WO2016073025A1

WO2016073025A1 - Demand forecasting and simulation

Info

Publication number: WO2016073025A1
Application number: PCT/US2015/022384
Authority: WO
Inventors: Sandip MUKHERJEE; Aparna MRIDUL
Original assignee: Hewlett Packard Enterprise Development Lp
Priority date: 2014-11-04
Filing date: 2015-03-25
Publication date: 2016-05-12

Abstract

A method for demand forecasting includes building a combined demand forecast models that is a weighted combination of individual demand forecast models each based on one driver, applying a weighting algorithm to optimize weights assigned to the individual demand forecast models based their accuracy, using the combined demand forecast model to simulate demand forecasts for a future time period, and placing a demand forecast for the future time period on a distribution of the simulated demand forecasts to assess the demand forecast.

Description

DEMAND FORECASTING AND SIMULATION

BACKGROUND

[0003 } Demand forecasting is an important component of any business. It enables organ zations to plan and allocate their resources in a more efficient manner, minimizing risks and losses that could otherwise arise. With rapidly changing technology, numerous choices for consumers, and increasing competitiveness in the market:, accuracy m prediction can be an important differentiator between successful organizations and others.

BRIEF DESCRIPTION OF THE DR A WINGS

[0002] In the drawings:

Fig. I is block diagram, of a computing device with a demand forecaster with consensus demand forecasting, simulation, and scenario analysis in examples of the present disc! osure;

Fig. 2 is a flowchart of a method for a processor of Fig. 1 to implement the demand forecaster of Fig. 1 in examples of the present disclosure;

Fig. 3 is a flowchart of a method for a processor of Fig. 1 to implement the demand forecaster of Fig. 1 in examples of the present disclosure;

Fig, 4 is a block diagram illustrating the method of Fig, 3 in examples of the present disclosure;

Fig. 5 is a chart plotting actual demand, demand forecasts from various models, and a combined forecast from a combined forecast model over time in examples of the present disclosure; Fig, 6 is a chart of a distribution of possible demand forecasts generated based on simulated values of drivers in examples of the present disclosure; and

Fig. 7 is a chart of an original bell curve based on original driver values and a new bell curve based on new driver values in examples of the present disclosure,

10903] Use of the same reference numbers in differen figures indicates similar or identical elements.

. ^■] . DETAILED DESCRIPTION

[0004] Time series and causal models have been used in the past to forecast demand, in a pure time series approach there is no scope to incorporate exogenous variables in the model. Time series approaches may work better in the short term but in the medium and longer term they do not pick up trends in the market as they are purely based on historical data,

J0005] I« the case of causal models, they encounter the problem of raulticolinearity where the exogenous or independent variables are highly correlated so they violate the standard assumptions in this approach, in causal models, the forecast of the demand is bas ed on the forecast of the exogeno us variables. Thus the accuracy of the demand forecast is largely- dependent on the accuracy of the forecast of the exogenous variables.

[Θ006] Neural networks may be another solution to obtain good forecasts considering a host of variables. However this does not explain the effect of different drivers on the demand.

Other dimension reduction techniques also pose a similar problem of extracting the actual impact of the independent variables on demand.

[0007] In examples of the present disclosure, a method for demand forecasting builds single driver models and uses a weighting algorithm to create a combined forecast model that outputs a combined forecast. The method leverages the richness of information from several factors (drivers) influencing demand while avoiding the molticolinearity constraint on causal models.

{0008] The method may apply the same concept to multiple demand forecasts available from different sources and techniques, including time series projections and qualitative and judgmental forecasts. To leverage ihe intelligence behind each of the forecasts and minimize the error arising from the individual forecasts, the individual forecasts may be^' combined with, optimal weighting to arrive at a combined forecast,

[0009] The method may run simulations to perform risk analysis to help a business assess if a demand .forecast for a future time period is conservative, optimistic, or in line with a most likely expectation. The method passes correlated random values of the drivers to the combined forecast model to generate possible demand forecasts for the future period, A demand forecast may be placed on a distribution of possible demand forecasts to assess the risk associated with the demand forecast. JO J.O] The method may pro v ide scenario analysis to per form what if analysis to plan and understand implication of changing drivers. As umin a driver has a new value, the method uses a historical correlation matrix to determine new values for the other drivers and uses the multiple driver based model to determine a ne demand forecast based on the new vaiues of the drivers. The method may run simulati ns to determine a new distribution of possible demand forecasts and place the new demand forecast on the new di s tribution to assess if the new driver values are realistic or not and what implication the change in the one driver means to demand.

[00111 Fig. 1 is a block diagram of a computing de vice 102 including demand forecaster 1 4 with consensus demand forecasting, simulation, and scenario analysis in examples of the present disclosure. Computing device 1.02 may he a server computer, a desktop computer, a laptop computer, a tablet computer, or a smart phone.

{^'001 3 Computing device 102 includes a processor 108, a volatile memory 110, a nonvolatile memory 1 12, and a wired or wireless network interface card (NIC) 11 . Nonvolatile memory 1 12 stores the code of demand forecaster 104. Processor 108 loads the code of demand, forecaster 104 from nonvolatile memory 1 12 to volatile memory 110, executes the code, and access data 1 16 in volatile memory 110. Data 1 16 includes forecast models, historical values of drivers and demand, consensus forecasts of drivers, and. simulated values of drivers for a future time period. Demand forecaster 1 4 performs consensus forecasting, simulation, and. scenario analysis.

{0013] Fig. 2 is a flowchart of a method 200 for processor 108 (Fig. I) to implement demand forecaster 104 (Fig... 1} in examples of the present disclosure. Method 200 may begin in block. 202.

1:0014] In block 202, processor 1 builds a combined demand forecast models that is a weighted combination of individual demand forecast models each based on one driver. Block 202 may be followed by block 204, 001S| In block 204, processor 108 applies a weighting algorithm to optimize weights assigned to the individual demand forecast models based their accuracy. Block 204 may be followed by block 206.

{0016] In block 206, processor 108 uses the combined demand forecast model to simulate demand forecasts for a future time period. Block 206 may be followed by block 208.

[Θ0Ϊ7] In block 208, processor 108 places a demand forecast for the future time period on a distribution: of the simulated demand forecasts to assess the demand forecast. j_.003.8] Fig. 3 is a .flowchart of a method 300 for processor 108 (Fig. 1) to implement demand forecaster 104 (Fig. 1 ) ia examples of the present disclosure. Method 300 is also graphically illustrated ia Fig. 4. Method 300 may be a variation of method 200 (Fig. 2). Hereafter the printer market is used to demonstrate method 300. The printer market may be influenced by three independent factors: number of personal computers (PCs) shipped, real gross domestic product (GDP), and unemployment rate. Referring to Fig. 3, method 300 may begin in block 302. Θ 19) In blocks 302 to 308, processor 108 performs consensus forecasting, in block 302, processor 108 builds a combined forecast model to predict the printer demand for next few time periods (e.g., first quarter 2013 to fourth quarter 20 7). The combined forecast, based .model is a weighted combination of individual (separate) forecast models each based on a different driver. Block 302 corresponds to block 202 (Fig. 2) in method 200 (Fig. 2).

[00201 The forecast models may be autoregressive integrated moving average with

exogenous variables (ARIMAX) models. The ARIMAX models ma be determined as follows:

¾ = Eq(l ) where Y, is the " time market forecast using i⁸* driver, Fi is the functional form of the ί^Λ model, X; is the i* driver, ε is the * error term, and i increments from 1 to where n is the number of drivers. In some examples processor 1 8 does not build the ARIMAX models when different forecasts for the printer market based o the drivers have been provided, in some examples, other regression models may be used.

[00211 Fig. 4 illustrates a demand, forecaster 402 based on. a first forecast model 404 based on the real GDP, a second iorecast model 406 based on the nomber of PCs shipped, and a third forecast model 408 based on the latemployment rate. Fig. 5 is a chart illustrating the actual number of printers sold from .first quarter in 2000 to fourth^' uarter 20.12, and demand forecasts from first forecast model 404 based on the real GDP, second forecast model 406 based on the number of PCs shipped, third forecast model 408 based on the unemployment rate from first quarter in 2000 to the fourth quarter 2017 in examples of the present:

disclosure. The demand iorecasts from forecast models 404, 406, and 408 are based on the actual GDP, the actual number of PCs shipped, and the actual unemployment rate until fourth quarter 2012, and then the are based on consensus forecasts of their drivers until fourth quarter 2017, Forecast models 404, 406, and 408 closel follow the actual number of printers sold until the fourth quarter 2012, after which they diverge in different direction based on the consensus forecasts of the CiDP, the number of PCs shipped, and the unemployment rate. Referring back to Fig. 3, block 302 may be followed by block 306.

1_.0922] In block 306, processor 108 applies a weighting algorithm to optimize weights for the forecasts models in a combined forecast model based on their accuracy in recent past time periods (e.g., first quarter 200 to fourth quarter 2012). Block 304 corresponds to block 204 (Fig. 2} in method 200. Applying the weighting algorithm is illustrated as block 410 in Fig, 4, The weights may be determined as follows:

(ICC- w.- --- ^:

y acc, where e_t is the mean error, subscript t indicates a variable in the time dimension, n is the number of time periods used to measure weights, Y_it is the time aciual printer demand, f_it is the t⁵ time market forecast using i^t¾ driver, acc. is the accuracy (inverse of the mean error), wi is the weight of the i^th model used to arrive at a combined forecast, and p is the total number of drivers (e.g., 3 in the example).

[Θ923] Instead of bttildmg the single driver models, processor 108 may apply the weighting algorithm to multiple demand forecasts already available from different sources and techniques in some examples of the prese t disclosure. In other examples of the present disclosure, weighting algorithm is applied to a combination of single driver models, multiple driver models, and available demand forecasts. The available demand forecasts may include qualitati ve and judgmental forecasts. [0024] Referring back to Fig, 3, block 306 may be followed by block 308,

[Θ025] In block 308, processor 108 uses the combined forecast mode! to determine a demand forecas t for a future time period based on consensus forecasts of the drivers (e.g. , GPD, the number of PCs shipped, and tSie unemployment rate) for the future time period. If the combined forecast model includes the available forecasts, the values from the available forecasts in the future period are simply weighted. Block 308 may be followed by block 3 10.

10026] In blocks 310 to 318, processor 108 performs simulation. In block 310, processor 10 generates ml sets of random con-elated values of the drives n the future time period.

Processor 108 generates the mi sets of driver values based on a correlation matrix derived from actual driver values in the recent past time periods (historical data) and the consensus forecasts of the drivers (e.g. , GDP, the number of PCs shipped, and the unemployment rate). This is illustrated by a block 412 in Fig. 4. Referring back to Fig. 3, block 10 may be followed by block 312.

J0027] In block 312, processor 1 8 passes the ml (e.g., > 10,000) sets of driver values to the combined forecast model to calculate ml possible demand forecasts for the next time period and the mean of the m l possible demand forecasts. This is illustrated by a loop 414 in Fig, 4, Referring back to Fig. 3, block 3 32 may be followed by block 314,

Ϊ0028) In block 314, processor 108 repeats blocks 310 to 3 12 m2 (e.g., 500 to 1 ,000 or greater) times to determine m2 means of the possible demand forecasts. This is illustrated by the m2 iterations of loop 414 in Fig . 4. Referring back to Fig. 3, block 14 may be followed by block 316.

\W⁾29} in block 316, processor 108 charts a distribution of simulated demand forecasts in the next time period based on the m2 means and calculates certain percentiles on the distribution. For example, processor tabulates the ni2 means to determine the 5 ^¾ percentile and different percentile points like 2,5^th percentile, 97,5^th percentile, 1 ^th percentile and 90^ih percentile of the bell curve. Fig. 6 illustrates a distribution 600 of simulated demand forecasts in examples of the present disclosure. The 50*^· percentile is the most likely demand forecast, which is indicated by a line 602 showing a simulated demand, forecast of 64.4 million. Referring back to Fig. 3, block 316 may be followed by block 3 18,

}Θ§30| in block 31$, processor 108 places a demand forecast on the distribution of simulated demand forecasts so (he risk associated with the demand forecast may be assessed. Blocks 316 and 31 correspond to block 208 (Fig. 2 } of method 200, The demand forecast may be the demand forecast determined in block 308 or an independently generated demand forecast. By placing the demand forecast on the distribution, of simulated demand forecasts, an entity can assess if the demand forecast is conservative, optimistic, or in line with the most likely demand forecast indicated by the 50* percentile. The distribution of simulated demand forecast gives the entity an idea of the risk associated with its demand forecast based on how close or far away it is from the most likely demand forecast For example. Fig. shows a demand forecast 604 of 65.7 million printers on the right of but relatively close to the .most likely demand iorecast 602, which indicates demand forecast 604 is optimistic but not overly optimistic. Referring back to Fig, 3, block 318 may be followed by block 320.

}0§3!J I block 320 to 326, processor 108 performs scenario analysis. In block 320, processor 108 receives user input specifying a change in the value of one driver in the next time period. This is illustrated b triangle 416 in Fig, 4. For example, the user input increases the GDP increasing by 5% instead of 3% expected in the next time period. In response, processor 108 uses the correlation matrix to determine the correlated values of the other drivers. For example, the historical correlation matrix provides a fall of 2% in the expected unemployment rate and an increase of 3% in the expected number of PCs shipped when the GDP increases by 5%. At this poi t the new driver values may be evaluated as realistic or not. For example, if it is known thai the PC market is declining doe to increase tablet computer safes, the growth, in GDP probably will not cause the PC market, to improve. Referring back to Fig, 3, block 320 may be followed by block. 322,

[6032} in block 322, processor 108 uses the combined forecast mode! to determine a new demand forecast for the next time period based on the new driver values for the next time period. This is illustrated by a lead line 418 in Fig. 4. Referring back to Fig. 3. block 322 may be followed by block. 324.

[0033] In block 324, processor 10 repeals blocks 310 to 3 16 to generate a new distribution of simulated demand forecasts and the various percentiles. As described before, processor 108 generates the ml sets of driver values based on. the correlation matrix derived from actual driver values in the recent, past, time periods (historical data) and the new forecasts of the drivers (e.g., GDP, the number of PCs shipped, and the unemployment rate). Block 324 may be followed by block 326, [9934] In block 326, processor 108 places the new demand forecast determined in block 322 on the new distribution of simulated demand forecasts to assess the risk of the new demand forecast. Processor 1.08 may also overlap the hell curves from original distribution and the new distribution as shown in. chart 700 of Fig. 7 to determine the implication of the change in the driver on demand. For example, when the bell curves 702 and 704 overlap significantly, the demand may not. significantly so adjustments may not need to be made, it the bell curves 702 and 704 overlap insignificantly, the demand may change significantly so adjustments may need to be made to meet the demand.

[0935] In term of hypothesis testing, the following are determined: HO: μΐ ^:::: μ2 (simulated means are same) or Ha: μί≠ μ2 (simulated means are different). This can be tested using the following formula: t = (xf - xa) / SB, Eq(3)

SE ~ sqrt|(si¾i) + {S2¾ ]_> and Eq(4)

DF - (sr/m + s2² m)³ / { ( (sr¹ / m f / ( - 1) ] + ] (sr / f f (m ~ l) ] } , Eq(5) where x i , x? are the mean values, st and s? are the corresponding standard deviations, nl and n.2 are the corresponding sample sizes, SE is the standard error, and DF is the degree of freedom. Using the formula above, we will get a t-vahie that is compared against tabulated value for a given DF to decide whether the difference is same or different.

[Θ936] Method 300 may be repeated for other scenarios.

[0037] ^'The methods and apparatus in examples of the present disclosure offer many advantages. They can be used to forecasi demand for products across various businesses and industries. The methods and apparatus can be easily expanded to more granular levels, such as form factor, segments, or countries. j y038] T he methods and apparatus are comprehensive. They allow different set of drivers to be included in different models. Drivers influencing say customer segment like consumer may differ from the commercial segment. The important drivers for each level of models are incorporated, making the model more holistic and reliable.

[0039] The methods and apparatus are dynamic. They can be easily adaptable to changing business trends where Impact of drivers can change over a period of time and new factors influencing the market can easily be included in the model

[Θ040] The .methods and apparatus are robust. They have a sound mathematical backing in each step, which makes them easy to deconstruct and track, accuracy at each step.

10041] The methods and apparatus easily incoroorate varying trends and drivers in the market and the economy in forecasting demand. The scope of incorporating the impact of multiple kiiLuencers on the demand mirrors the actual world scenario where markets are highly interdependent,

[0042] Various other adaptations and combinations of features of the examples disclosed are within the scope of the invention.

Claims

What is claimed is:

Claim I : A method for demand forecasting, comprising: building a combined demand forecast model that is a weighted combination of individual demand forecast models each based on one dri ver; applying a weighting algorithm to optimize weights assigned to the individual demand forecast models based their accuracy ; rising the combined demand forecast model to simulate demand forecasts for a future time period; and placing a demand forecast for the future time period on distribution of the simulated demand forecasts to assess the demand forecast.

Claim 2: The method of claim I , wherein using the combined demand forecast model to simulate demand forecasts for the future time period comprises: generating a first number of sets of correlated random driver values for the future time period based on a correlation matrix and consensus forecast of driver values in the future period; using the combined forecast model to determine the first number o possible demand forecasts from the number of sets of correlated random driver values; determining a mean of the number of possible demand forecasts; repeating said generating, said using, and said determining for a second number of times to determi ne the second number of means of the number of possible demand forecasts; and charting the distribution of the simulated demand forecasts based on the second number of means of the number of possible demand forecasts.

Claim 3; The method of claim 2, further comprising calculating and indicating one or more percentiles in the distribution of the simulated demand forecasts. Claim 4: The method of claim 2; furdier comprising using the combined demand forecast model io determine the demand forecast based on the consensus forecast of driver values in the future time period for the individual demand, forecast models.

Claim 5: The method of claim 2, further comprising: receiving a new value for a driver in the future time period; using a correlation matrix io determine new values for other drivers; and using the combined demand forecast model io determine a new demand forecast

Claim 6: The method of claim 5, further comprising; using the combined demand forecast model and the new values of the dr ivers to simulate new demand forecasts for the future tune period; and placing the new demand forecast for the Mure time period, on a new distribution of the simulated ne demand forecasts.

Claim 7; The method of claim 6, further comprising; displaying a first bell curve of (he distribution of the simulated, demand forecasts and a second hell curve of the new distribution of the simulated new demand forecasts.

Claim 8; The method of claim 1, wherein the demand forecast model further includes available demand forecasts and applying the weighting algorithm further optimize other weights assigned to the available demand forecasts.

Claim 9: An apparatus, comprising: a nonvolatile memory storing code of a demand forecaster; a processor executing the code of the demand forecaster to: build a combined demand forecast model by applying a weighting algorithm to optimize weights assigned to forecast models and available forecasts based their accuracy, the forecast models including single driver forecast models and multiple driver forecast models; use the combmed demand forecasi model io simulate demand forecasts for a future time period; and place a demand forecasi for the future time period on a distribution of the simulated demand forecasts to assess the demand forecast

Claim 10; The apparatus of claim 9, wherem using the combmed demand forecast model to simulate demand forecasts for the future time period comprises; generating a first number of sets of correlated random driver values for the future time period based on a correlation matrix and consensus forecast of driver values in the future period; using the combined forecasi model to determine the first n umber of possible demand forecasts from the number of sets of correlated random driver values; determinin a mean of the number of possible demand forecasts ; repeating said generating, said using, and said determining for a second number of times to determine the second number of means of the number of possible demand forecasts; and charting the distribution of the simula ted demand forecasts based on the second number of means of the number of possible demand forecasts.

Claim 11; The apparatus of claim 10, wherem the processor is to use the combined demand forecast model to determine the demand forecast based on the consensus forecast of driver values in. the future time period for the individual demand forecast models.

Claim 12 ; The apparatus of claim 1 , wherein the processor is to: receive a new value for a driver in the future time period; use a correlation matrix to determine new values for other drivers; and use the combined demand forecast model to determine a new demand forecasi .

Claim 13; The apparatus of claim 12, wherein the processor is to; use the combined demand forecast model and the new values of the drivers to simulate new demand forecasts for die future time period: and place the new demand forecast for the future time period on a new distribution of the simulated, new demand forecasts.

Claim 14: The apparatus of claim 13, wherein ihe processor is to: display a first bell curve of the distribution of the simulated demand forecasts and a second bell curve of die new distribution of the simulate new demand forecasts.

Claim 15; A non-iraosiiory computer-readable medium encoded with instructions executable by a processor to: build a combined demand forecast mode! that, is a weighted combination of: individual demand forecast models each based on one driver; and available demand forecasts; apply weighting algorithm to optimize weights assigned to the individual demand forecast models and the available demand forecasts based their accuracy; use the combined demand forecast model to simulate demand forecasts for a future time period; and place a demand forecast for the future time period on a distribution of the simulated demand forecasts to asses the demand forecast.