Systems and methods for forecasting supply or service consumption for a printing device
Methods and systems of forecasting consumption of a consumable for a machine are disclosed. A computing device receives consumption time series data for a consumable for a plurality of machines. The consumption time series data for each machine includes an amount of the consumable consumed by the machine during each of multiple time periods. For at least one of the plurality of machines, the computing device determines a model consumption forecast for the machine for each of multiple dynamic linear models based on the consumption time series data for the consumable for the machine and the dynamic linear model. The computing device further determines, for at least one of the machines, a final consumption forecast based on the model consumption forecasts. An amount of the consumable is provided for the at least one machine based on the final consumption forecast.
1. A system for forecasting consumption of a consumable for a multifunction device, the system comprising:
a processor;
a processor-readable non-transitory storage medium in communication with the processor, wherein the processor-readable storage medium contains one or more programming instructions that, when executed, cause the processor to:
compute consumption time series data for a consumable for a plurality of multifunction devices using an amount of the consumable consumed by each of the plurality of multifunction devices, measured using one or more of the following:
a print impression meter associated with each of the plurality of multifunction devices, or
a toner usage meter associated with each of the plurality of multifunction devices,
wherein the consumption time series data for each multifunction device comprises, for each of a plurality of time periods, the amount of the consumable consumed by the multifunction device during the time period,
store the consumption time series data, and
for at least one multifunction device of the plurality of multifunction devices:
select a plurality of dynamic linear models each of which has parameters that vary in time based on customer behavior;
for each selected dynamic linear model, determine a model consumption forecast for the multifunction device based on the consumption time series data for the consumable for the multifunction device and the dynamic linear model,
determine a final consumption forecast based on each determined model consumption forecast, and
determine an amount of the consumable for the multifunction device, to be provided to an operator of the multifunction device, based on the final consumption forecast.
2. The system of claim 1 , wherein the consumption time series data comprises print volume usage based on one or more of print impression meter reads and toner usage.
3. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to compute consumption time series data comprise one or more programming instructions that, when executed, cause the processor to compute consumption time series data for a consumable for a plurality of multifunction devices having a similar device type.
4. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to determine a final consumption forecast comprise instructions to determine an average forecast of the model consumption forecasts for the plurality of dynamic linear models.
5. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to determine a final consumption forecast comprise instructions to determine a median forecast of the model consumption forecasts for the plurality of dynamic linear models.
6. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to determine a final consumption forecast comprise instructions to determine an average forecast of a subset of the model consumption forecasts for the plurality of dynamic linear models.
7. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to determine a final consumption forecast comprise instructions to determine a weight for each of the plurality of dynamic linear models, wherein the weight for each dynamic linear model comprises a dynamically adjustable number determined based on the accuracy of the particular model with respect to the consumption time series data for the multifunction device over a plurality of trailing time periods.
8. The system of claim 1 , wherein each of the dynamic linear models comprises a Bayesian model.
9. The system of claim 1 , wherein the one or more programming instructions that, when executed, cause the processor to determine an amount of the consumable comprise instructions to:
determine a safety stock value; and
determine an amount of the consumable equal to a sum of the final consumption forecast and the safety stock value, to be provided to an operator of the multifunction device.
10. The system of claim 9 , wherein the one or more programming instructions that, when executed, cause the processor to determine the safety stock value comprise instructions to determine the safety stock value based on a variance in the consumption time series data for the consumable for the multifunction device.
11. A method of forecasting consumption of a consumable for a multifunction device, the method comprising:
computing, by a computing device, consumption time series data for a consumable for a plurality of multifunction devices using an amount of the consumable consumed by each of the plurality of multifunction devices, measured using one or more of the following:
a print impression meter associated with each of the plurality of multifunction devices, or
a toner usage meter associated with each of the plurality of multifunction devices,
wherein the consumption time series data for each multifunction device comprises, for each of a plurality of time periods, the amount of the consumable consumed by the multifunction device during the time period;
storing the consumption time series data; and
for at least one multifunction device of the plurality of multifunction devices:
selecting a plurality of dynamic linear models each of which has parameters that vary in time based on customer behavior,
for each selected dynamic linear model, determining, by the computing device, a model consumption forecast for the multifunction device based on the consumption time series data for the consumable for the multifunction device and the dynamic linear model,
determining, by the computing device, a final consumption forecast based on each determined model consumption forecast, and
providing an amount of the consumable for the multifunction device, to be provided to an operator of the multifunction device, based on the final consumption forecast.
12. The method of claim 11 , wherein the consumption time series data comprises print volume usage based on one or more of print impression meter reads and toner usage.
13. The method of claim 11 , wherein computing consumption time series data for a consumable comprises receiving consumption time series data for the consumable for a plurality of multifunction devices having a similar device type.
14. The method of claim 11 , wherein determining a final consumption forecast comprises determining an average forecast of the model consumption forecasts for the plurality of dynamic linear models.
15. The method of claim 11 , wherein determining a final consumption forecast comprises determining a median forecast of the model consumption forecasts for the plurality of dynamic linear models.
16. The method of claim 11 , wherein determining a final consumption forecast comprises determining an average forecast of a subset of the model consumption forecasts for the plurality of dynamic linear models.
17. The method of claim 11 , wherein determining a final consumption forecast comprises determining a weight for each of the plurality of dynamic linear models, wherein the weight for each dynamic linear model comprises a dynamically adjustable number determined based on the accuracy of the particular model with respect to the consumption time series data for the multifunction device over a plurality of trailing time periods.
18. The method of claim 11 , wherein each of the dynamic linear models comprises a Bayesian model.
19. The method of claim 11 , wherein providing an amount of the consumable comprises:
determining a safety stock value; and
determining an amount equal to a sum of the final consumption forecast and the safety stock value.
20. The method of claim 19 , wherein determining the safety stock value comprises determining the safety stock value based on a variance in the consumption time series data for the consumable for the multifunction device.
21. The method of claim 11 , wherein determining a model consumption forecast for the multifunction device is further based on consumption time series data for the consumable for one or more multifunction devices in the plurality of multifunction devices other than the multifunction device.
22. The system of claim 1 , wherein each of the dynamic linear models may comprise one or more trend components.
23. The method of claim 11 , wherein selecting, by the computing device, the plurality of dynamic linear models comprises selecting the plurality of dynamic linear models, wherein each of the dynamic linear models may comprise one or more trend components.