Methods, systems, devices, and media for predicting price and inventory relationships for a discount channel based on random demand

Abstract

The application discloses a price and inventory relationship prediction method, system, device and medium based on a discount channel under random demand, and the method comprises the following steps: collecting historical data; constructing a supply chain model of a discount merchant under random demand, a consumer demand function of a retailer product, a consumer demand function of a discount product, an expected profit function of a retailer, an expected profit function of a discount merchant and a profit function of a manufacturer; determining a retailer order adjustment amount and a discount product inventory level based on the consumer demand of the retailer product; calculating the optimal order adjustment amount of the retailer and obtaining an optimal order quantity expression of the retailer; taking the expected profit function of the discount merchant as a target function of a simulated annealing algorithm, solving an 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. The application makes inventory management more scientific.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of computer-aided supply chain management, and particularly relates to a method, system, device and medium for predicting the relationship between price and inventory of a discount channel based on random demand. BACKGROUND

[0002] A discount market refers to a sales activity in which goods are sold at a lower price than their retail price. Generally, such goods in the market include overstocked, out-of-season goods, or discounted goods provided due to brand promotion activities. Discount markets come in various forms, either online platforms or physical stores. Taking e-commerce platforms as an example, Vip.com focuses on time-limited sales, attracting a large number of price-sensitive users by providing time-limited discounted goods. In the physical retail sector, outlet stores are a widely adopted form of discount stores worldwide, mainly selling overstocked, discontinued, and inventory goods of brands. Consumers can purchase high-end brand goods at a lower price in outlet stores, enjoying the dual advantages of brand premium and discounts. Discount markets provide consumers with price-reduced product options, while reducing inventory pressure for manufacturers or retailers. The products in discount markets mainly come from authorized retailers transferring unsold products in the sales season to discount retailers. Discount retailers are retailers or intermediaries that specialize in selling goods at discounted prices. They usually obtain goods by purchasing overstocked or excess inventory products from manufacturers or by directly purchasing goods at a lower price through promotional activities. The core business model of discount retailers is to attract price-sensitive consumers with lower prices, providing more attractive product options than traditional retail channels. Discount products are not significantly different from regular channel products, often with lower prices but lack of supporting services. When consumers observe the existence of discounted products in the market, their perception of the brand image of the product will change, thereby affecting their choice of purchasing the product.

[0003] When products are sold in a market, they will be affected by market demand and may have excess or out-of-stock situations. The imbalance between order quantity and market demand will cause losses to retailers, who can transfer unsold products to discount retailers to maximize their own profits. This behavior may affect the profits of manufacturers, retailers, and discount retailers.

[0004] The existing problems in the calculation method of inventory control are that no appropriate inventory control strategy is set for the order quantity of the retailer facing random demand in the discount merchant environment, and the profit maximization of each member of the supply chain is realized. The conventional supply chain problem often focuses on pricing or inventory, and lacks a calculation method for the relationship between pricing and inventory. In the discount merchant problem, although the discount merchant is a member of the supply chain, it is always not concerned about the relationship between the pricing of the discount merchant and the inventory of the manufacturer and the retailer. In order to solve the problems related to the supply chain, the model assumption often deviates from the actual situation. Therefore, the present application is a prediction method for the relationship between price and inventory under the discount channel. SUMMARY

[0005] The present application provides a prediction method for the relationship between price and inventory under the discount channel based on random demand, system, device and medium, which solves the inventory management defects of the existing supply chain inventory decision without considering the discount merchant and demand uncertainty, and improves the overall profit of the supply chain.

[0006] In order to achieve the above-mentioned purpose, the present application adopts the following technical scheme:

[0007] A prediction method for the relationship between price and inventory under the discount channel based on random demand, comprising the following steps:

[0008] Step 1, collecting historical data, the historical data including product retail price, product wholesale price, product order quantity, product actual sales quantity, and storing into a historical database;

[0009] Step 2, constructing a supply chain model with discount merchant under random demand based on the historical data, the supply chain including manufacturer, retailer, discount merchant and consumer; constructing a consumer demand function for purchasing retailer products under the existence of discount merchant and a consumer demand function for purchasing discount products under the existence of discount merchant based on the historical data;

[0010] Step 3, constructing an expected profit function of the retailer based on the consumer demand function for purchasing retailer products under the existence of discount merchant, constructing an expected profit function of the discount merchant based on the consumer demand function for purchasing discount products under the existence of discount merchant, and constructing a profit function of the manufacturer;

[0011] Step 4, determining the order adjustment quantity of the retailer and the inventory level of the discount product under the existence of discount merchant based on the consumer demand for purchasing retailer products under the existence of discount merchant;

[0012] Step 5, taking the first derivative of the expected profit function of the retailer under the existence of discount merchant with respect to the order adjustment quantity of the retailer to obtain the optimal order adjustment quantity of the retailer under the existence of discount merchant, and using the optimal order adjustment quantity to obtain the expression of the optimal order quantity of the retailer under the existence of discount merchant;

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

[0014] 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;

[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, 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 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;

[0020] The expected demand of consumers for the retailer's products d 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 purchasing 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 discount dealer, and p SFor discounted product prices;

[0027] Let U R =U S , we get the indifference evaluation coefficient v between consumers in authorized channels 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 discounted products, δ is the discount coefficient of consumers on discounted products when there are discount dealers;

[0030] Based on the indifference evaluation coefficient v H Construct consumers' expected demand for retailers' 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 discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, 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 causes consumers not to purchase the product S =0, we get the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products. L :

[0038]

[0039] Where p SPd is the price of the discounted product, and δ is the discount factor of the discounted product when the discount merchant exists;

[0040] v is the indifference evaluation coefficient of the consumer between the authorized channel and the discounted product H v is the indifference evaluation coefficient of the consumer between purchasing the discounted product and not purchasing the discounted product L The expected demand function of the consumer for the discounted product is constructed as follows:

[0041]

[0042] wherein a represents the initial demand of the product, p represents the retail price of the product, p S Pd is the price of the discounted product, and δ is the discount factor of the discounted product when the discount merchant exists, v H v is the indifference evaluation coefficient of the consumer between the authorized channel and the discounted product L v is the indifference evaluation coefficient of the consumer between purchasing the discounted product and not purchasing the discounted product

[0043] Further, in step 3, the expected profit function of the retailer is as follows:

[0044]

[0045] wherein represents the expected profit of the retailer when the discount merchant exists, E[·] represents the expected function, p represents the retail price of the product, min(D R , Q) represents the minimum value between D R and Q, D j is the demand function of the consumer purchasing the product of the retailer when the discount merchant exists, and Q is the quantity of the product ordered by the retailer from the manufacturer before the sales season; w is the unit wholesale price of the product sold by the manufacturer to the retailer, w S is the unit wholesale price of the product transferred by the retailer to the discount merchant; (Q-D R ) + represents the guarantee that Q-D R is a non-negative value, (Q-D R ) + = max(0, Q-D R );

[0046] Q = e R +d R

[0047] wherein e R is the order adjustment quantity of the retailer, and d R is the expected demand of the consumer for the product of the retailer;

[0048] In step 3, the expected profit function of the discount merchant is as follows:

[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 expectation 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 unit wholesale price at which retailers transfer products to discounters;

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

[0052]

[0053] Where, 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 manufacturer's marginal unit cost of producing products, and Q is the number of products that retailers order from the manufacturer before the sales season.

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

[0055]

[0056] Where 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 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 ε is the uncertain part of the retailer's product demand R subject to a [k, l] normal distribution, k represents the minimum value of ε R and l represents the maximum value of ε R is expressed as μ D represents the mean value of the actual product demand calculated according to the historical actual product demand data, represents the standard deviation of the actual product demand calculated according to the historical actual product demand data, and the form of the probability density function f is determined using the calculation method.

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

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

[0059] An initial solution p is selected An initial temperature T0 and a cooling rate α are set; the iteration number t = 0;

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

[0061] The profit difference between the new solution and the current solution is calculated using the objective function π S ;

[0062] If Δπ > 0, the new solution p is accepted If Δπ ≤ 0, the new solution p Δπ / T is accepted with a probability e ; T is the current temperature;

[0063] The temperature T is updated as T = α × T; the iteration number is incremented by one;

[0064] When the temperature is lower than a minimum temperature threshold or the current iteration number reaches an iteration number limit, the algorithm stops, and the current solution p is taken as the optimal discount product price.

[0065] Further, in step 5, the optimal order adjustment amount table of the retailer's order is expressed as:

[0066]

[0067] In the formula, e R* F represents the optimal order adjustment of the retailer in the presence of the discount merchant, F -1 represents the uncertain part of the demand of the product of the retailer ε R , the inverse function of the cumulative distribution function F of the uncertain part of the demand of the product of the retailer, 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 of the product transferred by the retailer to the discount merchant, and a represents the initial demand of the product

[0068] In step 5, the expression of the optimal order quantity of the retailer in the presence of the discount merchant is as follows:

[0069]

[0070] In the formula, Q * represents the optimal order quantity of the retailer in the presence of the discount merchant, a represents the initial demand of the product, p represents the retail price of the product, p S is the discount price of the product, and δ is the discount coefficient of the product by the consumer in the presence of the discount merchant.

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

[0072] The optimal order quantity of the retailer in the presence of the discount merchant is substituted into the profit function of the manufacturer, and the profit of the manufacturer is obtained

[0073]

[0074] In the formula, w is the unit wholesale price of the product sold by the manufacturer to the retailer, c is the marginal unit cost of the product produced by the manufacturer, F -1 represents the cumulative distribution function F of the demand of the product in the market ε R , the inverse function of the cumulative distribution function F of the demand of the product in the market, 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 of the product transferred by the retailer to the discount merchant, a represents the initial demand of the product, p S is the discount price of the product.

[0075] The application further provides a prediction system based on the price and inventory relationship of the discount channel under random demand, comprising:

[0076] A data acquisition module is used for acquiring historical data, the historical data including a product retail price, a product wholesale price, a product order quantity, and a product actual sales quantity, and the historical data is stored into a historical database;

[0077] The supply chain and demand function construction module is used for constructing a supply chain model of the existence of the discount merchant under random demand based on historical data, the supply chain including a manufacturer, a retailer, a discount merchant and consumers; constructing a demand function of the consumers purchasing the products of the retailer under the existence of the discount merchant and a demand function of the consumers purchasing the discount products under the existence of the discount merchant based on the historical data;

[0078] The expected profit function construction module is used for constructing an expected profit function of the retailer based on the demand function of the consumers purchasing the products of the retailer under the existence of the discount merchant, constructing an expected profit function of the discount merchant based on the demand function of the consumers purchasing the discount products under the existence of the discount merchant, and constructing a profit function of the manufacturer;

[0079] The retailer order adjustment quantity and discount product inventory level calculation module is used for determining the order adjustment quantity of the retailer and the inventory level of the discount product under the existence of the discount merchant based on the demand of the consumers purchasing the products of the retailer under the existence of the discount merchant;

[0080] The retailer optimal order quantity prediction module is used for taking the first derivative of the expected profit function of the retailer under the existence of the discount merchant with respect to the order adjustment quantity of the retailer to obtain the optimal order adjustment quantity of the retailer under the existence of the discount merchant, and obtaining an expression of the optimal order quantity of the retailer under the existence of the discount merchant by using the optimal order adjustment quantity; taking the expected profit function of the discount merchant as a target function of a simulated annealing algorithm, and solving the optimal discount product price by using the simulated annealing algorithm and taking the maximum of the expected profit function of the discount merchant as a target; and solving the optimal order quantity of the retailer under the existence of the discount merchant by substituting the optimal discount product price into the expression of the optimal order quantity of the retailer under the existence of the discount merchant.

[0081] The manufacturer profit prediction module is used for substituting the optimal order quantity of the retailer under the existence of the discount merchant into the profit function of the manufacturer to obtain the profit of the manufacturer.

[0082] The application further provides a computer readable storage medium storing a computer program, wherein the computer program enables a computer to execute the prediction method based on the price and inventory relationship of the discount channel under random demand.

[0083] The application further provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to implement the prediction method based on the price and inventory relationship of the discount channel under random demand.

[0084] The application has the following beneficial effects:

[0085] The application solves the relationship and influence between the retail price, the discount merchant price, the order quantity of the retailer and the demand of the consumers and the profit function of the supply chain members under the existence of the discount merchant by using simple demand functions and profit functions.

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

[0087] The present application finds the relationship between the price of discount merchant and the demand of consumer and the order quantity of retailer by mathematical calculation, and obtains the expression of the price of discount merchant.

[0088] The present application calculates the change trend of the profit of manufacturer in the presence of discount merchant by the method of data analysis combined with model, finds the relationship between the discount merchant and the order quantity of retailer and the demand of consumer, and makes the inventory management more scientific. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 The figure is the demand change diagram of supply chain without discount merchant and supply chain with discount merchant in the present application.

[0090] Figure 2 The figure is the decision sequence diagram of supply chain members in the presence of discount merchant in the present application. DETAILED DESCRIPTION

[0091] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0092] Embodiment one, the present application proposes a prediction method of the price and inventory relationship of discount channel under random demand, comprising the following steps:

[0093] Step 1, collecting historical data, the historical data including product retail price, product wholesale price, product order quantity, product actual sales quantity, and storing into historical database;

[0094] Step 2, constructing a supply chain model in the presence of discount merchant under random demand based on historical data, the supply chain including manufacturer, retailer, discount merchant and consumer; constructing a consumer demand function of purchasing retailer product in the presence of discount merchant and a consumer demand function of purchasing discount product in the presence of discount merchant based on historical data.

[0095] The expression of the consumer demand function of purchasing retailer product in the presence of discount merchant is as follows:

[0096]

[0097] In the formula, D R is the consumer demand of purchasing retailer product in the presence of discount merchant, 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 d 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 purchasing 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 discount dealer, and p S For discounted product prices;

[0105] Let U R =U S , we get the indifference evaluation coefficient v between consumers in authorized channels 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 discounted products, δ is the discount coefficient of consumers on discounted products when there are discount dealers;

[0108] Based on the indifference evaluation coefficient v H Construct consumers' expected demand for retailers' 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 discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, 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 causes consumers not to purchase the product S =0, we get the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products. L :

[0116]

[0117] Where p S is the price of discounted products, δ is the discount coefficient of consumers on discounted products when there are discount dealers;

[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 discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, v H is the indifference evaluation coefficient of consumers between 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 consumer demand function of the retailer's products in the presence of the discounter, construct the expected profit function of the discounter based on the consumer demand function of the discounted products in the presence of the discounter, and construct the profit function of the manufacturer.

[0122] The retailer's expected profit function is:

[0123]

[0124] Where, 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 of 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] Where, 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 expectation 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 SQ S is the quantity of product diverted to the discount merchant, and S = (Q - D R ) + R + = max(0, Q - D R ) S , w S is the unit wholesale price at which the retailer diverts product to the discount merchant.

[0130] The manufacturer's profit function in Step 3 is:

[0131]

[0132] where is the manufacturer's profit when the discount merchant is present, w is the unit wholesale price at which the manufacturer sells product to the retailer, c is the marginal unit cost of producing product for the manufacturer, and Q is the quantity of product ordered by the retailer from the manufacturer prior to the sales season.

[0133] Step 4, determine the retailer's order adjustment and the discount product inventory level based on the demand for the retailer's product when the discount merchant is present.

[0134] The discount product inventory level is given by:

[0135]

[0136] where Q S is the discount product inventory level, Q is the quantity of product ordered by the retailer from the manufacturer prior to the sales season, D R is the demand for the retailer's product when the discount merchant is present, (Q - D R ) + = max(0, Q - D R ) R , and (Q - D + ) R = max(0, Q - D R ), e R is the retailer's order adjustment, and ε R is the uncertainty in the demand for the retailer's product, where the uncertainty in the demand for the retailer's product, ε R , is normally distributed with mean k and variance l, where k is the minimum value of ε R , and l is the maximum value of ε D . μ D is the mean of the actual demand for product based on historical data, and represents the standard deviation of the actual demand of the product calculated according to the historical actual demand data of the product, and the form of the probability density function f is determined using the calculation method.

[0137] Step 5, taking the first derivative of the expected profit function of the retailer in the presence of the discount merchant with respect to the order adjustment of the retailer to obtain the optimal order adjustment of the retailer in the presence of the discount merchant, and using the optimal order adjustment to obtain an expression of the optimal order quantity of the retailer in the presence of the discount merchant; in Step 5, the optimal order adjustment expression of the order of the retailer is:

[0138]

[0139] wherein e R * represents the optimal order adjustment of the order of the retailer in the presence of the discount merchant, F -1 represents the inverse function of the cumulative distribution function F of the uncertain part ε R of the product demand of the retailer, p represents the retail price of the product, and w is the unit wholesale price of the manufacturer selling the product to the retailer, w S is the unit wholesale price of the retailer transferring the product to the discount merchant;

[0140] In Step 5, the expression of the optimal order quantity of the retailer in the presence of the discount merchant is:

[0141]

[0142] wherein Q * represents the optimal order quantity of the retailer in the presence of the discount merchant, a is the initial demand of the product, p represents the retail price of the product, p S is the discount product price, and δ is the discount coefficient of the product by the consumer in the presence of the discount merchant.

[0143] Step 6, taking the expected profit function of the discount merchant as the objective function of the simulated annealing algorithm, and using the simulated annealing algorithm to solve the optimal discount product price with the maximum expected profit function of the discount merchant as the target; the simulated annealing algorithm is specifically:

[0144] taking the expected profit function π S of the discount merchant = E[p S min(D S , Q S )-w S Q S ] as the objective function of the simulated annealing algorithm,

[0145] selecting an initial solution setting an initial temperature T0 and a cooling rate α; iteration number t = 0;

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

[0147] The objective function π S The profit difference between the new solution and the current solution is calculated

[0148] If Δπ > 0, the new solution is accepted If Δπ < 0, the new solution is accepted with a probability e Δπ / T The new solution is accepted, and T is the current temperature;

[0149] The temperature T is updated to T = a x T, and the iteration number is increased by one.

[0150] When the temperature is lower than a minimum temperature threshold or the current iteration number reaches an iteration number limit, the algorithm stops, and the current solution is taken as the optimal discount product price.

[0151] Step 7, substitute the optimal discount product price into the expression of the optimal order quantity of the retailer when the discount merchant exists to solve the optimal order quantity of the retailer when the discount merchant exists.

[0152] Step 8, substitute the optimal order quantity of the retailer when the discount merchant exists into the profit function of the manufacturer to obtain the profit of the manufacturer. Specifically:

[0153] Substitute the optimal order quantity of the retailer when the discount merchant exists into the profit function of the manufacturer to obtain the profit of the manufacturer

[0154]

[0155] In the formula, w is the unit wholesale price of the manufacturer selling products to the retailer, c is the marginal unit cost of the manufacturer producing products, F -1 represents the cumulative distribution function F of the demand ε R of the market for the product, p represents the retail price of the product, w is the unit wholesale price of the manufacturer selling products to the retailer, w S is the unit wholesale price of the retailer transferring products to the discount merchant, a represents the initial demand for the product, and p S is the discount product price.

[0156] Example 2, comparison of the cases where the discount merchant does not exist and the discount merchant exists.

[0157] Step one: Construct the supply chain model of no-discount merchant under random demand, which contains manufacturer, retailer and consumer. The supply chain only sells one product. The manufacturer completes the production of the product before the sales season. The retailer orders a certain amount of products from the manufacturer according to the past demand prediction. In the sales season, 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 product is 0, the retailer needs to bear the loss of unsold products.

[0158] Step two: Set the utility function of the consumer under the condition of no-discount merchant. The utility U of the consumer buying the product is

[0159]

[0160] wherein v represents the evaluation of the consumer buying the product, v satisfies the uniform distribution between [0, 1], a is the initial demand of the product, and p represents the retail price of the product. When the utility U of the consumer is greater than 0, the consumer will choose to buy the product, otherwise not.

[0161] Step three: Construct the demand function under the condition of no-discount merchant.

[0162] D0=d+ε R =1-p+ε R

[0163] wherein D0 is the total demand of the market for the product under the condition of no-discount merchant, d is the expected demand of the product under the condition of no-discount merchant, ε R is a random variable in the demand of the product of the retailer, the probability density function of which is f(x), the cumulative distribution function is F(x), and p is the product price determined by the retailer.

[0164] Step four: Based on the condition of no-discount merchant, construct the profit function of each member of the supply chain. The expected profit function of the retailer is

[0165] π R =pmin(D0,Q0)-wQ0

[0166] wherein w is the unit wholesale price of the manufacturer selling the product to the retailer. Q0 is the order quantity of the retailer under the condition of no-discount merchant.

[0167] The profit function of the manufacturer is

[0168] π M =(w-c)Q0

[0169] wherein c is the marginal unit cost of the manufacturer producing the product.

[0170] Step five: Determine the order quantity of the retailer under the condition of no-discount merchant, which can be expressed as:

[0171] e = Q0- d

[0172] where e is the retailer's order adjustment, which is determined by the retailer, i.e., the retailer observes that the product demand is uncertain and adjusts the order based on the demand forecast. Taking the first derivative of the above equation with respect to e, we have

[0173]

[0174] where F -1 is the inverse function of the cumulative distribution function of demand.

[0175] Step 6: Solve the retailer's optimal order adjustment without discounters.

[0176]

[0177] Calculate the impact on the profits of manufacturers and retailers in the presence of discounters. Under the premise that consumers have a discount coefficient δ for discounted products and market demand is uncertain, the discounters' pricing prediction can be achieved through the Markov Chain Monte Carlo (MCMC) method. This includes the following steps:

[0178] 1. Establish a statistical model: First, define the probability model to describe how to generate the observed data π S from the given input parameters: a, p, w, w R , μ S , δ, k, l, m, n M , π R and p S * , including the generation process and expression of e * , e R * , and p * .

[0179] 2. Select the prior distribution: Select appropriate prior distributions for the model parameters. These priors can be reasonable assumptions based on prior knowledge, such as δ following a uniform distribution on (0, 1), ε R following a normal distribution on [k, l], and ε S following a normal distribution on [m, n], which can be represented as and Determine the form of the probability density functions f(·) and g(·) and the form of the cumulative distribution function F(·) through 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 adequacy of the model, including convergence tests and analysis of the posterior distribution.

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

[0183] Embodiment 3: The present invention proposes a forecasting 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 prices, product wholesale prices, product order quantities, and actual product sales, and store them in a historical database;

[0185] The supply chain and demand function construction module is used to construct a supply chain model with discounters under random demand based on historical data. The supply chain includes manufacturers, retailers, discounters, and consumers. The module also constructs the consumer demand function for purchasing retailer products under the presence of discounters and the consumer demand function for purchasing discounted products under the presence of discounters based on historical data.

[0186] an expected profit function construction module for constructing 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, constructing 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 constructing 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 retailer optimal order quantity prediction module is used to derive the first derivative of the expected profit function of the retailer with respect to the order adjustment quantity of the retailer, to obtain the optimal order adjustment quantity of the retailer with the discount merchant, and to obtain the expression of the optimal order quantity of the retailer with the discount merchant by using the optimal order adjustment quantity; the expected profit function of the discount merchant is used as the objective function of the simulated annealing algorithm, the simulated annealing algorithm is adopted, and the optimal discount product price is obtained by taking the maximum of the expected profit function of the discount merchant as the target; the optimal discount product price is substituted into the expression of the optimal order quantity of the retailer with the discount merchant to obtain the optimal order quantity of the retailer with the discount merchant.

[0189] The manufacturer profit prediction module is used to substitute the optimal order quantity of the retailer with the discount merchant into the profit function of the manufacturer to obtain the profit of the manufacturer.

[0190] The implementation manners of the modules and the functions of the modules in the system are completely consistent with the method steps of the first embodiment, and thus will not be described here.

[0191] In the fourth embodiment, a computer readable storage medium is provided, which stores a computer program, and the computer program enables a computer to execute the prediction method of the price and the inventory relationship of the discount channel based on the random demand as described in the first embodiment.

[0192] In the fifth embodiment, an electronic device is provided, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the prediction method of the price and the inventory relationship of the discount channel based on the random demand as described in the first embodiment is implemented.

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

[0194] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software manner depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0195] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled persons in the art, some improvements and refinements without departing from the principles of the present application shall be considered as the protection scope of the present application.

Claims

1. A method for predicting the relationship between price and inventory of discount channels under random demand, characterized by: The following steps are involved: Step 1: Collect historical data, including product retail price, product wholesale price, product order quantity, and product actual sales volume, and store them in a historical database; Step 2: Based on historical data, a supply chain model is constructed with discounters under random demand. The supply chain includes manufacturers, retailers, discounters, and consumers. Based on historical data, a consumer demand function for the retailer's products under the presence of discounters and a consumer demand function for the discounted products under the presence of discounters are constructed. Step 3: Construct the expected profit function of the retailer based on the consumer demand function for the retailer's products in the presence of the discounter, construct the expected profit function of the discounter based on the consumer demand function for the discounted products in the presence of the discounter, and construct the profit function of the manufacturer; in step 3, the expected profit function of the retailer is: Where, 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 of 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, and 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 ); Q=e R +d R Where, e R is the retailer's order adjustment, d R To meet 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 expectation 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 unit wholesale price at which retailers transfer products to discounters; In step 3, the manufacturer's profit function is: Where, 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 manufacturer's marginal unit cost of producing products, and Q is the number of products that retailers order from the manufacturer before the sales season; 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: Calculate 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 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 discounter's expected profit function as the objective function of the simulated annealing algorithm, the simulated annealing algorithm is used to maximize the discounter's expected profit function and solve the optimal discounted 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 consumer demand function for purchasing the retailer's products in the presence of the discounter is expressed 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 d 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 purchasing 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 discount dealer, and p S For discounted product prices; Let U R =U S , we get the indifference evaluation coefficient v between consumers in authorized channels 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 discounted products, δ is the discount coefficient of consumers on discounted products when there are discount dealers; Based on the indifference evaluation coefficient v H Construct consumers' expected demand for retailers' 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 discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, 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 causes consumers not to purchase the product S =0, we get the indifference evaluation coefficient v between consumers who buy discounted products and those who do not buy discounted products. L : Where p S is the price of discounted products, δ is the discount coefficient of consumers on discounted products when there are discount dealers; 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 discounted products, δ is the discount coefficient of consumers for discounted products when there are discount dealers, v H is the indifference evaluation coefficient of consumers between 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 4, the discounted product inventory level expression is: Where 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 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 Obeys [k,l] normal distribution, k represents ε R The minimum value of l represents ε R The maximum value of μ D Indicates that the average actual demand of a product is calculated based on historical actual demand data of the product. It means calculating the standard deviation of the actual demand for a product based on historical actual demand data, and using the calculation method to determine the form of the probability density function f.

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 5, the optimal order adjustment expression of the retailer is: Where, e R * F represents the optimal order adjustment quantity of the retailer under the existence of the discounter, -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 unit wholesale price at which retailers transfer products to discounters; In step 5, the expression of the retailer's optimal order quantity under the existence of the discounter is: Where 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.

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 6, the simulated annealing algorithm is specifically as follows: 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 an 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 discounted product price.

6. The method for predicting the relationship between price and inventory of discount channels under random demand according to claim 4, 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 product sold by the manufacturer to the retailer, c is the marginal unit cost of the manufacturer to produce the product, 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.

7. A forecasting system for the relationship between price and inventory of discount channels under random demand, implementing the method according to any one of claims 1 to 6, characterized in that: include: A data collection module is used to collect historical data, including product retail prices, product wholesale prices, product order quantities, and actual product sales, and store them in a historical database; The supply chain and demand function construction module is used to construct a supply chain model with discounters under random demand based on historical data. The supply chain includes manufacturers, retailers, discounters, and consumers. The module also constructs the consumer demand function for purchasing retailer products under the presence of discounters and the consumer demand function for purchasing discounted products under the presence of discounters based on historical data. an expected profit function construction module for constructing 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, constructing 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 constructing the profit function of the manufacturer; a module for calculating the retailer's order adjustment and the discounted product inventory level, for determining the retailer's order adjustment and the 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 retailer's optimal order quantity prediction module is used to calculate the first-order derivative of the retailer's expected profit function in the presence of the discounter, obtain the optimal order adjustment quantity for the retailer's order in the presence of the discounter, and use the optimal order adjustment quantity to obtain the expression of the retailer's optimal order quantity in the presence of the discounter; the discounter's expected profit function is used as the objective function of the simulated annealing algorithm, and the simulated annealing algorithm is used to maximize the discounter's expected profit function to solve the optimal discount product price; the optimal discount product price is substituted into the expression of the retailer's optimal order quantity in the presence of the discounter to solve the retailer's optimal order quantity in the presence of the discounter; 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.

8. 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 6.

9. 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 discount channels under random demand as described in any one of claims 1 to 6 is implemented.

Images