Method and system for predicting life cycle of unmanned retail container based on Coxian model
The Coxian model predicts the life cycle of unmanned retail containers, solves the problem of lag in operation planning in the existing technology, improves prediction accuracy and reliability, and optimizes operation costs and resource allocation.
Patent Information
- Application Number
- CN202410500391.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-24
- Publication Date
- 2024-12-24
AI Technical Summary
The existing technology cannot accurately predict the life cycle of unmanned retail containers, resulting in lagging operational planning and increasing operating costs and losses.
The Coxian model is used to construct Markov chain and maximum likelihood training models, calculate the retention time coefficient, risk coefficient and shelf withdrawal risk coefficient, and predict the life cycle of shelf points.
It improves the accuracy and reliability of predictions, reduces subjective judgment bias, provides scientific decision-making support, optimizes resource allocation and operation costs, and realizes automated operations.
Smart Images
Figure CN119180510A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of unmanned retail containers, and in particular to a method and system for predicting the life cycle of an unmanned retail container based on a Coxian model. Background Art
[0002] In recent years, with the continuous development of science and technology, intelligent identification systems have become more and more mature, the security and stability of online transactions have also been greatly improved, and consumer demand has also increased, and the unmanned retail cabinet market has ushered in new development opportunities. As time goes by, companies change, and personnel change, the sales of shelf locations will change over time. When sales are too poor and the income of the location cannot make up for the operating expenses, the location needs to withdraw goods to reduce the company's losses, that is, the life cycle of the location has reached the end. From the perspective of the life cycle of shelf locations (equivalent to retention time), each shelf needs to go through a nascent period, a rapid development period, a peak period, a decline period, and a withdrawal period. By predicting the life cycle of a location, it is possible to plan the withdrawal of locations at the end of the shelf in advance. Planned withdrawal of locations helps improve operational quality and reduce the risk of losses. For example, if the economic benefits of a location at the end of its life are low, the risk of commodity stagnation in the unmanned retail cabinet can be reduced by withdrawing the shelves. At the same time, if the unmanned retail cabinet is moved to a new location, higher economic benefits can be obtained without increasing the cost of purchasing the machine. Planned shelf withdrawal can effectively control the volatility of the number of operating shelf points, which is conducive to the planning and arrangement of replenishment capacity and the company's financing.
[0003] The current mainstream shelf life cycle assessment is based on qualitative assessment of product sales data, market demand, competition, and supplier cooperation through manual business analysis. For example, the life cycle stage of the current shelf location is assessed through business experience and actual shelf withdrawal requests (not all shelf withdrawal requests will be accepted). However, the disadvantage of this method is that it cannot be estimated in advance. When there is an actual shelf withdrawal request, it is already too late, which is not conducive to operational planning. Summary of the invention
[0004] The purpose of the present invention is to provide a method and system for predicting the life cycle of unmanned retail containers based on the Coxian model, so as to estimate the life cycle of shelf locations earlier and more accurately.
[0005] In order to achieve the above purpose, the following technical solutions are adopted:
[0006] A method for predicting the life cycle of unmanned retail containers based on the Coxian model includes the following steps:
[0007] S1: construct a Coxian model, wherein the Coxian model includes a Markov chain consisting of m+1 states, wherein states 1 to m are transient states, and the m+1 state is an absorbing state;
[0008] S2: Coxian model constructed by training S1 based on maximum likelihood method;
[0009] S3: Based on the Coxian model trained in S2, calculate the retention time coefficient, retention risk coefficient, shelf removal risk coefficient and retention time expectation of unmanned retail container locations;
[0010] S4: Based on the results calculated in S3, predict the life cycle of unmanned retail container locations.
[0011] Furthermore, in S1, it is also necessary to construct the transfer rate λ of the Coxian model i , Absorption rate μ i , degenerate transfer matrix Q, optimization target, where the transfer rate λ of the Coxian model i is the rate of transition from state i to state i+1, and the absorption rate μ of the Coxian model i is the rate from state i to the absorbing state, the degenerate transition matrix of the Coxian model is
[0012] The optimization goal of the Coxian model is to maximize the log-likelihood function.
[0013] Furthermore, the S2 specifically includes the following steps:
[0014] S21: Calculate the likelihood function of the Coxian model with given parameters based on the historical shelf location data, wherein the historical shelf location data includes the retention period data of the unmanned retail containers;
[0015] S22: Update Coxian model parameters using gradient descent method or EM algorithm;
[0016] S23: Repeat the loop steps S21-S22 to obtain the trained Coxian model.
[0017] Furthermore, in S3, the calculation formulas for the retention time coefficient f(t) and the retention risk coefficient S(t) of the unmanned retail container point are respectively:
[0018] f(t)=αe Qt μ,
[0019] S(t)=αe Qt 1,
[0020] Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix exponential.
[0021] Furthermore, in S3, the calculation formulas for the shelf removal risk coefficient h(t) and the expected retention time CTE(t) of the unmanned retail container point are respectively:
[0022]
[0023]
[0024] Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix index, μ=(μ1,…,μ m ) is the absorption rate μ i 1 is a column vector whose elements are all 1; Q -1 is the inverse matrix of Q.
[0025] A system for predicting the life cycle of unmanned retail containers based on the Coxian model is also provided, including
[0026] A data collection module, used to collect the retention cycle data of unmanned retail containers;
[0027] Coxian model building module, used to build Coxian model;
[0028] Model training module, used to train Coxian model based on maximum likelihood method;
[0029] The life cycle prediction module is used to predict the life cycle of unmanned retail container locations based on the trained Coxian model.
[0030] Furthermore, the Coxian model estimates the life cycle of unmanned retail container locations based on the calculated retention time coefficient, retention risk coefficient, shelf removal risk coefficient and retention time expectation of the unmanned retail container locations.
[0031] By adopting the above scheme, the beneficial effects of the present invention are:
[0032] 1) The present invention can accurately simulate and predict the life cycle of unmanned retail containers by constructing the Coxian model and using historical point data for training. Compared with traditional manual business analysis, the present invention can reduce the deviation of subjective judgment and improve the accuracy and reliability of prediction;
[0033] 2) The present invention can predict the survival probability and risk coefficient of shelf points, and provide scientific decision-making support for operators. That is, operators can adjust the layout of containers and commodity strategies according to the prediction results, and plan shelf removal or re-layout in advance, thereby optimizing resource allocation and reducing unnecessary operating costs;
[0034] 3) The model training and reasoning process of the present invention can be automated, reducing manual intervention and labor costs. At the same time, the scalability of the model enables it to be integrated with other intelligent systems, such as inventory management systems and sales forecasting systems, to achieve a higher level of intelligent operation. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 A Markov chain-like graph of the Coxian model of the present invention;
[0036] Figure 2 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION
[0037] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.
[0038] Reference Figures 1 to 2 As shown, the present invention provides a method for predicting the life cycle of unmanned retail containers based on the Coxian model, comprising the following steps:
[0039] S1: construct a Coxian model, wherein the Coxian model includes a Markov chain consisting of m+1 states, wherein states 1 to m are transient states, and the m+1 state is an absorbing state;
[0040] S2: Coxian model constructed by training S1 based on maximum likelihood method;
[0041] S3: Based on the Coxian model trained in S2, calculate the retention time coefficient, retention risk coefficient, shelf removal risk coefficient and retention time expectation of unmanned retail container locations;
[0042] S4: Based on the results calculated in S3, predict the life cycle of unmanned retail container locations.
[0043] In the present invention, firstly, it is necessary to train the Coxian model according to the historical shelf point data of the unmanned retail container, such as the historical retention cycle data. In the present invention, the training method adopts the Maximum Likelihood Estimation MLE. The trained Coxian model is used to infer the required information, such as the retention time coefficient, retention risk coefficient, shelf withdrawal risk coefficient and retention time expectation of the unmanned retail container point. Then, based on the above information, the life cycle of the unmanned retail container point is comprehensively predicted. In order for those skilled in the art to better understand the technical solution of the present invention, the following terms are first explained:
[0044] State i: Assume that a Markov chain has a total of m+1 states. States 1 to m are different transient states, and state m+1 is an absorbing state. Each transient state jumps to the absorbing state at a different rate, and once it enters the absorbing state, it stays in the absorbing state.
[0045] Transfer rate λ i : The rate of transition from state i to state i+1;
[0046] Absorption rate μ i : The rate from state i to the absorbing state;
[0047] The transition probability matrix P(t) is an m+1×m+1 matrix whose (i, j) element P i,j (t) is the probability of going from state i to state j after time t;
[0048] Degenerate transfer matrix Q: is an m×m matrix, where (i, j), i≠j, the element is the transition rate from state i to state j, and the diagonal element (i, i) is equal to the negative sum of the total transition rate and absorption rate of state i;
[0049] Initial probability α: is an m-dimensional row vector, representing the initial probability of each state. In particular, when it is determined to start from state 1, α = (1, 0, ..., 0);
[0050] Retention time coefficient f(t): probability distribution of shelf point retention time;
[0051] Shelf withdrawal risk coefficient h(t): the risk of shelf point withdrawal. The larger the value, the higher the probability risk of shelf withdrawal.
[0052] Retention risk coefficient S(t): The shelf location can continue to be retained. The larger the value, the higher the probability of retention and the lower the risk of withdrawal;
[0053] Expected retention time CTE(t): The expected retention time under the condition that the shelf retention time exceeds t, that is, the estimated retention time when the shelf point retention time is observed to be t.
[0054] The Coxian model is a type of random process that uses Markov Chain to simulate the evolution of survival. It is widely used in survival analysis and reliability analysis to describe the failure or survival time of systems, components, and people. The model idea is a computational random process: the time spent in each state follows a random distribution, and each state has a certain probability of jumping to an absorbing state (i.e., shelf removal, machine failure, or human death). This random process constitutes a Markov chain, such as Figure 1As shown in the figure, each newly built shelf point enters state 1, and then after staying in state 1 for a period of time, there is a certain probability that it will jump to state 2 or state m+1 (absorption state); once it enters state m+1, it will stay in state m+1; if it jumps to state 2, it will repeat the process similar to that in state 1, and after staying in state 2 for a period of time, it will either jump to state m+1 or jump to state 3, and this jumping process will continue until it jumps to state m+1. The total time from entering the system to state m+1 is the life time (retention time) of the shelf point.
[0055] For the training of Coxian model, Figure 1 As shown, the Coxian model of the present invention has a total of m+1 states, and a total of 2m-1 parameters (m-1 λ i and m μ i ), and model training is to find the optimal parameter estimation based on historical data and the objective function. In the present invention, the parameter estimation method adopted is the maximum likelihood method MLE (Maximum Likelihood Estimation), that is, maximizing the objective function - the likelihood function (likelihood). Since the MLE of this model has no analytical solution, it can only be solved by a numerical solution, such as first calculating the likelihood function and solving it with a numerical solver, or using the EM (Expectation-Maximization Algorithm) algorithm to iteratively solve it.
[0056] In the present invention, the specific training steps are as follows:
[0057] First, the Coxian model is constructed, the total length of the Markov chain m is fixed (the total length of the Markov chain m can be fixed according to the historical point data of the container, and different integers can be tried to take the minimum integer m so that the trained Coxian model can better fit the empirical distribution of historical data), and the transfer rate λ of the Coxian model is constructed. i , Absorption rate μ i , degenerate transfer matrix Q, optimization target, where the transfer rate λ of the Coxian model i is the rate of transition from state i to state i+1, and the absorption rate μ of the Coxian model i is the rate from state i to the absorbing state, the degenerate transition matrix of the Coxian model is
[0058] The optimization goal of the Coxian model is to maximize the log-likelihood function, that is,
[0059]
[0060] The retention time is t i , the indicator function δi =1When the point has been withdrawn,δ i = 0 When the point is still in operation, f(t i ) and S(t i ) are the retention time coefficient and the retention risk coefficient respectively.
[0061] Then, all parameters of the Coxian model are initialized, and 2m-1 decimals greater than 0 are randomly generated and assigned to the λ vector and μ vector, where λ=(λ1,λ2,…,λ m-1 ), is the transition rate λ of the Coxian model from state i to state i+1 i The transfer rate column vector is composed of μ = (μ1, μ2, …, μ m ), is the absorption rate μ of the Coxian model from state i to the absorbing state i The absorbance column vector.
[0062] Subsequently, the likelihood function of the Coxian model with given parameters is calculated based on the historical shelf location data, where the historical shelf location data includes the retention period data of unmanned retail containers. The Coxian model parameters are then updated using the gradient descent method or the EM algorithm. Finally, the above two steps are repeated to obtain the trained Coxian model.
[0063] Among them, the historical point retention data can be defined as t i , if the point has been withdrawn, then δ i =1, if the point is still in operation, then δ i =0, for any set of Coxian model parameters, the log-likelihood function is numerically solved by formula (1).
[0064] For the gradient descent method: given any set of Coxian model parameters, its log-likelihood function can be numerically solved by formula (1), and its gradient can be solved Gradient Descent Update Among them, α represents the learning rate of algorithm update.
[0065] For the EM algorithm: E step update 1 of them i =(0,…,0,1,0,…) i.e., a column vector whose i-th element is 1 and other elements are 0, 1 i ′ is the corresponding row vector. i With N i,i+1 The numerator part can be solved by numerical integration;
[0066] M-step update
[0067] Repeat the iterative calculation of the E step and the M step until the maximum number of iterations or the convergence threshold (i.e., λ i , μ i The difference before and after the update is less than the convergence threshold.
[0068] Finally, the MLE is obtained and applied to the estimated retention time coefficient f(t), retention risk coefficient S(t), shelf removal risk coefficient h(t), and retention time expectation CTE(t). The calculation formulas for the retention time coefficient f(t) and retention risk coefficient S(t) of unmanned retail container locations are:
[0069] f(t)=αe Qt μ, (2)
[0070] S(t)=αe Qt 1, (3)
[0071] Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix exponential.
[0072] The calculation formulas for the shelf removal risk coefficient h(t) and the expected retention time CTE(t) of unmanned retail container locations are:
[0073]
[0074]
[0075] Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix index, μ=(μ1,…,μ m ) is the absorption rate μ i 1 is a column vector whose elements are all 1; Q -1 is the inverse matrix of Q.
[0076] By setting the maximum number of iterations and the convergence threshold, Then, MLE is substituted into formulas (2), (3), (4), and (5) to calculate the retention time coefficient, retention risk coefficient, withdrawal risk coefficient, and retention time expectation, respectively.
[0077] Substitute MLE into formula (2), where S(100) is the probability that the point will be retained for at least 100 days;
[0078] Substitute MLE into formula (3), where h(100) is the risk factor of the point after 100 days of retention. For points with higher risk factors, plan the withdrawal plan in advance.
[0079] Substituting MLE into formula (4), CTE(100) is the expected remaining retention time for points with a retention time greater than 100 days. This indicator can be used to evaluate the quality of points and add points with shorter remaining time to the planned withdrawal plan.
[0080] In addition, for each shelf, additional dimensional data (such as sales data) can be used to estimate its status. The status of a location with good sales will be relatively forward, and the status of a location with poor sales will be relatively backward. By modeling and analyzing the relationship between sales data and status, the current status of the location can be estimated, and then the Coxian model can be used to personalize and update the life cycle probability distribution of each location.
[0081] A system for predicting the life cycle of unmanned retail containers based on the Coxian model is also provided, including
[0082] A data collection module, used to collect the retention cycle data of unmanned retail containers;
[0083] Coxian model building module, used to build Coxian model;
[0084] Model training module, used to train Coxian model based on maximum likelihood method;
[0085] The life cycle prediction module is used to predict the life cycle of unmanned retail container locations based on the trained Coxian model.
[0086] The Coxian model estimates the life cycle of unmanned retail container locations based on the calculated retention time coefficient, retention risk coefficient, shelf withdrawal risk coefficient and retention time expectation of the unmanned retail container locations.
[0087] The system builds a Coxian model and uses historical point data for training (the specific working principle is the same as the above method and will not be repeated here). It can accurately simulate and predict the life cycle of unmanned retail containers. Compared with traditional manual business analysis, the present invention can reduce the deviation of subjective judgment and improve the accuracy and reliability of prediction.
[0088] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for predicting the life cycle of unmanned retail containers based on the Coxian model, characterized in that: The steps include: S1: construct a Coxian model, wherein the Coxian model includes a Markov chain consisting of m+1 states, wherein states 1 to m are transient states, and the m+1 state is an absorbing state; S2: Coxian model constructed by training S1 based on maximum likelihood method; S3: Based on the Coxian model trained in S2, calculate the retention time coefficient, retention risk coefficient, shelf removal risk coefficient and retention time expectation of unmanned retail container locations; S4: Based on the results calculated in S3, predict the life cycle of unmanned retail container locations.
2. The method for predicting the life cycle of unmanned retail containers based on the Coxian model according to claim 1 is characterized in that: In S1, it is also necessary to construct the transfer rate λ of the Coxian model i , Absorption rate μ i , degenerate transfer matrix Q, optimization target, where the transfer rate λ of the Coxian model i is the rate of transition from state i to state i+1, and the absorption rate μ of the Coxian model i is the rate from state i to the absorbing state, the degenerate transition matrix of the Coxian model is The optimization goal of the Coxian model is to maximize the log-likelihood function.
3. The method for predicting the life cycle of unmanned retail containers based on the Coxian model according to claim 2 is characterized in that: The S2 specifically includes the following steps: S21: Calculate the likelihood function of the Coxian model with given parameters based on the historical shelf location data, wherein the historical shelf location data includes the retention period data of the unmanned retail containers; S22: Update Coxian model parameters using gradient descent method or EM algorithm; S23: Repeat the loop steps S21-S22 to obtain the trained Coxian model.
4. The method for predicting the life cycle of unmanned retail containers based on the Coxian model according to claim 3 is characterized in that: In S3, the calculation formulas for the retention time coefficient f(t) and the retention risk coefficient S(t) of the unmanned retail container point are: f(t)=αe Qt m, S(t)=αe Qt 1, Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix exponential.
5. The method for predicting the life cycle of unmanned retail containers based on the Coxian model according to claim 4 is characterized in that: In S3, the calculation formulas for the unmanned retail container point's shelf removal risk coefficient h(t) and retention time expectation CTE(t) are: Among them, α = (1, 0, ..., 0) is the initial probability row vector, Q is the degradation transfer matrix, e Qt is the Q matrix index, μ=(μ1,…,μ m ) is the absorption rate μ i 1 is a column vector whose elements are all 1; Q -1 is the inverse matrix of Q.
6. A system for predicting the life cycle of unmanned retail containers based on the Coxian model, characterized in that: It includes a data collection module for collecting the retention cycle data of unmanned retail containers; Coxian model building module, used to build Coxian model; Model training module, used to train Coxian model based on maximum likelihood method; The life cycle prediction module is used to predict the life cycle of unmanned retail container locations based on the trained Coxian model.
7. The system for predicting the life cycle of unmanned retail containers based on the Coxian model according to claim 6 is characterized in that: The Coxian model estimates the life cycle of unmanned retail container locations based on the calculated retention time coefficient, retention risk coefficient, shelf removal risk coefficient and retention time expectation of the unmanned retail container locations.