Method, system and equipment for predicting price and inventory relationship of discount channel based on random demand, and medium

Abstract

The invention discloses a method, a system and equipment for predicting a price and inventory relationship of a discount channel based on a random demand, and a medium. The method comprises the following steps: collecting historical data; constructing a supply chain model of the discount dealer under the random demand, a consumer demand function for purchasing a retailer product, a consumer demand function for purchasing a discount product, an expected profit function of the retailer, an expected profit function of the discount dealer and a profit function of the manufacturer; determining a retailer order adjustment amount and a discount product inventory level based on a consumer demand of purchasing a retailer product; calculating an optimal order adjustment amount of the retailer and obtaining an optimal order amount expression of the retailer; taking the expected profit function of the discount dealer as the target function of the simulated annealing algorithm, solving the optimal discount product price, and substituting the optimal discount product price into the optimal order quantity expression of the retailer to solve the optimal order quantity of the retailer; and substituting the optimal order quantity of the retailer into the profit function of the manufacturer to obtain the profit of the manufacturer. According to the invention, inventory management is more scientific.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer-aided supply chain management, and in particular relates to a prediction method, system, device and medium for price and inventory relationship of a discount channel under random demand. Background Art

[0002] Discount markets refer to sales activities where goods are sold at prices lower than their retail prices. Usually, goods in such markets include excess inventory, out-of-season goods, or discounted goods offered due to brand promotions. Discount markets are diverse and can be online platforms or physical stores. Taking e-commerce platforms as an example, Vipshop focuses on limited-time sales and attracts a large number of price-sensitive users by providing consumers with limited-time discounted goods. In the field of physical retail, outlet stores are a form of discount stores widely used around the world, mainly selling out-of-season, out-of-stock and inventory goods of brands. Consumers can buy high-end brand goods at lower prices in outlets, enjoying the dual advantages of brand premium and discounts. Discount markets provide consumers with preferential product choices while reducing inventory pressure for manufacturers or retailers. Products in discount markets mainly come from authorized retailers who resell unsold products during the sales season to discount dealers. Discount dealers are retailers or middlemen who specialize in selling goods at discounted prices. They usually obtain goods by purchasing out-of-season and excess inventory products from manufacturers; or directly purchase goods at lower prices through promotional activities. The core business model of discounters is to attract price-sensitive consumers with lower prices and provide more attractive product choices compared to traditional retail channels. Discount products are not much different from regular channel products. Discount products are often cheaper but lack supporting services. When consumers observe the existence of discounted products in the market, it will change their perception of the product brand image, which in turn affects their choice of products to buy.

[0003] When a product is sold in a market, it may be affected by market demand and there may be surplus or shortage. The mismatch between order quantity and market demand will cause losses to retailers. Retailers can transfer unsold products to discounters to maximize their own profits. This behavior may affect the profits of manufacturers, retailers and discounters.

[0004] The problem with existing inventory control calculation methods is that they do not set appropriate inventory control strategies for retailers' order quantities facing random demand in a discounter environment, thereby maximizing the profits of each supply chain participant. Conventional supply chain problems often focus on pricing or inventory, and lack calculation methods that show the relationship between pricing and inventory. When it comes to discounter issues, although discounters are members of the supply chain, they always ignore the relationship between discounter pricing and the inventory of manufacturers and retailers. In solving supply chain-related problems, model assumptions are often out of touch with reality. Therefore, the present invention is a method for predicting the relationship between product prices and inventory under discount channels. Summary of the invention

[0005] The present invention aims at the deficiencies in the prior art and provides a method, system, device and medium for predicting the relationship between price and inventory of discount channels under random demand, thereby solving the defects of inventory management of existing supply chain inventory decisions that do not target discounters and demand uncertainty, and thus improving the overall profit of the supply chain.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A forecasting method for the relationship between price and inventory of a discount channel under random demand includes the following steps:

[0008] Step 1: Collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database;

[0009] Step 2: Based on historical data, a supply chain model with discounters under random demand is constructed, and the supply chain includes manufacturers, retailers, discounters, and consumers; based on historical data, a consumer demand function for purchasing retailer products under the existence of discounters and a consumer demand function for purchasing discounted products under the existence of discounters are constructed;

[0010] Step 3: construct the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, construct the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and construct the profit function of the manufacturer;

[0011] Step 4, determining the retailer's order adjustment amount and the discounted product inventory level in the presence of the discounter based on the consumer demand for the retailer's products in the presence of the discounter;

[0012] Step 5, find the first-order derivative of the retailer's expected profit function under the existence of the discounter, and obtain the optimal order adjustment quantity of the retailer's order under the existence of the discounter. Use the optimal order adjustment quantity to obtain the expression of the retailer's optimal order quantity under the existence of the discounter;

[0013] Step 6: Taking the expected profit function of the discount dealer as the objective function of the simulated annealing algorithm, the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer and solve the optimal discount product price;

[0014] Step 7, substitute the optimal discounted product price into the expression of the optimal order quantity of the retailer when the discounter exists to solve the optimal order quantity of the retailer when the discounter exists;

[0015] Step 8: Substitute the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function to obtain the manufacturer's profit.

[0016] To optimize the above technical solutions, the specific measures taken also include:

[0017] Furthermore, in step 2, the expression of the consumer demand function for purchasing the retailer's products in the presence of the discounter is as follows:

[0018]

[0019] Where D R is the consumer demand for the retailer's products in the presence of discounters, d R is the expected demand of consumers for the retailer's products, ε R is the uncertain part of the retailer's product demand, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, δ is the discount coefficient of the consumer on the product when there is a discounter;

[0020] The expected demand of consumers for the retailer's products R The calculation method is as follows:

[0021] Construct the utility function of consumers purchasing retailer products:

[0022]

[0023] Where U R is the utility of consumers purchasing retailer products, v represents the subjective evaluation of the same product by different consumers, p represents the retail price of the product, The cost of purchasing products for consumers;

[0024] Construct the utility function for consumers to purchase discounted products:

[0025]

[0026] Where U S is the utility of consumers buying discounted products, v represents the subjective evaluation of the same product by different consumers, δ is the discount coefficient of consumers for discounted products when there is a discounter, and p SFor discounted product prices;

[0027] Let U R =U S , we get the indifference evaluation coefficient v between consumers in the authorized channel and discounted products H :

[0028]

[0029] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter;

[0030] Based on the indifference evaluation coefficient v H Construct the expected demand of consumers for the retailer's products R Function:

[0031]

[0032] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient of consumers between authorized channels and discounted products;

[0033] In step 2, the expression of the consumer demand function for purchasing discounted products in the presence of the discounter is as follows:

[0034]

[0035] Where, d S is the expected demand function of consumers for discounted products, ε S is the uncertain part of the demand for discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, p represents the retail price of the product, and p S For discounted product prices;

[0036] Consumers' expected demand function for discounted products d S The construction process is as follows:

[0037] The utility function U that makes consumers not buy the product S =0, and the indifference evaluation coefficient v between consumers buying discounted products and not buying discounted products is obtained. L :

[0038]

[0039] In the formula, p Sis the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter;

[0040] Based on the indifference evaluation coefficient v between consumers in authorized channels and discounted products H and the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products L Construct the consumer's expected demand function for discounted products:

[0041]

[0042] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient between consumers in authorized channels and discounted products, v L The indifference evaluation coefficient between consumers purchasing discounted products and not purchasing discounted products.

[0043] Furthermore, in step 3, the expected profit function of the retailer is:

[0044]

[0045] In the formula, represents the expected profit of the retailer when the discounter exists, E[·] represents the expected function, p represents the retail price of the product, min(D R ,Q) indicates that in D R Take the minimum value among D and Q, j is the consumer demand function for retailer products in the presence of discounters, Q is the quantity of products that retailers order from manufacturers before the sales season; w is the unit wholesale price that manufacturers sell products to retailers, w S The unit wholesale price at which a retailer transfers a product to a discounter; (QD R ) + Guaranteed QD R is a non-negative value, (QD R ) + =max(0,QD R );

[0046] Q=e R +d R

[0047] In the formula, e R is the retailer's order adjustment, d R To meet consumers' expectations of retailers' products;

[0048] In step 3, the discounter's expected profit function is:

[0049] π S =E[p S min(D S ,Q S )-w S Q S ]

[0050] Among them, π s is the expected profit of the discount dealer, E[·] represents the expected function, and p s is the discounted product price, min(D s ,Q s ) means in D s and Q s Take the minimum value, D s is the demand for discounted products, Q s is the quantity of products transferred to the discounter, satisfying Q S =(QD R ) + , (QD R ) + Guaranteed QD R is a non-negative value, w S the wholesale price per unit for retailers to transfer products to discounters;

[0051] In step 3, the manufacturer's profit function is:

[0052]

[0053] In the formula, is the manufacturer's profit when the discounter exists, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and Q is the number of products ordered by the retailer from the manufacturer before the sales season.

[0054] Furthermore, in step 4, the discounted product inventory level expression is:

[0055]

[0056] In the formula, Q S is the inventory level of discounted products, Q is the quantity of products that retailers order from manufacturers before the sales season, and D R is the consumer demand for retailer products in the presence of discounters, (QD R ) + Guaranteed QD R is a non-negative value, (QD R ) + =max(0,QD R ), e R is the retailer's order adjustment, εR is the uncertain part of the retailer's product demand, and the uncertain part of the retailer's product demand ε R It follows the [k,l] normal distribution, where k represents ε R The minimum value of , l represents ε R The maximum value of μ D It indicates that the average actual demand of the product is calculated based on the historical actual demand data of the product. It means calculating the standard deviation of the actual demand for a product based on the historical actual demand data of the product, and using the calculation method to determine the form of the probability density function f.

[0057] Furthermore, in step 6, the simulated annealing algorithm is specifically:

[0058] Let the discounter's expected profit function π S =E[p S min(D S ,Q S )-w S Q S ] as the objective function of the simulated annealing algorithm,

[0059] Select initial solution Set the initial temperature T0 and cooling rate α; the number of iterations t = 0;

[0060] In the current solution A new solution p is randomly generated in the neighborhood of ′ S ;

[0061] Using the objective function π S Calculate the profit difference between the new solution and the current solution

[0062] If Δπ>0, accept the new solution If Δπ≤0, then with probability e Δπ / T Accept the new solution, T is the current temperature;

[0063] Update temperature T = α × T; the number of iterations increases by one;

[0064] When the temperature is lower than the minimum temperature threshold or the current number of iterations reaches the iteration limit, the algorithm stops and the current solution is As the best discount product price.

[0065] Furthermore, in step 5, the optimal order adjustment expression of the retailer's order is:

[0066]

[0067] In the formula, e R* represents the optimal order adjustment quantity of the retailer in the presence of the discounter, F -1 represents the uncertain part of retailer product demand ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S the wholesale price per unit for retailers to transfer products to discounters;

[0068] In step 5, the expression of the retailer's optimal order quantity in the presence of the discounter is:

[0069]

[0070] In the formula, Q * represents the optimal order quantity of the retailer under the existence of discount dealers, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, and δ is the discount coefficient of the consumer on the product when there is a discounter.

[0071] Furthermore, step 8 is specifically as follows:

[0072] Substituting the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function, the manufacturer's profit is obtained

[0073]

[0074] In the formula, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and F -1 Represents the market demand for the product ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S is the unit wholesale price at which the retailer transfers the product to the discounter, a is the initial demand for the product, and p S Discounted product prices.

[0075] The present invention also proposes a forecasting system for the relationship between price and inventory of discount channels under random demand, comprising:

[0076] A data collection module is used to collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database;

[0077] Supply chain and demand function building module, used to build a supply chain model with discounters under random demand based on historical data, the supply chain includes manufacturers, retailers, discounters and consumers; build a consumer demand function for purchasing retailer products under the existence of discounters and a consumer demand function for purchasing discounted products under the existence of discounters based on historical data;

[0078] An expected profit function building module, used to build the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, to build the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and to build the profit function of the manufacturer;

[0079] A module for calculating the retailer's order adjustment and discounted product inventory level, for determining the retailer's order adjustment and discounted product inventory level in the presence of the discounter based on consumer demand for the retailer's products in the presence of the discounter;

[0080] The module for predicting the optimal order quantity of retailers is used to calculate the first-order derivative of the expected profit function of retailers in the presence of discount dealers, obtain the optimal order adjustment quantity of retailers' orders in the presence of discount dealers, and use the optimal order adjustment quantity to obtain the expression of the optimal order quantity of retailers in the presence of discount dealers; the expected profit function of the discount dealer is used as the objective function of the simulated annealing algorithm, and the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer to solve the optimal discount product price; the optimal discount product price is substituted into the expression of the optimal order quantity of retailers in the presence of discount dealers to solve the optimal order quantity of retailers in the presence of discount dealers;

[0081] The manufacturer profit prediction module is used to substitute the retailer's optimal order quantity when the discount dealer exists into the manufacturer's profit function to obtain the manufacturer's profit.

[0082] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the above-mentioned method for predicting the relationship between price and inventory of a discount channel under random demand.

[0083] The present invention also proposes an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for predicting the relationship between price and inventory of discount channels under random demand as described above is implemented.

[0084] The beneficial effects of the present invention are:

[0085] The present invention solves the relationship and influence between the retail price, discounter price, retailer order quantity and consumer demand and the profit function of the supply chain members in the presence of discounters through simple demand function and profit function.

[0086] The present invention determines consumer demand for different products from the perspective of consumer utility.

[0087] The present invention finds the relationship between discounter pricing and consumer demand and retailer order quantity through mathematical calculation, and obtains a formula representing the discounter price.

[0088] The present invention will calculate the changing trend of manufacturer's profits under the existence of discounters through a method combining data analysis with models, discover the relationship between discounters' orders to retailers and consumer demand, and make inventory management more scientific. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a schematic diagram of demand changes in a supply chain without discounters and a supply chain with discounters in the present invention.

[0090] Figure 2 Schematic diagram of the decision-making sequence of supply chain members in the presence of discount dealers in the present invention. DETAILED DESCRIPTION

[0091] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0092] Embodiment 1: The present invention proposes a method for predicting the relationship between price and inventory of a discount channel based on random demand, comprising the following steps:

[0093] Step 1: Collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database;

[0094] Step 2: Based on historical data, construct a supply chain model with discounters under random demand. The supply chain includes manufacturers, retailers, discounters, and consumers. Based on historical data, construct the consumer demand function for purchasing retailers' products under the presence of discounters and the consumer demand function for purchasing discounted products under the presence of discounters.

[0095] The expression of the consumer demand function for the retailer's products in the presence of the discounter is as follows:

[0096]

[0097] Where D R is the consumer demand for the retailer's products in the presence of discounters, d Ris the expected demand of consumers for the retailer's products, ε R is the uncertain part of the retailer's product demand, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, δ is the discount coefficient of the consumer on the product when there is a discounter;

[0098] The expected demand of consumers for the retailer's products R The calculation method is as follows:

[0099] Construct the utility function of consumers purchasing retailer products:

[0100]

[0101] Where U R is the utility of consumers purchasing retailer products, v represents the subjective evaluation of the same product by different consumers, p represents the retail price of the product, The cost of purchasing products for consumers;

[0102] Construct the utility function for consumers to purchase discounted products:

[0103]

[0104] Where U S is the utility of consumers buying discounted products, v represents the subjective evaluation of the same product by different consumers, δ is the discount coefficient of consumers for discounted products when there is a discounter, and p S For discounted product prices;

[0105] Let U R =U S , we get the indifference evaluation coefficient v between consumers in the authorized channel and discounted products H :

[0106]

[0107] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter;

[0108] Based on the indifference evaluation coefficient v H Construct the expected demand of consumers for the retailer's products R Function:

[0109]

[0110] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p Sis the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient of consumers between authorized channels and discounted products;

[0111] In step 2, the expression of the consumer demand function for purchasing discounted products in the presence of the discounter is as follows:

[0112]

[0113] Where, d S is the expected demand function of consumers for discounted products, ε S is the uncertain part of the demand for discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, p represents the retail price of the product, and p S For discounted product prices;

[0114] Consumers' expected demand function for discounted products d S The construction process is as follows:

[0115] The utility function U that makes consumers not buy the product S =0, and the indifference evaluation coefficient v between consumers buying discounted products and not buying discounted products is obtained. L :

[0116]

[0117] In the formula, p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter;

[0118] Based on the indifference evaluation coefficient v between consumers in authorized channels and discounted products H and the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products L Construct the consumer's expected demand function for discounted products:

[0119]

[0120] In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient between consumers in authorized channels and discounted products, v L The indifference evaluation coefficient between consumers purchasing discounted products and not purchasing discounted products.

[0121] Step 3: Construct the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, construct the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and construct the profit function of the manufacturer.

[0122] The expected profit function of the retailer is:

[0123]

[0124] In the formula, represents the expected profit of the retailer when the discounter exists, E[·] represents the expected function, p represents the retail price of the product, min(D R ,Q) indicates that in D R Take the minimum value among D and Q, R is the consumer demand function for retailer products in the presence of discounters, Q is the quantity of products that retailers order from manufacturers before the sales season; w is the unit wholesale price that manufacturers sell products to retailers, w S The unit wholesale price at which a retailer transfers a product to a discounter; (QD R ) + Guaranteed QD R is a non-negative value, (QD R ) + =max(0,QD R );

[0125] Q=e R +d R

[0126] In the formula, e R is the retailer's order adjustment, d R To meet consumers' expectations of retailers' products;

[0127] In step 3, the discounter's expected profit function is:

[0128] π S =E[p S min(D S ,Q S )-w S Q S ]

[0129] Among them, π S is the expected profit of the discount dealer, E[·] represents the expected function, and p S is the discounted product price, min(D S ,Q S ) means in D S and Q S Take the minimum value, D Sis the demand for discounted products, Q S is the quantity of products transferred to the discounter, satisfying Q S =(QD R ) + , (QD R ) + Guaranteed QD R is a non-negative value, w S the wholesale price per unit for retailers to transfer products to discounters;

[0130] In step 3, the manufacturer's profit function is:

[0131]

[0132] In the formula, is the manufacturer's profit when the discounter exists, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and Q is the number of products ordered by the retailer from the manufacturer before the sales season.

[0133] Step 4: Determine the retailer's order adjustment amount and discounted product inventory level in the presence of the discounter based on the consumer demand for the retailer's products in the presence of the discounter.

[0134] The discounted product inventory level expression is:

[0135]

[0136] In the formula, Q S is the inventory level of discounted products, Q is the quantity of products that retailers order from manufacturers before the sales season, and D R is the consumer demand for retailer products in the presence of discounters, (QD R ) + Guaranteed QD R is a non-negative value, (QD R ) + =max(0,QD R ), e R is the retailer's order adjustment, ε R is the uncertain part of the retailer's product demand, and the uncertain part of the retailer's product demand ε R It follows the [k,l] normal distribution, where k represents ε R The minimum value of , l represents ε R The maximum value of μ D It indicates that the average actual demand of the product is calculated based on the historical actual demand data of the product. It means calculating the standard deviation of the actual demand for a product based on the historical actual demand data of the product, and using the calculation method to determine the form of the probability density function f.

[0137] Step 5, the first-order derivative of the expected profit function of the retailer under the existence of the discounter is calculated to obtain the optimal order adjustment of the retailer under the existence of the discounter, and the expression of the optimal order quantity of the retailer under the existence of the discounter is obtained by using the optimal order adjustment; in step 5, the expression of the optimal order adjustment of the retailer is:

[0138]

[0139] In the formula, e R * represents the optimal order adjustment quantity of the retailer in the presence of the discounter, F -1 represents the uncertain part of retailer product demand ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S the wholesale price per unit for retailers to transfer products to discounters;

[0140] In step 5, the expression of the retailer's optimal order quantity in the presence of the discounter is:

[0141]

[0142] In the formula, Q * represents the optimal order quantity of the retailer under the existence of discount dealers, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, and δ is the discount coefficient of the consumer on the product when there is a discounter.

[0143] Step 6: Taking the expected profit function of the discount dealer as the objective function of the simulated annealing algorithm, the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer and solve the optimal discount product price; the simulated annealing algorithm is specifically as follows:

[0144] Let the discounter's expected profit function π S =E[p S min(D S ,Q S )-w S Q S ] as the objective function of the simulated annealing algorithm,

[0145] Select initial solution Set the initial temperature T0 and cooling rate α; the number of iterations t = 0;

[0146] In the current solution A new solution p is randomly generated in the neighborhood of ′ S ;

[0147] Using the objective function π S Calculate the profit difference between the new solution and the current solution

[0148] If Δπ>0, accept the new solution If Δπ≤0, then with probability e Δπ / T Accept the new solution, T is the current temperature;

[0149] Update temperature T = α × T; the number of iterations increases by one;

[0150] When the temperature is lower than the minimum temperature threshold or the current number of iterations reaches the iteration limit, the algorithm stops and the current solution is As the best discount product price.

[0151] Step 7, substitute the optimal discounted product price into the expression of the optimal order quantity of the retailer when the discounter exists to solve the optimal order quantity of the retailer when the discounter exists;

[0152] Step 8: Substitute the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function to obtain the manufacturer's profit. Specifically:

[0153] Substituting the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function, the manufacturer's profit is obtained

[0154]

[0155] In the formula, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and F -1 Represents the market demand for the product ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S is the unit wholesale price at which the retailer transfers the product to the discounter, a is the initial demand for the product, and p S Discounted product prices.

[0156] Embodiment 2: Compare the two situations where the discount dealer does not exist and the discount dealer does exist.

[0157] Step 1: Construct a supply chain model without discounters under random demand. The supply chain includes manufacturers, retailers, and consumers. Only one product is sold in the supply chain. Before the sales season, the manufacturer completes the production of the product, and the retailer orders a certain number of products from the manufacturer based on previous demand forecasts. When the sales season begins, the demand is determined, and the retailer sets the retail price of the product to sell the product. Since the residual value of the remaining products is 0, the retailer needs to bear the loss of unsold products.

[0158] Step 2: Set the consumer's utility function without a discounter. The consumer's utility U for purchasing a product is

[0159]

[0160] Among them, v represents the evaluation of consumers to buy products, v satisfies the uniform distribution between [0,1], a is the initial demand for the product, and p represents the retail price of the product. When the consumer utility U>0, the consumer will choose to buy the product, otherwise he will not buy it.

[0161] Step 3: Construct the demand function without discounters.

[0162] D0=d+ε R =1-p+ε R

[0163] Where D0 is the total market demand for the product without discounters, d is the expected demand for the product without discounters, and ε R is a random variable in the demand for retailer products, its probability density function is f(x), its cumulative distribution function is F(x), and p is the retailer product price determined by the retailer.

[0164] Step 4: Construct the profit function of each supply chain member under the condition of no discounter. The expected profit function of the retailer is:

[0165] π R =pmin(D0,Q0)-wQ0

[0166] Where w is the unit wholesale price of the manufacturer's products to the retailer. Q0 is the retailer's order quantity without the discounter.

[0167] The manufacturer's profit function is

[0168] π M =(wc)Q0

[0169] Where c is the marginal unit cost of the manufacturer's product.

[0170] Step 5: Determine the retailer's order quantity without the discounter, which can be expressed as:

[0171] e=Q0-d

[0172] Among them, e is the retailer's order adjustment, which is determined by the retailer, that is, the retailer observes that the product demand is uncertain and adjusts the order quantity based on the demand forecast. Solving the first-order derivative of e in the above formula yields:

[0173]

[0174] Among them, F -1 Represents the inverse of the cumulative distribution function of demand.

[0175] Step 6: Find the optimal order adjustment quantity for retailers without discounters.

[0176]

[0177] Calculate the impact of discounters on the profits of manufacturers and retailers. Under the premise that the discount coefficient of consumers for discounted products is δ and the market demand is uncertain, the Markov Chain Monte Carlo (MCMC) method can be used to predict the pricing of discounters. The specific steps include:

[0178] 1. Build a statistical model: First, define the probability model, describing how to get the given input parameters: a, p, w, w S , μ R , μ S , δ, k, l, m, n generate observation data π M , π R and Enter p calculated from the discounter demand forecast S * , including the specified * , e R * , and p * The generation process and its expression.

[0179] 2. Choose a prior distribution: Choose an appropriate prior distribution for the model parameters. These priors can be reasonable assumptions based on prior knowledge, such as δ follows a (0,1) uniform distribution, ε R obeys the [k,l] normal distribution, ε S All obey the [m,n] normal distribution, which can be expressed as and The form of the probability density functions f(·) and g(·) and the form of the cumulative distribution function F(·) are determined by formula calculation.

[0180] 3. MCMC sampling: Use the Metropolis-Hastings or NUTS (No-U-TurnSampler) algorithm in the MCMC method to sample. To estimate π M , π R and The expected value or distribution of .

[0181] 4. Analysis and diagnostics: Analyze the samples generated by MCMC to determine the appropriateness of the model, including convergence tests and analysis of the posterior distribution.

[0182] 5. Results: By adjusting p, w, w S Comparison of the size of π M , π R and The impact of the existence of discounters on the profits of manufacturers and retailers is analyzed.

[0183] Embodiment 3: The present invention proposes a prediction system for the relationship between price and inventory of discount channels under random demand corresponding to the method of embodiment 1, comprising:

[0184] A data collection module is used to collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database;

[0185] Supply chain and demand function building module, used to build a supply chain model with discounters under random demand based on historical data, the supply chain includes manufacturers, retailers, discounters and consumers; build a consumer demand function for purchasing retailer products under the existence of discounters and a consumer demand function for purchasing discounted products under the existence of discounters based on historical data;

[0186] An expected profit function building module, used to build the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, to build the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and to build the profit function of the manufacturer;

[0187] A module for calculating the retailer's order adjustment and discounted product inventory level, for determining the retailer's order adjustment and discounted product inventory level in the presence of the discounter based on consumer demand for the retailer's products in the presence of the discounter;

[0188] The module for predicting the optimal order quantity of retailers is used to calculate the first-order derivative of the expected profit function of retailers in the presence of discount dealers, obtain the optimal order adjustment quantity of retailers' orders in the presence of discount dealers, and use the optimal order adjustment quantity to obtain the expression of the optimal order quantity of retailers in the presence of discount dealers; the expected profit function of the discount dealer is used as the objective function of the simulated annealing algorithm, and the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer to solve the optimal discount product price; the optimal discount product price is substituted into the expression of the optimal order quantity of retailers in the presence of discount dealers to solve the optimal order quantity of retailers in the presence of discount dealers;

[0189] The manufacturer profit prediction module is used to substitute the retailer's optimal order quantity when the discount dealer exists into the manufacturer's profit function to obtain the manufacturer's profit.

[0190] The implementation methods of each module and module function in the system are completely consistent with the steps of the method in Example 1, so they will not be repeated here.

[0191] Embodiment 4: The present invention proposes a computer-readable storage medium storing a computer program, wherein the computer program enables a computer to execute the method for predicting the relationship between price and inventory of a discount channel under random demand as described in Embodiment 1.

[0192] Embodiment 5: The present invention proposes an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for predicting the relationship between price and inventory of discount channels under random demand as described in Embodiment 1 is implemented.

[0193] In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium that can contain or store a program for use by or in conjunction with an instruction execution system, device or equipment. The computer storage medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the above. More specific examples of computer storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above.

[0194] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0195] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for predicting the relationship between price and inventory of a discount channel under random demand, characterized in that: The following steps are involved: Step 1: Collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database; Step 2: Based on historical data, a supply chain model with discounters under random demand is constructed, and the supply chain includes manufacturers, retailers, discounters, and consumers; based on historical data, a consumer demand function for purchasing retailer products under the existence of discounters and a consumer demand function for purchasing discounted products under the existence of discounters are constructed; Step 3: construct the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, construct the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and construct the profit function of the manufacturer; Step 4, determining the retailer's order adjustment amount and the discounted product inventory level in the presence of the discounter based on the consumer demand for the retailer's products in the presence of the discounter; Step 5, find the first-order derivative of the retailer's expected profit function under the existence of the discounter, and obtain the optimal order adjustment quantity of the retailer's order under the existence of the discounter. Use the optimal order adjustment quantity to obtain the expression of the retailer's optimal order quantity under the existence of the discounter; Step 6: Taking the expected profit function of the discount dealer as the objective function of the simulated annealing algorithm, the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer and solve the optimal discount product price; Step 7, substitute the optimal discounted product price into the expression of the retailer's optimal order quantity when the discounter exists to solve the retailer's optimal order quantity when the discounter exists; Step 8: Substitute the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function to obtain the manufacturer's profit.

2. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 1, characterized in that: In step 2, the expression of the consumer demand function for purchasing the retailer's products in the presence of the discounter is as follows: Where D R is the consumer demand for retailer products in the presence of discounters, d R is the expected demand of consumers for the retailer's products, ε R is the uncertain part of the retailer's product demand, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, δ is the discount coefficient of the consumer on the product when there is a discounter; The expected demand of consumers for the retailer's products R The calculation method is as follows: Construct the utility function of consumers purchasing retailer products: Where U R is the utility of consumers purchasing retailer products, v represents the subjective evaluation of the same product by different consumers, p represents the retail price of the product, The cost of purchasing products for consumers; Construct the utility function for consumers to purchase discounted products: Where U S is the utility of consumers buying discounted products, v represents the subjective evaluation of the same product by different consumers, δ is the discount coefficient of consumers for discounted products when there is a discounter, and p S For discounted product prices; Let U R =U S , we get the indifference evaluation coefficient v between consumers in the authorized channel and discounted products H : In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter; Based on the indifference evaluation coefficient v H Construct the expected demand of consumers for the retailer's products R Function: In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient of consumers between authorized channels and discounted products; In step 2, the expression of the consumer demand function for purchasing discounted products in the presence of the discounter is as follows: Where, d S is the expected demand function of consumers for discounted products, ε S is the uncertain part of the demand for discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, p represents the retail price of the product, and p S For discounted product prices; Consumers' expected demand function for discounted products d S The construction process is as follows: The utility function U that makes consumers not buy the product S =0, and the indifference evaluation coefficient v between consumers buying discounted products and not buying discounted products is obtained. L : In the formula, p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter; Based on the indifference evaluation coefficient v between consumers in authorized channels and discounted products H and the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products L Construct the consumer's expected demand function for discounted products: In the formula, a represents the initial demand for the product, p represents the retail price of the product, and p S is the price of the discounted product, δ is the discount coefficient of the consumer for the discounted product when there is a discounter, v H is the indifference evaluation coefficient between consumers in authorized channels and discounted products, v L The indifference evaluation coefficient between consumers purchasing discounted products and not purchasing discounted products.

3. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 1, characterized in that: In step 3, the retailer's expected profit function is: In the formula, represents the expected profit of the retailer when the discounter exists, E[·] represents the expected function, p represents the retail price of the product, min(D R , Q) indicates that in D R Take the minimum value among D and Q, R is the consumer demand function for retailer products in the presence of discounters, Q is the quantity of products that retailers order from manufacturers before the sales season; w is the unit wholesale price that manufacturers sell products to retailers, w S The unit wholesale price at which a retailer transfers a product to a discounter; (QD R ) + Guaranteed QD R is a non-negative value, (Q-D R ) + =max(0,Q-D R ); Q=e R +d R In the formula, e R is the retailer's order adjustment, d R To determine consumers' expectations of retailers' products; In step 3, the discounter's expected profit function is: π S =E[p S min(D S ,Q S )-w S Q S ] Among them, π S is the expected profit of the discount dealer, E[·] represents the expected function, and p S is the discounted product price, min(D S , Q S ) means in D S and Q S Take the minimum value, D S is the demand for discounted products, Q S is the quantity of products transferred to the discounter, satisfying Q S =(QD R ) + , (QD R ) + Guaranteed QD R is a non-negative value, w S the wholesale price per unit for retailers to transfer products to discounters; In step 3, the manufacturer's profit function is: In the formula, is the manufacturer's profit when the discounter exists, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and Q is the number of products ordered by the retailer from the manufacturer before the sales season.

4. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 1, characterized in that: In step 4, the discounted product inventory level expression is: In the formula, Q S is the inventory level of discounted products, Q is the quantity of products that retailers order from manufacturers before the sales season, and D R is the consumer demand for retailer products in the presence of discounters, (QD R ) + Guaranteed QD R is a non-negative value, (QD R ) + =max(0,QD R ), e R is the retailer's order adjustment, ε R is the uncertain part of the retailer's product demand, and the uncertain part of the retailer's product demand ε R It follows the [k, l] normal distribution, where k represents ε R The minimum value of , l represents ε R The maximum value of μ D It indicates that the average actual demand of the product is calculated based on the historical actual demand data of the product. It means calculating the standard deviation of the actual demand for a product based on the historical actual demand data of the product, and using the calculation method to determine the form of the probability density function f.

5. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 1, characterized in that: In step 5, the optimal order adjustment expression of the retailer is: In the formula, e R * represents the optimal order adjustment quantity of the retailer in the presence of the discounter, F -1 represents the uncertain part of retailer product demand ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S the wholesale price per unit for retailers to transfer products to discounters; In step 5, the expression of the retailer's optimal order quantity in the presence of the discounter is: In the formula, Q * represents the optimal order quantity of the retailer under the existence of discount dealers, a is the initial demand for the product, p is the retail price of the product, and p S is the discounted product price, and δ is the discount coefficient of the consumer on the product when there is a discounter.

6. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 3, characterized in that: In step 6, the simulated annealing algorithm is specifically: Let the discounter's expected profit function π S =E[p S min(D S , Q S )-w S Q S ] as the objective function of the simulated annealing algorithm, Select initial solution Set the initial temperature T0 and cooling rate α; the number of iterations t = 0; In the current solution A new solution p′ is randomly generated in the neighborhood of S ; Using the objective function π S Calculate the profit difference between the new solution and the current solution If Δπ>0, accept the new solution If Δπ≤0, then with probability e Δπ / T Accept the new solution, T is the current temperature; Update temperature T = α × T; the number of iterations increases by one; When the temperature is lower than the minimum temperature threshold or the current number of iterations reaches the iteration limit, the algorithm stops and the current solution is As the best discount product price.

7. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 5, characterized in that: Step 8 is as follows: Substituting the retailer's optimal order quantity when the discounter exists into the manufacturer's profit function, the manufacturer's profit is obtained In the formula, w is the unit wholesale price of the manufacturer's products sold to retailers, c is the marginal unit cost of the manufacturer's products, and F -1 Represents the market demand for the product ε R The inverse function of the cumulative distribution function F, p represents the retail price of the product, w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S is the unit wholesale price at which the retailer transfers the product to the discounter, a is the initial demand for the product, and p S Discounted product prices.

8. A forecasting system based on the relationship between price and inventory of discount channels under random demand, characterized in that: include: A data collection module is used to collect historical data, including product retail price, product wholesale price, product order quantity, and actual product sales volume, and store them in a historical database; Supply chain and demand function building module, used to build a supply chain model with discounters under random demand based on historical data, the supply chain includes manufacturers, retailers, discounters and consumers; build a consumer demand function for purchasing retailer products under the existence of discounters and a consumer demand function for purchasing discounted products under the existence of discounters based on historical data; An expected profit function building module, used to build the expected profit function of the retailer based on the demand function of consumers who purchase the retailer's products in the presence of the discounter, to build the expected profit function of the discounter based on the demand function of consumers who purchase discounted products in the presence of the discounter, and to build the profit function of the manufacturer; A module for calculating the retailer's order adjustment and discounted product inventory level, for determining the retailer's order adjustment and discounted product inventory level in the presence of the discounter based on consumer demand for the retailer's products in the presence of the discounter; The module for predicting the optimal order quantity of retailers is used to calculate the first-order derivative of the expected profit function of retailers in the presence of discount dealers, obtain the optimal order adjustment quantity of retailers' orders in the presence of discount dealers, and use the optimal order adjustment quantity to obtain the expression of the optimal order quantity of retailers in the presence of discount dealers; the expected profit function of the discount dealer is used as the objective function of the simulated annealing algorithm, and the simulated annealing algorithm is used to maximize the expected profit function of the discount dealer to solve the optimal discount product price; the optimal discount product price is substituted into the expression of the optimal order quantity of retailers in the presence of discount dealers to solve the optimal order quantity of retailers in the presence of discount dealers; The manufacturer profit prediction module is used to substitute the retailer's optimal order quantity when the discount dealer exists into the manufacturer's profit function to obtain the manufacturer's profit.

9. A computer-readable storage medium storing a computer program, characterized in that: The computer program enables the computer to execute the method for predicting the relationship between price and inventory of discount channels under random demand as described in any one of claims 1 to 7.

10. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for predicting the relationship between price and inventory of a discount channel under random demand as described in any one of claims 1 to 7 is implemented.

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