CN117522267A - Order decision method and system for information update in uncertain supply scene - Google Patents

Order decision method and system for information update in uncertain supply scene Download PDF

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Publication number
CN117522267A
CN117522267A CN202311500344.4A CN202311500344A CN117522267A CN 117522267 A CN117522267 A CN 117522267A CN 202311500344 A CN202311500344 A CN 202311500344A CN 117522267 A CN117522267 A CN 117522267A
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order
yield
case
distribution
information update
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余玉刚
言小明
朱钰
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University of Science and Technology of China USTC
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/087—Inventory or stock management, e.g. order filling, procurement or balancing against orders
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/30—Computing systems specially adapted for manufacturing

Abstract

The invention relates to an order decision method and a system for information update in a supply uncertain scene, wherein the method comprises the following steps: s1: acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprises the order quantity of each order and the quantity of received qualified products; s2: in the case of two orders before sales season, analyzing the case where the vendor yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, considering information update of the vendor yield and giving a desired maximum profit per order and an optimal order strategy by an inverse solution; s3: in the case of multiple orders before sales season, the case where the vendor yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution are analyzed, information update of vendor yield is considered and the desired maximum profit per order and the optimal order strategy are given by inverse solution. The method provided by the invention introduces uncertainty factors to the supplier's supply and optimizes the retailer's order policies on a per-day basis.

Description

Order decision method and system for information update in uncertain supply scene
Technical Field
The invention relates to the technical field of inventory management, in particular to an order decision method and system for information update under a supply uncertain scene.
Background
Random yield is a common manifestation of supply uncertainty, namely that retailers will receive random portions of orders placed to suppliers. The existence of uncertainty in the provisioning process requires retailers to pay attention to both the supply side and demand side information and to continually adjust decisions based on the information. Although many students have noted the importance of enterprise strategic inventory setting and purchasing strategy optimization at supply risk. However, how to set strategic inventory policies, how to optimize purchasing patterns, etc. are not appreciated and systematically studied.
One type of study is an order problem in a random yield scenario. There are several studies (Peng et al 2022) that consider production and procurement plans in a two-level supply chain consisting of randomly produced suppliers and randomly demanded retailers, demonstrating that updating demand information in the case of random production can improve supplier performance. At the same time, research has also been done (Rekik et al, 2007) to consider a single-stage inventory system with random throughput and to refine the conclusions in the literature assuming uniform demand and throughput. Their studies have also shown that random yield problems can cause significant losses to the company. In the past literature, studies on random yields have focused mainly on single-cycle ordering strategies and inventory management. Meanwhile, previous studies mostly assume that the suppliers actually issue a linear random proportion of qualifying goods for the retailer's order, or that the suppliers are entirely reliable and entirely unreliable.
Yet another category of research is to consider information updates in supply chain management. One commonly used method of information updating in management studies is bayesian updating. The bayesian approach well exploits a priori knowledge in combination with the current acquired data to update information about unknown parameters. Standard models of consistent bayesian learning have been applied to several topics in economics and management. For example, in early studies, (Cyert et al, 1978; tonks, 1983) a Bayesian learning model (formulated within a normal distribution framework) was applied to decision-making problems for different technological flows of enterprise investments. There are also studies (Zhou Guwen and Deng Li, 2019) that consider how remorse affects consumer purchasing decisions with uncertainty in demand, and then give optimal pricing strategies for retailers based on dynamic playing and bayes updating methods. In the prior art, the update and prediction of the information on the demand side are considered, but the update and prediction on the supply side are not given. Therefore, how to consider the influence of uncertainty of the supplier supply when deciding on the amount purchased by the retailer enterprise per period and optimize its ordering form is a urgent problem to be solved.
Disclosure of Invention
In order to solve the technical problems, the invention provides an order decision method and system for information update in a supply uncertain scene.
The technical scheme of the invention is as follows: an order decision method for information update in a provisioning uncertainty scenario, comprising:
step S1: acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprises the order quantity of each order and the quantity of received qualified products;
step S2: in the case of two orders before the sales season, respectively analyzing the case that the provider yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, considering the information update of the provider yield and giving the expected maximum profit and the optimal order strategy for each order by an inverse solution;
step S3: in the case of multiple orders before sales season, the case where the vendor yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution are analyzed, respectively, information update of the vendor yield is considered and a desired maximum profit per order and an optimal order strategy are given by inverse solution.
Compared with the prior art, the invention has the following advantages:
1. the invention discloses an order decision method for information update in a supply uncertainty scene, which gives a solution assuming that the yield is a binomial distribution and a normal distribution according to a mixed form of a discrete distribution and a continuous distribution of the yield of a provider.
2. The invention is based on the fact that the retailer makes multiple orders before the sales season, and with feedback of each order, the retailer also knows the specific form of supply uncertainty.
3. The invention also provides a new view for retailers in purchasing decisions, converting traditional information updating on the demand side into information updating on the supply side.
Drawings
FIG. 1 is a flow chart of an order decision method for information update in a provisioning uncertainty scenario in accordance with an embodiment of the present invention;
FIG. 2 is a block diagram of an order decision system for information update in a provisioning uncertainty scenario in accordance with an embodiment of the present invention.
Detailed Description
The invention provides an order decision method for updating information under uncertain supply scenes, which introduces uncertain supply factors of suppliers and optimizes each-period order strategy of retailers.
The present invention will be further described in detail below with reference to the accompanying drawings by way of specific embodiments in order to make the objects, technical solutions and advantages of the present invention more apparent.
Example 1
As shown in fig. 1, an order decision method for updating information in a supply uncertainty scene according to an embodiment of the present invention includes the following steps:
step S1: acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprises the order quantity of each order and the quantity of received qualified products;
step S2: in the case of two orders before sales season, analyzing the case where the provider yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, respectively, considering information update of the provider yield and giving a desired maximum profit per order and an optimal order strategy by an inverse solution method;
step S3: in the case of multiple orders before sales season, the case where the provider yield is a discrete 0-1 binomial distribution and the case where it is a continuous normal distribution are analyzed, respectively, information update of the provider yield is considered and a desired maximum profit per order and an optimal order strategy are given by an inverse solution method.
In one embodiment, step S1 described above: the method comprises the steps of acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprise the order quantity of each order and the received qualified product quantity, and specifically comprises the following steps:
after the invention obtains the historic purchasing data of the retail business distribution and a plurality of suppliers, the invention discovers that the supply qualification rate of the suppliers is a mixed form of discrete 0-1 binomial distribution and continuous normal distribution through analysis. Thus, embodiments of the present invention consider order decisions in the case of discrete and continuous distribution, respectively.
In one embodiment, step S2 above: in the case of two orders before sales season, the case where the vendor yield is a discrete 0-1 binomial distribution and the case where it is a continuous normal distribution are analyzed, respectively, taking into consideration the information update of the vendor yield and giving the desired maximum profit per order and the optimal order strategy by the inverse solution method, specifically including:
the retailer has two purchasing opportunities before the arrival of the sales season, each order having a different cost, and the expected profit function for the retailer at order 2 is represented by the following equation:
wherein,b represents binomial distribution, N represents normal distribution; />Represents the actual order yield of 1 st, < >>Representing the predicted 2 nd order yield by information updating; p is p 2 For the price of the good after the completion of the 2 nd order, linear with the stock quantity of the retailer, +.>a represents market capacity, b is a parameter related to stock quantity; c j Unit cost for jth order, < >>For the j-th order quantity +.>To solve for the projected profit after the 2 nd order;
the second and first expected maximum profit obtained in the case of binomial distributionAnd optimal order policy->Represented by the following formulas, respectively:
wherein k is 1 N, p are parameters of beta distribution, alpha 1 B (n, p), actual yield of first orderThe predicted second order yield can be obtained from Bayes updates of beta distribution c 1 And c 2 Representing the cost prices of the first and second orders, respectively;
the second and first expected maximum profit obtained in normal distributionAnd optimal order policy->Represented by the formula:
wherein mu 1 ，γ 1 ，σ 2 Is a normal distributed parameter, alpha 1 ～N(μ,σ 2 ) WhereinActual yield of first order +.>
First, in the case where the yield of the analysis provider satisfies the binomial distribution,is about->Is a concave function of (2), then a second sub-optimal order decision->Maximum profit->The expression is as follows:
therefore, it is possible to obtain,is about->And each term has a coefficient of k 1 Function of (2), thus let->
The optimal order quantity and maximum profit of the first order stage are then calculated from the results of the second order stage:
is about->Is a concave function of (1), and optimal order decision in the first order stage>Maximum profit->The expression is as follows:
on the premise that two purchasing opportunities exist before the sales season, the optimal order quantity and the expected maximum profit can be obtained for each purchasing on the premise that the random yield is distributed at two points. It is noted that, first, in the model of the present invention, the price is related to the number of stock items of the retailer, which also complies with the law of sales supply, so that the result is to balance the sales supply and the sales price with the help of the retailer to meet the market demand, thereby deriving the maximum profit. Second, the present invention assumes in the model that the cost price per purchase of the retailer is changing, which also conforms to the actual supply chain scenario. As sales seasons approach, suppliers 'supply costs increase and corresponding retailers' stock costs increase, which also requires retailers to learn supply side information to determine the optimal order, which would otherwise result in greater profit losses.
Secondly, under the condition that the yield of the analysis provider meets the normal distribution, based on Bayesian updated knowledge, the conjugated prior distribution of the mean value of the normal distribution can be known to be the normal distribution. In the following calculations and analyses, the present invention is assumed for the sake of simplicity of expressionSimultaneously make price->Accordingly, the expected profit function of the retailer enterprise after the second purchase can be obtained:
is about->Is a concave function of (1), and a second sub-optimal order decision->Maximum profit->The expression is as follows:
in the same way as described above,is about->Is a quadratic function of each term and the coefficients of each term are +.>And thus let(s) function of
According to the reverse-push method, the predicted profit after the first order is then solved:
is about->Is a concave function of (1), then the first optimal order decision +.>Maximum profit->The expression is as follows:
in one embodiment, the step S3: in the case of multiple orders before sales season, the case where the vendor yield is a discrete 0-1 binomial distribution and the case where it is a continuous normal distribution are analyzed, respectively, taking into account the information update of the vendor yield and giving the desired maximum profit per order and the optimal order strategy by the inverse solution method, specifically including:
the retailer enterprise has multiple purchasing opportunities before the sales season comes, each time the order costs are different, the expected profit function for the j+1st order of the enterprise is represented by the following equation:
wherein,represents the j-th actual order yield, < >>Representing the predicted j+1st order yield by information updating; p is p j+1 Price of the good after completion of j+1 orders, related to the stock quantity of the retailer, +.>
The j+1st and j-th expected maximum profit obtained in the binomial distribution caseAnd optimal order policy->Represented by the following formulas, respectively:
the j+1st and j-th expected maximum profit obtained in normal distributionAnd optimal order policy->Represented by the following formulas, respectively:
in the case of multiple orders before sales season, the case where the yield of suppliers is a discrete 0-1 binomial distribution and the case of a continuous normal distribution are analyzed, respectively, considering information update and giving the expected maximum profit for each order by inverse solution. Assume that the retailer enterprise has multiple purchasing opportunities before the sales season comes, the cost per order is different, and that the sales price is related to the current hold of the good. This situation is a two-order opportunity popularization and is also more consistent with actual retailer inventory.
First, consider that the yield of the supplier satisfies binomial distribution under the condition of multiple orders. Similar to the scenario of the two purchasing opportunities of step S2, a reverse solution is adopted. Firstly, calculating j+1st order to obtain optimum order quantity of said orderAnd expected maximum profit->After the j+1th purchase is made, the price +.>Accordingly, the desired profit function for the retailer enterprise at this time can be obtained:
is about->Is a concave function of (1) and j+1st optimal order decision +.>Maximum profit->The expression is as follows:
and solving the j-th situation according to the obtained j+1th purchase expected maximum profit. In a corresponding manner,is about->And each term has a coefficient of k j Thus making:
and then can obtainIs represented by the formula (i),
is about->And j th optimal order decision +.>Maximum expected profit for retailersThe expression is as follows:
the j+1st optimal order decision for the binomial distribution of yield under multiple order opportunities is obtainedMaximum profit->The j-th optimal order decision->Maximum profit->According to the reverse solution, the optimal order decision and the maximum profit of each previous purchase can be sequentially deduced, and guidance is made for the stock decision of the retailer enterprise.
Next, it is assumed that the yield of the supplier satisfies the normal distribution under the condition of multiple orders. For the convenience of analysis and calculation, letAt the same time, the sales price of the (j+1) -th order can be obtained>
According to the modeling, the expected profit after the (j+1) th purchase can be obtained:
is about->Is a concave function of (1) and j+1st optimal order decision +.>Maximum profit->The expression is as follows:
at this time, the optimal number and the maximum expected profit of the j+1th order have been obtained, and then the related information of the j order is solved continuously according to the reverse pushing method, so that a general solution of a purchase model similar to the real scene in each stage is obtained.
First, let theThe j-th order expected profit function may be known,
is about->And j th optimal order decision +.>Retail salesMaximum expected profit of quotientThe expression is as follows:
in one embodiment, the (j+1) -th order yield predicted in the above stepThe calculation method of (1) specifically comprises:
expected yield alpha of jth order in binomial distribution j ～B(n j ,p j ) Actual yield of jth orderBayes updates based on binomial distribution can yield the predicted j+1st order yield +.>It is marked +.>And->From the properties of the binomial distribution, it is possible to obtain:
the conjugate posterior distribution of the mean value of the normal distribution in the case of the normal distribution is also the normal distribution, the expected yield α of the jth order j ～N(μ,σ 2 ) WhereinActual yield of order j>Predicted second order yield +.>It is marked +.>And is also provided withWherein->
When j=1, the above formula applies to α in step S2 2 Is a prediction of (2).
Because of the uncertainty of supply, the most practical solution for retailers is to optimize the purchase quantity and control inventory levels. In the current supply chain management research field, most research assumes that the information at the supply end is completely known or understood about its specific distribution, and based on real enterprise data analysis, it is found that the vendor yield may not be a more desirable form, but a mixed form of discrete distribution and continuous distribution. Thus, the present invention gives solutions assuming that the yield is binomial and normal distribution, respectively, under the model of information update per order. Meanwhile, compared with a model of purchasing before selling at each stage considered in many prior researches, the invention researches the scene of multiple orders of retailers before the arrival of the selling season. With feedback on each order, the retailer is also more aware of the specific form of supply uncertainty.
Meanwhile, in the aspect of information updating, most of the previous researches focus the view angle on the requirement side, and learn and update the information of the requirement side. However, as economies develop, the supply chain structure becomes more complex and information on the supply side is also an important factor affecting retailer decisions and profits. The invention thus also provides a new perspective for retailers on the supply side in purchasing decisions.
Example two
As shown in fig. 2, an embodiment of the present invention provides an order decision system for information update in a supply uncertainty scenario, including the following modules:
an acquisition and analysis history data module 41 for acquiring and analyzing history data of orders from the retailer to the supplier, including the order quantity of each order, and the number of received qualified products;
an optimal order strategy module 42 for two orders, for analyzing the case where the provider yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, respectively, in the case of two orders before sales season, considering information update of the provider yield and giving a desired maximum profit and an optimal order strategy for each order by an inverse solution;
an optimal order strategy module 43 for multiple orders, for analyzing the case where the provider yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, respectively, in the case of multiple orders before sales season, considering information update of the provider yield and giving a desired maximum profit per order and an optimal order strategy by inverse solution.
The above examples are provided for the purpose of describing the present invention only and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalents and modifications that do not depart from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (5)

1. An order decision method for information update in a provisioning uncertainty scenario, comprising:
step S1: acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprises the order quantity of each order and the quantity of received qualified products;
step S2: in the case of two orders before the sales season, respectively analyzing the case that the provider yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, considering the information update of the provider yield and giving the expected maximum profit and the optimal order strategy for each order by an inverse solution;
step S3: in the case of multiple orders before sales season, the case where the vendor yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution are analyzed, respectively, information update of the vendor yield is considered and a desired maximum profit per order and an optimal order strategy are given by inverse solution.
2. The order decision method for information update in a provisioning uncertainty scenario according to claim 1, wherein said step S2: in the case of two orders before sales season, the case where the provider yield is a discrete 0-1 binomial distribution and the case where it is a continuous normal distribution are analyzed, respectively, taking into account the information update of the provider yield and giving the desired maximum profit per order and the optimal order strategy by inverse solution, specifically including:
the retailer has two purchasing opportunities before the arrival of the sales season, each order having a different cost, and the expected profit function for the retailer at order 2 is represented by the following equation:
wherein,b represents binomial distribution, N represents normal distribution; />Representing the 1 st actual orderRate of->Representing the predicted 2 nd order yield by information updating; p is p 2 For the price of the good after the completion of the 2 nd order, linear with the stock quantity of the retailer, +.>a represents market capacity, b is a parameter related to stock quantity; c j Unit cost for jth order, < >>For the j-th order quantity +.>To solve for the projected profit after the 2 nd order;
the second and first expected maximum profit obtained in the case of binomial distributionOptimal order strategyRepresented by the following formulas, respectively:
wherein k is 1 N, p are parameters of beta distribution, alpha 1 B (n, p), actual yield of first orderBayes updates based on beta distribution can yield the predicted second order yield +.> c 1 And c 2 Representing the cost prices of the first and second orders, respectively;
the second and first expected maximum profit obtained in normal distributionOptimal order strategyRepresented by the formula:
wherein mu 1 ，γ 1 ，σ 2 Is a normal distributed parameter, alpha 1 ～N(μ,σ 2 ) WhereinActual yield of first order +.>
3. The order decision method for information update in a provisioning uncertainty scenario according to claim 1, wherein said step S3: in the case of multiple orders before sales season, the analysis of the case where the vendor yield is a discrete 0-1 binomial distribution and the case of a continuous normal distribution, respectively, takes into account the information update of the vendor yield and gives the desired maximum profit per order and the optimal order strategy by inverse solution, specifically includes:
the retailer enterprise has multiple purchasing opportunities before the sales season comes, each time the order costs are different, the expected profit function for the j+1st order of the enterprise is represented by the following equation:
wherein,represents the j-th actual order yield, < >>Representing the predicted j+1st order yield by information updating; p is p j+1 Price of the goods after j+1 orders are completed and is prepared with retailersQuantity of goods related->
The j+1st and j-th expected maximum profit obtained in the binomial distribution caseOptimal order strategyRepresented by the following formulas, respectively:
the j+1st and j-th expected maximum profit obtained in normal distributionOptimal order strategyRepresented by the following formulas, respectively:
4. a method of order decision making for information updating in a supply uncertainty scenario as claimed in claim 2 or 3, wherein said predicted j+1st order yieldThe calculation method of (1) specifically comprises:
expected yield alpha of jth order in binomial distribution j ～B(n j ,p j ) Actual yield of jth orderBayes updates based on binomial distribution can yield the predicted j+1st order yield +.>It is marked +.>And->From the properties of the binomial distribution, it is possible to obtain:
the conjugate posterior distribution of the mean value of the normal distribution in the case of the normal distribution is also the normal distribution, the expected yield α of the jth order j ～N(μ,σ 2 ) WhereinActual yield of order j>Predicted second order yield +.>It is marked +.>And->Wherein->
5. An order decision system for information updating in a provisioning uncertainty scenario, comprising the following modules:
the acquisition and analysis historical data module is used for acquiring and analyzing historical data of orders of retailers to suppliers, wherein the historical data comprises the order quantity of each order and the quantity of received qualified products;
an optimal order strategy module for twice orders, which is used for respectively analyzing the situation that the yield of the supplier is discrete 0-1 binomial distribution and continuous normal distribution in the case of twice orders before sales season, taking the information update of the yield of the supplier into consideration and giving the expected maximum profit and the optimal order strategy of each order by an inverse solution method;
and the optimal order strategy module is used for respectively analyzing the situation that the yield of the supplier is in a discrete 0-1 binomial distribution and the situation of a continuous normal distribution in the case of multiple orders before sales season, taking the information update of the yield of the supplier into consideration and giving the expected maximum profit and the optimal order strategy of each order by an inverse solution method.
CN202311500344.4A 2023-11-13 2023-11-13 Order decision method and system for information update in uncertain supply scene Pending CN117522267A (en)

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