Method and system of demand forecasting for inventory management of slow-moving inventory in a supply chain
A system and method are disclosed for a supply chain planner to generate a distributional demand forecast for slow-moving inventory in a supply chain. The distributional demand forecast model takes into account explanatory variables and historical sales data to address seasonality and special events and permits sharing of demand information across different stores and stock-keeping units. The supply chain planner performs inference on the explanatory variables and historical sales data to generate process parameters and latent variables. Other embodiments are also disclosed.
1. A system, comprising:
a computer comprising a memory and a processor and configured to:
model a supply chain comprising one or more supply chain entities and a supply chain inventory comprising one or more supply chain products;
receive historical sales data comprising at least two demand time series and explanatory variables;
model observed values of the at least two demand time series according to a hierarchical negative-binomial state space model;
model a set of global parameters that are constant at each location, wherein the set of global parameters comprise global process parameters that condition local process parameters;
perform inference using a Gaussian Markov Random Field and a sparse tridiagonal precision matrix over a time series of unobserved supply chain model variables to generate the local and global process parameters, a latent variable, and an effective latent variable, wherein the use of the sparse tridiagonal precision matrix increases the computing speed of computing a prior term in the time series;
generate forecasted latent variables based on the generated inferred local and global process parameters, latent variable, and effective latent variable;
generate a distributional demand forecast comprising probabilities of integer values of demand for one or more time steps into the future based, at least in part, on the forecasted latent variables;
in response to a current time period elapsing to become one of the plurality of past time periods, repeating the receiving historical sales data, modelling, performing inference, generating the forecasted latent variables and generating the distributional demand forecast based on the actual sales data corresponding to the elapsed current time period being added to the historical sales data; and
in response to the generated distributional demand forecast, generate one or more replenishment orders for the one or more supply chain products.
2. The system of claim 1 , wherein the replenishment order is generated according to one or more replenishment rules, wherein the one or more replenishment rules ensure a service level of the one or more supply chain entities is met with a certain probability.
3. The system of claim 1 , wherein the one or more supply chain products are one or more slow moving products whose demand is characterized by lumpiness and intermittence.
4. The system of claim 3 , wherein the lumpiness and the intermittence are expressed by a variance of demand and a mean time interval between non-zero demands.
5. The system of claim 1 , wherein the supply chain is modelled as a network of nodes and edges.
6. The system of claim 1 , wherein the observed values are conditioned by the effective latent variable, wherein the effective latent variable is conditioned by the latent variable and an explanatory variable of the received explanatory variables, and the latent variable is conditioned by a prior latent variable and local process parameters.
7. The system of claim 1 , wherein the received explanatory variables are one or more of:
past indicators, current indicators, future indicators, data associated with promotions, data associated with seasonality, data associated with special events and weather data.
8. A computer-implemented method, comprising:
modeling, by a computer comprising a memory and a processor, a supply chain comprising one or more supply chain entities and a supply chain inventory comprising one or more supply chain products;
receiving, by the computer, historical sales data comprising at least two demand time series and explanatory variables;
modeling, by the computer, observed values of the at least two demand time series according to a hierarchical negative-binomial state space model;
modeling, by the computer, a set of global parameters that are constant at each location, wherein the set of global parameters comprise global process parameters that condition the local process parameters;
performing, by the computer, inference using a Gaussian Markov Random Field and a sparse tridiagonal precision matrix over a time series of unobserved supply chain model variables to generate the local and global process parameters, a latent variable, and an effective latent variable, wherein the use of the sparse tridiagonal precision matrix increases the computing speed of computing a prior term in the time series;
generating, by the computer, forecasted latent variables based, at least in part, on the generated inferred local and global process parameters, latent variable, and effective latent variable;
generating, by the computer, a distributional demand forecast comprising probabilities of integer values of demand for one or more time steps into the future based, at least in part, on the forecasted latent variables;
in response to a current time period elapsing to become one of the plurality of past time periods, repeating the receiving historical sales data, modelling, performing inference, generating the forecasted latent variables and generating the distributional demand forecast based on the actual sales data corresponding to the elapsed current time period being added to the historical sales data; and
generating, by the computer, in response to the generated distributional demand forecast, one or more replenishment orders for the one or more supply chain products.
9. The method of claim 8 , wherein the replenishment order is generated according to one or more replenishment rules, wherein the one or more replenishment rules ensure a service level of the one or more supply chain entities is met with a certain probability.
10. The method of claim 8 , wherein the one or more supply chain products are one or more slow moving products whose demand is characterized by lumpiness and intermittence.
11. The method of claim 10 , wherein the lumpiness and the intermittence are expressed by a variance of demand and a mean time interval between non-zero demands.
12. The method of claim 8 , wherein the supply chain is modelled as a network of nodes and edges.
13. The method of claim 8 , wherein the observed values are conditioned by the effective latent variable, wherein the effective latent variable is conditioned by the latent variable and an explanatory variable of the received explanatory variables, and the latent variable is conditioned by a prior latent variable and local process parameters.
14. The method of claim 8 , wherein the received explanatory variables are one or more of:
past indicators, current indicators, future indicators, data associated with promotions, data associated with seasonality, data associated with special events and weather data.
15. A non-transitory computer-readable medium embodied with software, the software when executed configured to:
model a supply chain comprising one or more supply chain entities and a supply chain inventory comprising one or more supply chain products;
receive historical sales data comprising at least two demand time series and explanatory variables;
model observed values of the at least two demand time series according to a hierarchical negative-binomial state space model;
model a set of global parameters that are constant at each location, wherein the set of global parameters comprise global process parameters that condition local process parameters;
perform inference using a Gaussian Markov Random Field and a sparse tridiagonal precision matrix over a time series of unobserved supply chain model variables to generate the local and global process parameters, the latent variable, and the effective latent variable, wherein the use of the sparse tridiagonal precision matrix increases the computing speed of computing a prior term in the time series;
generate forecasted latent variables based, at least in part, on the generated inferred local and global process parameters, latent variable, and effective latent variable;
generate a distributional demand forecast comprising probabilities of integer values of demand for one or more time steps into the future based, at least in part, on the forecasted latent variables;
in response to a current time period elapsing to become one of the plurality of past time periods, repeating the receiving historical sales data, modelling, performing inference, generating the forecasted latent variables and generating the distributional demand forecast based on the actual sales data corresponding to the elapsed current time period being added to the historical sales data; and
in response to the generated distributional demand forecast, generate one or more replenishment orders for the one or more supply chain products.
16. The non-transitory computer-readable medium of claim 15 , wherein the replenishment order is generated according to one or more replenishment rules, wherein the one or more replenishment rules ensure a service level of the one or more supply chain entities is met with a certain probability.
17. The non-transitory computer-readable medium of claim 15 , wherein the one or more supply chain products are one or more slow moving product whose demand is characterized by lumpiness and intermittence.
18. The non-transitory computer-readable medium of claim 17 , wherein the lumpiness and the intermittence are expressed by a variance of demand and a mean time interval between non-zero demands.
19. The non-transitory computer-readable medium of claim 15 , wherein the supply chain is modelled as a network of nodes and edges.
20. The non-transitory computer-readable medium of claim 15 , wherein the observed values are conditioned by the effective latent variable, wherein the effective latent variable is conditioned by the latent variable and an explanatory variable of the received explanatory variables, and the latent variable is conditioned by a prior latent variable and local process parameters.