supply cost and transportation cost. The transportation cost is the sum of the product of the supplier's unit transportation cost, transportation distance, corresponding purchase quantity, and expected product demand.

[0021] Furthermore, the iterative solution steps of the nested enhanced sine and cosine algorithm include:

[0022] S1. Initialize the upper-level population, encode the upper-level decision variables with integers, calculate the fitness of each upper-level individual based on the objective function of the upper-level manufacturer optimization sub-model, and determine the initial upper-level optimal solution.

[0023] S2. Using the initial upper-level optimal solution as input constraints, initialize the lower-level population, and use the sine and cosine algorithm with Q-learning adaptive parameter adjustment to iteratively optimize the lower-level supplier optimization sub-model, outputting the current lower-level optimal solution and the corresponding lower-level fitness.

[0024] S3. The current optimal solution of the lower layer is fed back to the upper layer. The upper-layer manufacturer optimization sub-model is iteratively optimized using the sine and cosine algorithm with Q-learning adaptive parameter adjustment, and the optimal solution of the upper layer and the corresponding upper-layer fitness are updated.

[0025] S4. Repeat S2 to S3 until the preset maximum number of iterations is reached. The optimal solution obtained in the last iteration is taken as the optimal decision result on the manufacturer's side, and the corresponding optimal solution on the lower level is taken as the optimal decision result on the supplier's side.

[0026] Furthermore, in the sine and cosine algorithm with Q-learning adaptive parameter adjustment, the position update parameters of the sine and cosine algorithm... Dynamic adjustments are made through Q-learning, specifically including:

[0027] The state space S is defined as a 9×9 grid space, where each grid consists of a set of... Composition, in which, y represents the stagnation level, and y represents the improvement level.

[0028]

[0029]

[0030] in, For stag algebra, , For the first The objective function value of the substitute. For the first Substitute the objective function value;

[0031] Action Space A: , For algebra, For the maximum number of generations, ;

[0032] In each generation, adopt Strategy on parameters Select Action Set to 0.2:

[0033]

[0034] In state implement Then calculate the reward function and transition to the new state. reward function Designed as follows:

[0035]

[0036] Furthermore, Q-learning applies to the action value function. The update is performed using the following formula:

[0037]

[0038] Among them, learning rate =0.1, control information update magnitude, discount factor To measure the importance of future rewards For instant rewards, The optimal action value for the next state.

[0039] Furthermore, the position update output of the sine and cosine algorithm is a continuous value. The round function is used to map the continuous output value to an integer to complete the discretization of the decision variable. The mapped integer value needs to be checked for boundaries. If it exceeds the preset range of the decision variable, it is truncated to the nearest boundary value.

[0040] Furthermore, the configuration basic data includes the raw material module division of the tea product family, the candidate categories of each raw material module, the processing cost corresponding to each candidate category, the price sensitivity coefficient of each product, the potential market demand quantity of each product, and the unit inventory cost of each product.

[0041] The basic supply chain data includes the supplier set corresponding to each raw material candidate category, the production cost of each supplier, the unit transportation cost of each supplier, and the transportation distance of each supplier.

[0042] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the tea product family association decision optimization method described above.

[0043] The present invention also provides a feature comprising a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the steps of the tea product family association decision optimization method described above.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. For the first time, a master-slave game model between manufacturers and suppliers is constructed specifically for the process manufacturing characteristics of the tea beverage industry. It is compatible with real-world constraints such as continuous raw material proportioning, modular design, a hybrid model of self-production / outsourcing, and demand uncertainty, and solves the problem that general discrete manufacturing models cannot adapt to the cost accounting logic of tea beverages.

[0046] 2. By adaptively adjusting the non-smooth parameters of the sine and cosine algorithms using Q-learning, combined with integer encoding discretization and a double-layer nested iterative architecture, the inherent weakness of double-layer discrete nonlinear NP-hard problems in easily getting trapped in local optima is effectively overcome. Experiments demonstrate that, compared to standard sine and cosine algorithms, genetic algorithms, and particle swarm optimization, this method achieves higher upstream and downstream bidirectional profits and converges faster.

[0047] 3. It can directly output product family configuration schemes (raw material selection, pricing, inventory) and supplier negotiation strategies (quotation, order acceptance). Taking the actual test data of a tea beverage line as an example, it has achieved a two-way increase in the profits of manufacturers and suppliers, and provided quantitative basis for enterprise supply chain collaborative decision-making. Attached Figure Description

[0048] Figure 1 This invention provides an optimization model linking tea product line design and supplier decision-making.

[0049] Figure 2 Encode the decision variables for the upper and lower level models.

[0050] Figure 3 This is a flowchart of a nested RSCA algorithm.

[0051] Figure 4 A comparison chart of the average convergence trends of different algorithms.

[0052] Figure 5 Comparison of boxplot results for different algorithms.

[0053] Figure 6 A comparison chart of the average convergence trend of the algorithm under different learning rate settings. Detailed Implementation

[0054] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0055] This invention provides a tea product family association decision optimization method based on nested reinforced sine and cosine algorithms, including:

[0056] Obtain basic configuration data and supply chain data for tea product families;

[0057] A Stackelberg master-slave optimization model is constructed, which includes an upper-level manufacturer optimization sub-model and a lower-level supplier optimization sub-model. The upper-level manufacturer optimization sub-model aims to maximize the expected profit of the tea beverage manufacturer, and the decision variables include product ingredient category selection variables, supplier selection variables, product inventory quantity variables, and product retail price variables. The lower-level supplier optimization sub-model aims to maximize the expected profit of the supplier, and the decision variables include supplier order acceptance decision variables and supplier quotation variables.

[0058] The Stackelberg master-slave correlation optimization model is iteratively solved using a nested reinforced sine and cosine algorithm, outputting the optimal decision results on the manufacturer's side and the optimal decision results on the supplier's side; in the nested reinforced sine and cosine algorithm, the position update parameters of the sine and cosine algorithm are... Through dynamic adjustment using Q-learning, the state space is defined as a stagnation level. Improved level 9 A 9-grid layout is used, with the reward function being the difference between the objective functions of adjacent generations. Furthermore, the upper-level manufacturer optimization sub-model and the lower-level supplier optimization sub-model share the same Q-table, achieving optimization through alternating iterations between the upper and lower layers. Cross-layer transmission.

[0059] The following is a detailed implementation process of the present invention.

[0060] This invention, for the first time, extends product family design and supply chain-related decision-making to the tea beverage industry. Considering the unique cost structure of tea beverage manufacturing, including specific raw material proportioning principles and measurement methods, it proposes a nested reinforced sine and cosine algorithm-based optimization method for tea product family-related decisions. It constructs a product family design and supplier decision-making-related optimization model for the tea beverage industry and designs an efficient solution algorithm. Specifically, it includes:

[0061] (1) Combining the main business module and outsourcing business module of tea beverage manufacturers and the bidding characteristics of suppliers, we study the cost structure and profit module of tea beverage manufacturers and suppliers, analyze the interaction decision-making mechanism between the two, and thus construct a master-slave relationship optimization model;

[0062] (2) To address issues such as parameter adaptation, bi-level optimization process design, problem encoding, and solution space discretization, an algorithm improvement design is proposed, and a nested enhanced sine and cosine algorithm is put forward to efficiently solve the bi-level optimization model.

[0063] (3) Based on the raw material modules and proportions of the product line in the actual case, calculate the cost and profit composition of the model, and use the method of the present invention to solve the problem, further verifying the feasibility and effectiveness of the model and algorithm proposed in the present invention.

[0064] 1. Optimization Model for the Correlation between Tea Product Line Design and Supplier Decisions (see...) Figure 1 )

[0065] 1.1 Problem Description

[0066] Suppose a tea producer has Each tea beverage production line Each tea contains K types of raw materials, consisting of a fixed tea base and optional ingredients. Each raw material module contains L candidate categories, and each candidate category has a unequal number of suppliers. Let the supplier set for each candidate category be {1, 2}. ,s, Different suppliers will charge certain production costs, while the manufacturer will also incur its own production and transportation costs. Therefore, the design of a tea beverage product line is essentially the tea beverage manufacturer's selection of the optimal candidate product categories from J options, taking into account product profits. The selection of suppliers is essentially the decision of whether to offer a price based on their own interests and whether to be selected, under the constraint of available raw materials for the product line. Thus, the two are nested constraint optimization problems.

[0067] 1.2 Profit Model for Upper-Level Tea Beverage Manufacturers

[0068] Based on the above problem description, the present invention constructs a two-layer optimization model consisting of one manufacturer and S suppliers. The upper and lower layers of the model aim to maximize the expected profits of the tea beverage manufacturer and the suppliers, respectively.

[0069] Expected profits of top-tier tea beverage manufacturers From expected income Composed of expected costs, of which expected revenue Based on the retail price of tea drinks Sales volume Composition, expected cost includes the sum of the tea beverage manufacturer's reprocessing costs. Raw material costs paid to suppliers Inventory costs Decision variables for upper-level tea beverage manufacturers include: selection of tea beverage ingredient categories. Supplier selection Product inventory quantity decision And the decision on tea beverage sales prices .

[0070] The sales volume of the tea beverage in this invention takes into account the uncertainty of product market demand, and will be [the following text is incomplete and likely refers to a different topic:] The market demand function for a product variant is expressed as:

[0071] (1)

[0072] in, Indicates the first The sensitivity coefficient of a product to its market selling price. No. The potential market demand for each product The value reflects the fluctuations in market demand due to uncertainty.

[0073] The optimization model for upper-level tea beverage manufacturers can be expressed as maximizing expected profit. ,Right now:

[0074] (2)

[0075] in,

[0076] (3)

[0077] (4)

[0078] (5)

[0079] (6)

[0080] (7)

[0081] (8)

[0082] (9)

[0083] (10)

[0084] (11)

[0085] (12)

[0086] (13)

[0087] Among them, decision variables Indicates the first The selling price of each beverage; Indicates the first The first product The first raw material module The procurement cost of each candidate product category; Indicates the first The first product The first raw material module The reprocessing cost of each candidate product category; Indicates for the first If the manufacturer selects the first product The first raw material module If there are 1 candidate categories, the value is 1; otherwise, the value is 0. S represents the total number of candidate product categories, and S represents the total number of suppliers. Indicates for the first For product , if the manufacturer purchases the from the s-th supplier... The first raw material module If there are 1 candidate categories, the value is 1; otherwise, the value is 0. This means that if the s-th supplier provides the first... The first product The first basic module If the raw material supply for each candidate is 1, then the value is 0; otherwise, the value is 0. Indicates the first The supplier for the first The first product The first basic module The offers from each candidate; Indicates the first Inventory cost of each product; Indicates the first Inventory quantity of each product; To minimize demand, ; For remaining inventory, It is a probability density function used to describe the demand. Probability distribution of occurrence ,obey The upper mean is The variance is Distribution; Yes The points.

[0088] Equation (3) represents the expected demand of tea beverage manufacturers. At the horizontal level, with Equation (4) represents the expected revenue from unit price sales; Equation (5) represents the expected production cost of the tea beverage manufacturer, including the cost of self-owned raw materials and remanufacturing processing costs; Equation (6) represents the purchase price of the tea beverage manufacturer; Equation (7) represents the inventory cost of the tea beverage manufacturer to cope with the uncertainty of market demand; Equation (8) represents the constraint on the product variation difference; Equation (9) represents the constraint on the self-purchase of some raw materials; Equation (10) represents the constraint on the option of purchasing raw materials, which is to choose only one supplier or self-produced raw materials. Equations (11) and (12) represent the constraints on the range of values ​​of the manufacturer's decision variables; Equation (13) represents the constraints on the range of values ​​of the model parameters.

[0089] 1.3 Profit Model for Lower-Level Suppliers

[0090] Supplier profits Expected income It consists of expected costs. Among them, expected revenue... The cost originates from the manufacturer's payment for raw materials, while the supplier's expected cost... Including procurement costs provided to tea beverage manufacturers and transportation costs The lower-level model decision variables include: whether to accept the manufacturer's choice. Supplier quotes .

[0091] The lower-level supplier optimization model is expressed as maximizing expected profit. ,Right now:

[0092] (14)

[0093] in,

[0094] (15)

[0095] (16)

[0096] (17)

[0097] (18)

[0098] (19)

[0099] Among them, decision variables Indicates the first The supplier for the first The first of the products The first raw material module Supply costs of candidate products in each category; Indicates the first The supplier for the first The first of the products The first raw material module Unit transportation cost for each product category candidate.

[0100] Equation (15) represents the supplier's expected revenue, which mainly comes from the purchase funds provided by the tea beverage manufacturer; Equation (16) represents the supplier's expected costs, which mainly include procurement costs. Transportation costs ,in, Let s be the transportation distance of the s-th supplier; Equation (17) represents the supplier's ability to supply raw materials for at least one module; Equations (18) and (19) represent the range of values ​​for the decision variables in the supplier optimization model.

[0101] 2. Design of Nested Enhanced Sine and Cosine Optimization Algorithms

[0102] The tea product line and supplier decision-making two-level correlation optimization problem belongs to the two-level mixed integer nonlinear programming problem. Its decision variables include discrete and continuous variables, the objective function and constraints are non-convex and non-differentiable, and cost accounting involves processes such as demand integration and cost accumulation, resulting in high complexity and exhibiting many characteristics of NP-hard problems. Traditional mathematical programming methods for solving this type of problem suffer from the curse of dimensionality and difficulties in constraint handling. The Sine Cosine Algorithm (SCA) is a population-driven metaheuristic intelligent optimization algorithm whose search process is not limited by nonlinearity and multiple constraints. Its core is a population search mechanism driven by sine and cosine mathematical models, a smooth-controlled intelligent optimization algorithm for exploration and development. Compared with two classic algorithms, namely genetic algorithms and particle swarm optimization, the SCA algorithm has a simpler structure, fewer parameters, and its population update mechanism effectively reduces the destruction of the previous generation's excellent solution structure in genetic algorithms and the uncontrolled speed and unstable search behavior of particle swarm optimization. Based on the bi-layer solution characteristic of the problem in this invention, a nested reinforcement sine and cosine optimization algorithm is proposed, including an adaptive parameter adjustment strategy based on reinforcement learning, a discretization processing method, and a nested bi-layer optimization process design.

[0103] In the SCA algorithm, multiple initial random candidate solutions are iterated through an update formula (20) based on sine and cosine functions.

[0104] These candidate solutions dynamically adjust their search behavior based on the random variables and adaptive parameters in the formula, effectively avoiding local optima and converging to the global optimum.

[0105] (20)

[0106] In the formula: It is the current individual's first The individual in the first The position of the tth generation, The updated position See formula (21). From 0 to random numbers, A random number between 0 and 2. A random number between 0 and 1. This represents the position of the d-th dimension of the optimal individual position variable at iteration t. The movement step size is used to balance exploration and development; This is the random oscillation coefficient, introducing randomness into the search; The target weighting coefficient is used to randomly amplify or reduce the influence of the optimal solution on the current solution, thereby enhancing the exploration capability. This is the switching coefficient between sine and cosine modes.

[0107] (twenty one)

[0108] in: It is a constant with a value of 2. This represents the current iteration number. The maximum number of iterations, The algebraic dynamic decrease refers to focusing on overall development in the early stages and local exploration in the later stages. For random factors, parameters Defines whether the current solution tends towards or moves away from the optimal solution; parameters The target weight coefficient is used to randomly amplify or reduce the influence of the optimal solution on the current solution, thereby enhancing the exploration capability. (Parameter) Switch sine and cosine functions with equal probability.

[0109] Different optimization problems have different solution spaces with varying "topography." For complex, multi-modal problems, stronger exploratory capabilities are required (more...). For smooth, single-peak problems, it is necessary to move to the development stage more quickly (smaller) );when When the value is too large, it causes the algorithm to jump continuously, resulting in unstable solution quality; when When the value is too small, the algorithm is prone to getting trapped in local optima; and because the search process for the optimal solution is not entirely linear (such as in non-smooth, multi-peak problems), only a linear decreasing strategy is used to update the algorithm. The value is not reasonable for specific problems, and it is necessary to find a non-smooth parameter adjustment mode based on the characteristics of the state or problem.

[0110] 2.1 Q-learning-based adaptive optimization method for SCA parameters (RSCA)

[0111] This invention introduces Q-learning pairs We perform adaptive parameter optimization and propose a non-smooth parameter adjustment strategy. Based on the algorithm's stagnation state and degree of improvement, we use reinforcement learning to interactively select parameter values ​​that yield high long-term rewards.

[0112] The state space S is defined as a 9×9 grid space, where each grid consists of a set of... Composition, in which, y represents the stagnation level, and y represents the improvement level.

[0113]

[0114]

[0115] in, For stag algebra, , For the first The objective function value of the substitute. For the first Substitute the objective function value.

[0116] Action Space A: , For algebra, For the maximum number of generations, .

[0117] In each generation, adopt Strategy on parameters Select Action Set to 0.2:

[0118] (twenty two)

[0119] In state implement Then calculate the reward function and transition to the new state. reward function Designed as follows:

[0120] (twenty three)

[0121] Furthermore, Q-learning applies to the action value function. The update is performed using the following formula:

[0122] (twenty four)

[0123] Among them, learning rate =0.1, control information update magnitude, discount factor To measure the importance of future rewards For instant rewards, The optimal action value for the next state.

[0124] 2.2 Discretization Method Based on Integer Encoding and Problem Solution Space Transformation

[0125] The original CSA algorithm is a continuous optimization algorithm. However, considering that the optimization problem in this invention is a combinatorial optimization problem, the algorithm is discretized in terms of both problem encoding and solution space transformation. Integer encoding is used to encode the decision variables as follows: Figure 2 As shown.

[0126] The round function is used to map the continuous output values ​​of formula (20) to a set of integers to transform the solution space of the problem.

[0127] (25)

[0128] in, Same as formula (20).

[0129] 2.3 Nested Reinforcement SCA Algorithm Framework Design

[0130] To address the bilevel optimization problem in this invention, a nested bilevel RSCA algorithm is designed. The algorithm's design is as follows: First, an initial set of solutions to the upper-level optimization problem is generated. Under the constraints of this solution, the lower-level optimization model is solved using the SCA algorithm, and the lower-level optimization result is then incorporated into the upper-level optimization model. Second, the upper-level optimization model is further solved using the SCA algorithm. Finally, the optimization results from the upper and lower levels are passed between each other through the objective function. The algorithm iterates repeatedly between the upper and lower-level optimization models, gradually approaching the optimal solution to the bilevel programming problem. The nested RSCA algorithm flow is as follows: Figure 3 As shown in Table 1, the main program pseudocode for the nested RSCA algorithm is as follows. The detailed steps are as follows:

[0131] Step 1: Initialize the upper-level population. (Refer to...) Figure 2 The code scheme generates a random initial solution. The stagnant pedometer is then initialized. , The initial value is 2, and it will be dynamically adjusted later based on the pull probability (RL). Random numbers in the data, Random numbers in the data, Random numbers in the array.

[0132] Step 1.1: Boundary correction. Perform boundary checks on the randomly generated solutions based on the range of values ​​of the decision variables, and perform boundary correction on infeasible solutions according to formula (26).

[0133] (26)

[0134] in, It is a variable The Values ​​of decision variables. and They are variables The maximum and minimum values ​​within the range of values.

[0135] Step 1.2: Evaluate the value of the upper-level objective function The objective function value of the upper-level initial solution is calculated according to formula (2).

[0136] Step 2: Optimize the lower-level model using RSCA

[0137] Step 2.1: Initialize the lower-level population. (Refer to...) Figure 2 The coding scheme randomly generates a set of initial solutions to initialize the stationary pedometer. , The initial value is 2, and it will be dynamically adjusted later based on the pull probability (RL). Random numbers in the data, Random numbers in the data, Random numbers in the array.

[0138] Step 2.2: Evaluate the value of the lower-level objective function Calculate the objective function value of the lower-level initial solution according to equation (14). The higher the objective function value, the better the solution.

[0139] Step 2.3: Iterative optimization. Repeat the following steps until the preset maximum number of iterations is reached. .

[0140] Step 2.3.1: Determine the current state space and update it using formula (22). value.

[0141] Step 2.3.2: Determine the current position of each individual in the lower layer. The new position is obtained by updating using formula (25). And use formula (26) to adjust the boundary.

[0142] in, For the first The middle generation The first individual Dimensional decision variable values, and These represent the maximum and minimum values ​​within the range of the decision variable, respectively.

[0143] Step 2.3.3: Reassessment The objective function value is obtained Compared with the previous generation objective function value Comparison,

[0144] If the solution is better than the previous generation, then update the current solution.

[0145] Step 2.3.4: Calculate the reward function using formula (23) and update the Q table using formula (24).

[0146] Step 2.4: When the maximum number of iterations is satisfied, output the current optimal solution. and objective function value As the optimal solution.

[0147] Step 3: Optimize the upper-level model using RSCA

[0148] Step 3.1: Determine the current position of each individual in the upper layer. The new position is obtained by updating using formula (25). .

[0149] Step 3.2: Same as step 1.

[0150] Step 3.3: Determine the current state space and update it using formula (22). value.

[0151] Step 3.3: Update the current optimal solution and optimal objective value. If the current objective function value... Compared with the previous generation objective function value The solution is compared with the previous one. If the current solution is better, the current solution and the target value are updated.

[0152] Step 3.4: Calculate the reward function using formula (23) and update the Q table using formula (24).

[0153] Step 4: Interactive optimization between upper and lower layers. Pass the current optimal solution to the lower layer, re-execute Step 2 to optimize the lower layer's problem model, and obtain the lower layer's optimal solution; continue executing Step 3 to optimize the upper layer, iterating sequentially until the maximum number of iterations for each layer is reached.

[0154] Step 5: Output the final result. After the upper layer reaches the maximum number of iterations, output the current optimal solution of both the upper and lower layers and the optimal objective function value as the final optimization result.

[0155] Table 1. Pseudocode of the main program for the nested RSCA algorithm

[0156]

[0157] The time complexity of the nested reinforced sine and cosine algorithm is: ,in, The maximum number of iterations in the upper layer ( ), Population size ( ), For the dimensions of upper-level decision variables, Maximum number of iterations per optimization in the lower layer (same as the upper layer) ), This represents the dimension of lower-level decision variables.

[0158] 3. Experiment and Analysis

[0159] 3.1 Case Studies and Data Introduction

[0160] This invention uses the practical optimization problem of tea product line design and supplier-related decision-making at Company N to verify the feasibility of the proposed model and algorithm. Data related to three product lines—sugar-free tea, milk tea, and fruit tea—was collected. Manufacturer data primarily came from Company N's annual financial reports and relevant management personnel from consulting firms, while supplier data mainly came from a survey of tea product cost structure network data. To ensure the research's rationality, the product raw material composition module and supplier structure were appropriately simplified, as shown in Table 2.

[0161] Table 2 Raw Material Module for Tea Beverage Product Line

[0162]

[0163] Note: drinking water, Purified water; Ordinary tea leaves High-quality tea; Modified milk, Fresh milk; jam, Concentrated fruit juice.

[0164] In addition to the core raw material module of the tea beverage product line in Table 1, the production line also includes raw material procurement and processing modules such as sugars, other seasonings, additives, and outer packaging. However, since their proportion in raw material costs is relatively small, and their selection has little impact on beverage design and development, they are included in the raw material reprocessing cost calculation in Table 3. This case study takes three popular tea products on the market as examples. Based on N Company's actual data, the production line design and supplier selection for these three types of products are optimized. The relevant parameter values ​​in the market demand function of the three types of products are shown in Table 3, which also provides N Company's inventory cost information.

[0165] Table 3 Market Information and Inventory Cost Information for Three Types of Tea Products

[0166]

[0167] Note: As a basic product, there are many competing products on the market, so the sensitivity factor is relatively high; and For high-end products, such as milk tea and fruit tea, the price sensitivity coefficient is relatively low; a price sensitivity index of 15 means that for every 1 yuan increase in unit price, the sales volume fluctuates by 150,000 bottles.

[0168] Considering that water is a core industry for Company N and does not require outsourcing, constraint (27) is used to restrict its decision variables, i.e., in product line design. drinking water and The supplier decision variable for purified water is constrained to 0. Table 4 shows the processing cost information for each raw material candidate module for the manufacturer. The specific constraint is as follows:

[0169] (27)

[0170] Table 4. Processing cost information for each raw material candidate module by the manufacturer (RMB / 10,000 bottles)

[0171]

[0172] Note: The reprocessing cost is calculated according to the ratio of pure tea sugar-free beverages: 500ml / bottle, 500ml water, 1.5g tea leaves, water cost 40%; according to the ratio of milk tea beverages, water:milk = 3:1, tea leaves 1g; according to the ratio of fruit tea beverages, water:fruit juice = 10:1, tea leaves 1g.

[0173] Assume that each product's raw material module has 3 suppliers, and the transportation distance for each supplier is as follows: , km and The production costs and transportation costs per kilometer for each supplier are shown in Table 5.

[0174] Table 5. Supplier's generation and transportation costs for each raw material candidate module (RMB / 10,000 bottles)

[0175]

[0176] Note: and The tea beverage manufacturer produces its own modules, eliminating the need for procurement.

[0177] 3.2 Experimental Setup

[0178] The experimental platform for this invention is Matlab R2020b, the experimental environment is AMD Ryzen 7 5800H with Radeon Graphics, operating system Windows 11, 16GB of memory.

[0179] To verify the effectiveness of the method of this invention, RSCA was compared with two classic algorithms, GA and PSO, and the original algorithm SCA. Specifically, the nested GA algorithm uses binary crossover and polynomial mutation, with a crossover rate of 0.75 and a mutation rate of 0.2; the nested PSO algorithm has an inertia factor of 1 and a learning rate of 2; and the nested SCA and nested RSCA algorithms... The settings are consistent, and all are random numbers. , , In nested SCA, ,in, For evolutionary generations, In nested RSCA, The initial value is 2. Dynamic updates are guided by reinforcement learning.

[0180] In the comparative experiments, all experiments were set with a population size of 50 and 100 iterations. Each comparative algorithm was independently repeated 10 times. The mean and variance of the producer and supplier profits (i.e., the objective function value) after optimization of each algorithm were calculated as the evaluation results of the performance of each algorithm.

[0181] 3.3 Evaluation Indicators

[0182] Average profit at the top level:

[0183] (28)

[0184] Upper-level profit variance:

[0185] (29)

[0186] Average profit at the lower level:

[0187] s (30)

[0188] Upper-level profit variance:

[0189] s (31)

[0190] in, The number of independent repeated experiments. See formula (2). See formula (14). The higher the average profit value, the better the algorithm optimization effect, the lower the profit variance, and the stronger the algorithm robustness.

[0191] 3.4 Experimental Results

[0192] Nested RSCA was used to solve the case of this invention. In 10 independent repeated experiments, the solution with the highest profit in the upper optimization was selected as the final optimization result, and it was analyzed as the decision result of the relevant factors in the model, as shown in Table 6.

[0193] Table 6 Optimal Results of the Decision-Making Correlation Problem between Tea Beverage Production Line and Suppliers

[0194]

[0195] Note: Gross profit margin = (Revenue - Cost) / Revenue. Company N's 2025 financial report shows a gross profit margin of 60.5%.

[0196] As shown in Table 6, Company N can optimize the design of its three tea product production lines, and the products... For the pure tea series, each uses Water source and For tea products, the suggested retail price is 3.0785 yuan, with an estimated market demand of 588,225 bottles and an inventory of 10,000 bottles (a pre-planned inventory quantity to address uncertainties in demand). For the milk tea series, use respectively Water source Tea categories and The milk series has a suggested retail price of 5.9505 yuan, an estimated market demand of 303,465 bottles, and an inventory of 120,000 bottles. For the fruit tea series, use respectively Water source Tea categories and The juice series has a suggested retail price of 5.6708 yuan, an estimated market demand of 323,044 bottles, and an inventory of 60,000 bottles. The combined design of these three product lines could generate a profit of 4,854,500 yuan. During the supplier negotiation process, the product... Tea supplier S2 quoted 16,793 yuan for the product. Tea supplier S2 quoted 11,399 yuan, and milk supplier S2 quoted 8,183 yuan. Tea supplier S3 bid 20,247 yuan, and juice supplier S2 won the bid with 12,130 yuan. It is estimated that the above suppliers can make a total profit of 3,101,900 yuan.

[0197] To further verify the effectiveness of the RSCA method proposed in this invention, an algorithm comparison experiment was conducted using the case of Company N as an example. The comparison results are shown in Table 7.

[0198] Table 7 Comparison of Average Optimization Results of Different Algorithms

[0199]

[0200] As shown in Table 7, the average profit of both the upper and lower layers of the nested SCA algorithm improved by reinforcement learning is higher than that of the other three comparative algorithms in repeated independent experiments, demonstrating that reinforcement learning is crucial for the key parameters in SCA. As analyzed above, the effectiveness of the regulatory effect of reinforcement learning is consistent with the previous analysis. For complex optimization problems with multiple constraints and variables, the exploration and development of the solution space does not completely conform to the linear equilibrium structure. Reinforcement learning is needed to explore its search rules and guide the algorithm's search process. Compared with the classic nested GA and PSO algorithms, the nested RSCA and nested SCA algorithms, based on the update mechanism of sine and cosine amplitudes, can effectively preserve the optimal individual structure and reduce the instability of the search behavior. Therefore, they can find the optimal solution more stably in the optimization problem of the model in this invention.

[0201] from Figure 4 The average convergence trend of the four comparative algorithms shows that the RSCA algorithm can achieve rapid convergence in earlier algebras and still has the ability to continue exploring in later stages. This demonstrates that the algorithm can maintain stable performance improvement in both the early development and later exploration stages by reasonably adjusting the parameters.

[0202] from Figure 5 The box plots of the four comparative algorithms show that the median height of the RSCA algorithm is higher than that of the SCA algorithm, proving that in repeated independent experiments, the solution quality on the median is better than that of the SCA algorithm, significantly better than the classical algorithm, and has fewer outliers. However, the box height indicates that the RSCA algorithm is less stable than the SCA algorithm.

[0203] 3.5 Parameter Sensitivity Analysis

[0204] To further analyze the learning rate in Q-learning The impact on RSCA algorithm performance is determined by setting the upper and lower layers respectively. , , ,as well as , Other experimental parameters are described in section 3.2, and the experimental results are shown in Table 8. The average convergence trend plot is shown in the figure below. Figure 6 As shown.

[0205] Table 8 Learning Rate of Nested RSCA Parameter comparison experiment results

[0206]

[0207] As shown in Table 8, different learning rate settings affect the optimization results. When both the upper and lower layers use a small learning rate (0.05), the average profit of the upper layer is optimal, but the profit of the lower layer is low; when both the upper and lower layers use a large learning rate (0.2), the average profit of both layers is relatively poor; and when both the upper and lower layers use a medium learning rate (0.1), the total profit of both layers reaches its maximum. When further attempts are made to use asymmetric learning rate settings ( ; Its optimization results are better than and Two setups are available, but the total profit between the upper and lower levels is slightly lower. Therefore, based on the analysis of the coupling relationship between the upper and lower layers, it can be concluded that an increase in the profit of the upper-level manufacturer will, to some extent, compress the profit margin of the lower-level supplier. Thus, adopting a uniform and moderate learning rate (0.1) is beneficial for balancing the game between the two and achieving optimal overall profit. In summary, and from... Figure 6 As can be seen in the average convergence curve of the lower-level optimization, The learning rate setting results in the fastest convergence speed within 10 generations, and the final convergence value is significantly higher than other learning rate settings. Therefore, this invention selects... The learning rate is used as the optimization algorithm of this invention.

[0208] To further analyze the impact of the price sensitivity coefficient on the model, we observed the changes in total profit, unit price, and sales volume when the three tea products fluctuated simultaneously, as well as the changes in total profit, unit price, and sales volume when a single tea product fluctuated. The price sensitivity coefficient settings and experimental results are shown in Table 9.

[0209] Table 9. Comparison of Experimental Results of Price Sensitivity Coefficients of the Models

[0210]

[0211] As shown in Table 9, the baseline elasticity coefficients for the three product lines of this invention are: =15, =7, =7 (unit: 10,000 bottles / yuan), representing the change in sales volume corresponding to a 1 yuan fluctuation in the unit price of the product. When the price elasticity coefficients of the three products decrease simultaneously (i.e., price sensitivity decreases), the company can achieve higher profits by increasing unit price and sales volume; conversely, if the elasticity coefficients increase simultaneously, profits decrease. This proves that the tea beverage manufacturing industry is a price-sensitive industry, and that the producer's profit is negatively correlated with the price sensitivity coefficient. Further, by adjusting the elasticity coefficients of the three product lines separately, we observed their impact on the product lines: when the price elasticity coefficient of a certain product increases, while the other products remain at the baseline (e.g., ...), (Product 1) Increased, (Product 2) and (Product 3 remains unchanged). The average profits of the manufacturers of the three products are basically flat or slightly decreased, but the expected sales volume and pricing strategies diverge: the sales volume of Product 1 decreases significantly, while the price remains relatively unchanged; while Products 2 and 3 adopt price reduction strategies to maintain sales volume and profits. Conversely, when the price elasticity coefficient of a certain product decreases, the three products all increase to varying degrees in terms of pricing and expected sales volume, and the average profit increases accordingly. From this analysis, it can be seen that the profit margin of Product 1 (pure tea beverage) is limited, and the possibility of reducing costs is low. Therefore, when the market elasticity coefficient increases, profits are maintained by reducing expected demand; while the profit margins of Products 2 (milk tea) and 3 (fruit tea) are larger, and sales volume and profits can be maintained by compressing costs and lowering prices. Therefore, when market elasticity increases, the method of this invention can combine the attributes of each product to synergistically optimize pricing and sales strategies to maintain profit stability. When market elasticity decreases, the method of this invention can also keenly perceive market changes and maximize profits.

[0212] This invention targets the supply chain model of the tea beverage industry, deeply analyzing the game relationship between manufacturers and suppliers, and designing a master-slave related decision-making model that conforms to the cost-profit composition pattern of tea beverage enterprises. Furthermore, considering the characteristics of the problem-solving process, an improved sine and cosine algorithm based on reinforcement learning adaptive adjustment is proposed, along with a discrete encoding method for the solution space and a two-layer interactive optimization process. Finally, the effectiveness is verified with a practical case. The method of this invention optimizes the design of three differentiated tea beverage product lines for Company N, providing suggestions on the selling price and inventory of the three products, as well as expected market demand. Simultaneously, through algorithmic interactive design, the optimal price under supplier cost constraints and competitive conditions is derived. The model ultimately maximizes the profits of both product manufacturers and suppliers. Moreover, in comparative experiments, the average profit of the solution set obtained by the algorithm proposed in this invention is significantly better than that of the comparative algorithms, further verifying the effectiveness of the algorithm design of this invention.

[0213] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A tea product family association decision optimization method based on nested reinforced sine and cosine algorithms, applicable to resource allocation decisions in the tea beverage industry's process manufacturing supply chain, characterized in that... include: Acquire basic configuration data and supply chain data for tea product families; wherein, the basic configuration data and supply chain data are technical parameters at the physical production level of the tea beverage supply chain. A Stackelberg master-slave relationship optimization model is constructed. The model includes an upper-level manufacturer optimization sub-model and a lower-level supplier optimization sub-model. The upper-level manufacturer optimization sub-model aims to maximize the expected profit of the tea beverage manufacturer. The decision variables include product ingredient category selection variables, supplier selection variables, product inventory quantity variables, and product retail price variables. The lower-level supplier optimization sub-model takes maximizing the supplier's expected profit as the optimization objective, and the decision variables include supplier order acceptance decision variables and supplier quotation variables. A nested reinforced sine and cosine algorithm is used to iteratively solve the Stackelberg master-slave correlation optimization model, outputting the optimal decision results on the manufacturer's side and the optimal decision results on the supplier's side to guide the allocation of supply chain technical resources for tea beverage product families; in the nested reinforced sine and cosine algorithm, the position update parameters of the sine and cosine algorithm are... Through dynamic adjustment using Q-learning, the state space is defined as a stagnation level. Improved level 9 A 9-grid layout is used, with the reward function being the difference between the objective functions of adjacent generations. Furthermore, the upper-level manufacturer optimization sub-model and the lower-level supplier optimization sub-model share the same Q-table, achieving optimization through alternating iterations between the upper and lower layers. Cross-layer transmission.

2. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 1, characterized in that, In the upper-level manufacturer optimization sub-model, the tea beverage manufacturer's expected profit equals expected revenue minus expected cost, where: Expected revenue is the sum of the products of the retail price of each product and the expected demand for the corresponding product; The expected costs include the tea beverage manufacturer's reprocessing costs, raw material procurement costs, and inventory costs. The tea beverage manufacturer's reprocessing costs are the sum of the products of the reprocessing costs corresponding to the selected ingredient categories for each product and the expected demand for the corresponding product. The raw material procurement costs are the sum of the products of the suppliers' quotations for the supplied raw materials and the corresponding purchase quantities and expected demand for the product. The purchase quantities are determined by the product ingredient category selection variables and the supplier selection variables.

3. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 2, characterized in that, The expected demand for the product is determined by the following formula: in, for The expected market demand for each product Indicates the first The sensitivity coefficient of a product to its market selling price. For the first The potential market demand for each product For the first Retail price of each product This is the demand fluctuation term, reflecting the volatility caused by uncertainty in market demand. , This represents the total number of products. The inventory cost is determined by the following formula: in, Total inventory cost For the first Unit holding cost of each product For the first Inventory quantity of each product To minimize demand, ; For remaining inventory, It is a probability density function used to describe the demand. Probability distribution of occurrence ,obey The upper mean is The variance is Distribution; Yes The points.

4. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 1, characterized in that, In the lower-level supplier optimization sub-model, the supplier's expected profit equals expected revenue minus expected cost, where: Expected revenue is the sum of the products of the supplier's quoted price for the raw materials supplied and the corresponding purchase quantity and expected demand for the product; The expected cost includes raw material supply cost and transportation cost. The transportation cost is the sum of the product of the supplier's unit transportation cost, transportation distance, corresponding purchase quantity, and expected product demand.

5. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 1, characterized in that, The iterative solution steps of the nested enhanced sine and cosine algorithm include: S1. Initialize the upper-level population, encode the upper-level decision variables with integers, calculate the fitness of each upper-level individual based on the objective function of the upper-level manufacturer optimization sub-model, and determine the initial upper-level optimal solution. S2. Using the initial upper-level optimal solution as input constraints, initialize the lower-level population, and use the sine and cosine algorithm with Q-learning adaptive parameter adjustment to iteratively optimize the lower-level supplier optimization sub-model, outputting the current lower-level optimal solution and the corresponding lower-level fitness. S3. The current optimal solution of the lower layer is fed back to the upper layer. The upper-layer manufacturer optimization sub-model is iteratively optimized using the sine and cosine algorithm with Q-learning adaptive parameter adjustment, and the optimal solution of the upper layer and the corresponding upper-layer fitness are updated. S4. Repeat S2 to S3 until the preset maximum number of iterations is reached. The optimal solution obtained in the last iteration is taken as the optimal decision result on the manufacturer's side, and the corresponding optimal solution on the lower level is taken as the optimal decision result on the supplier's side.

6. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 5, characterized in that, In the aforementioned sine and cosine algorithm with Q-learning adaptive parameter adjustment, the position update parameters of the sine and cosine algorithm are... Dynamic adjustments are made through Q-learning, specifically including: The state space S is defined as a 9×9 grid space, where each grid consists of a set of... Composition, in which, y represents the stagnation level, and y represents the improvement level. in, For stag algebra, , For the first The objective function value of the substitute. For the first Substitute the objective function value; Action Space A: , For algebra, For the maximum number of generations, ; In each generation, adopt Strategy on parameters Select Action Set to 0.2: In state implement Then calculate the reward function and transition to the new state. reward function Designed as follows: Furthermore, Q-learning applies to the action value function. The update is performed using the following formula: Among them, learning rate =0.1, control information update magnitude, discount factor To measure the importance of future rewards For instant rewards, The optimal action value for the next state.

7. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 5, characterized in that, The position update output of the sine and cosine algorithm is a continuous value. The round function is used to map the continuous output value to an integer to complete the discretization of the decision variable. The mapped integer value needs to be checked for boundaries. If it exceeds the preset range of the decision variable, it is truncated to the nearest boundary value.

8. The tea product family association decision optimization method based on nested reinforced sine and cosine algorithms according to claim 1, characterized in that, The configuration data includes the raw material module division of the tea product family, the candidate categories of each raw material module, the processing cost of each candidate category, the price sensitivity coefficient of each product, the potential market demand of each product, and the unit inventory cost of each product. The basic supply chain data includes the supplier set corresponding to each raw material candidate category, the production cost of each supplier, the unit transportation cost of each supplier, and the transportation distance of each supplier.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the tea product family association decision optimization method according to any one of claims 1 to 8.

10. An electronic device, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the steps of the tea product family association decision optimization method as described in any one of claims 1-8.

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