Homework 7

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Supply Chain Management: Strategy, Planning, and Operation

Seventh Edition

Chapter 7

Demand Forecasting in a Supply Chain

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Learning Objectives

7.1 Understand the role of forecasting for both an enterprise and a supply chain.

7.2 Identify the components of a demand forecast and some basic approaches to forecasting.

7.3 Forecast demand using time-series methodologies given historical demand data in a supply chain.

7.4 Analyze demand forecasts to estimate forecast error.

7.5 Use Excel to build time-series forecasting models.

Role of Forecasting in a Supply Chain

The basis for all planning decisions in a supply chain

Used for both push and pull processes

Production scheduling, inventory, aggregate planning

Sales force allocation, promotions, new production introduction

Plant/equipment investment, budgetary planning

Workforce planning, hiring, layoffs

All of these decisions are interrelated

Characteristics of Forecasts

Forecasts are always inaccurate and should thus include both the expected value of the forecast and a measure of forecast error

Long-term forecasts are usually less accurate than short-term forecasts

Aggregate forecasts are usually more accurate than disaggregate forecasts

In general, the farther up the supply chain a company is, the greater is the distortion of information it receives

Summary of Learning Objective 1 (1 of 2)

Forecasting is a key input for virtually every design and planning decision made in a supply chain. It is important to recognize that all forecasts are likely to be wrong. Thus, an estimation of forecast error is essential to effectively use the forecast. Reducing the forecast horizon (by reducing the lead time of the associated decision) and aggregation are two effective approaches to decrease forecast error.

Summary of Learning Objective 1 (2 of 2)

A relatively recent phenomenon, however, is to create collaborative forecasts for an entire supply chain and use these as the basis for decisions. Collaborative forecasting greatly increases the accuracy of forecasts and allows the supply chain to maximize its performance. Without collaboration, supply chain stages farther from demand will likely have poor forecasts that will lead to supply chain inefficiencies and a lack of responsiveness.

Components and Methods (1 of 2)

Companies must identify the factors that influence future demand and then ascertain the relationship between these factors and future demand

Past demand

Lead time of product replenishment

Planned advertising or marketing efforts

Planned price discounts

State of the economy

Actions that competitors have taken

Notes:

Components and Methods (2 of 2)

Qualitative

Primarily subjective

Rely on judgment

Time Series

Use historical demand only

Best with stable demand

Causal

Relationship between demand and some other factor

Simulation

Imitate consumer choices that give rise to demand

Notes:

Components of An Observation

Observed demand (O) = systematic component (S)

+ random component (R)

Systematic component – expected value of demand

Level (current deseasonalized demand)

Trend (growth or decline in demand)

Seasonality (predictable seasonal fluctuation)

Random component – part of forecast that deviates from systematic part

Forecast error – difference between forecast and actual demand

Five Important Points in the Forecasting Process

Understand the objective of forecasting.

Integrate demand planning and forecasting throughout the supply chain.

Identify the major factors that influence the demand forecast.

Forecast at the appropriate level of aggregation.

Establish performance and error measures for the forecast.

Notes:

Summary of Learning Objective 2

Demand consists of a systematic and a random component. The systematic component measures the expected value of demand. The random component measures fluctuations in demand from the expected value. The systematic component consists of level, trend, and seasonality. Level measures the current de-seasonalized demand. Trend measures the current rate of growth or decline in demand. Seasonality indicates predictable seasonal fluctuations in demand. The goal of forecasting is to estimate the systematic component and the size (not direction) of the random component (in the form of a forecast error). Good forecasting requires a clear understanding of the objective of the forecast and should be integrated across the supply chain.

Time-Series Forecasting Methods

Three ways to calculate the systematic component

Multiplicative

S = level × trend × seasonal factor

Additive

S = level + trend + seasonal factor

Mixed

S = (level + trend) × seasonal factor

Static Methods

Systematic component = (level+trend)×seasonal factor

Where

L = estimate of level at t = 0

T = estimate of trend

St = estimate of seasonal factor for Period t

Dt = actual demand observed in Period t

Ft = forecast of demand for Period t

Tahoe Salt (1 of 5)

Table 7-1 Quarterly Demand for Tahoe Salt

Year	Quarter	Period, t	Demand, Dt
1	2	1	8,000
1	3	2	13,000
1	4	3	23,000
2	1	4	34,000
2	2	5	10,000
2	3	6	18,000
2	4	7	23,000

Tahoe Salt (2 of 5)

Table 7-1 [continued]

Year	Quarter	Period, t	Demand, Dt
3	1	8	38,000
3	2	9	12,000
3	3	10	13,000
3	4	11	32,000
4	1	12	41,000

Tahoe Salt (3 of 5)

Figure 7-1 Quarterly Demand at Tahoe Salt

Deseasonalize demand and run linear regression to estimate level and trend.

Estimate seasonal factors.

Estimate Level and Trend (1 of 2)

Periodicity p = 4, t = 3

Notes:

Estimate Level and Trend (2 of 2)

Notes:

Tahoe Salt (4 of 5)

Figure 7-2 Excel Workbook with Deseasonalized Demand for Tahoe Salt

Tahoe Salt (5 of 5)

Figure 7-3 Deseasonalized Demand for Tahoe Salt

A linear relationship exists between the deseasonalized demand and time based on the change in demand over time

Estimating Seasonal Factors (1 of 3)

Figure 7-4 Deseasonalized Demand and Seasonal Factors for Tahoe Salt

Estimating Seasonal Factors (2 of 3)

Estimating Seasonal Factors (3 of 3)

Adaptive Forecasting (1 of 2)

The estimates of level, trend, and seasonality are updated after each demand observation

Estimates incorporate all new data that are observed

Adaptive Forecasting (2 of 2)

Where

Lt = estimate of level at the end of Period t

Tt = estimate of trend at the end of Period t

St = estimate of seasonal factor for Period t

Ft = forecast of demand for Period t (made Period t – 1 or earlier)

Dt = actual demand observed in Period t

Et = Ft – Dt = forecast error in Period t

Steps in Adaptive Forecasting

Initialize

Compute initial estimates of level (L0), trend (T0), and seasonal factors (S1,…,Sp)

Forecast

Forecast demand for period t + 1

Estimate error

Compute error Et+1 = Ft+1 – Dt+1

Modify estimates

Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1

Moving Average

Used when demand has no observable trend or seasonality

Systematic component of demand = level

The level in period t is the average demand over the last N periods

After observing the demand for period t + 1, revise the estimates

Moving Average Example (1 of 2)

A supermarket has experienced weekly demand of milk of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons over the past four weeks

Forecast demand for Period 5 using a four-period moving average

What is the forecast error if demand in Period 5 turns out to be 125 gallons?

Moving Average Example (2 of 2)

Forecast demand for Period 5

F5 = L4 = 120.75 gallons

Error if demand in Period 5 = 125 gallons

E5 = F5 – D5 = 120.75 – 125 = – 4.25

Revised demand

Simple Exponential Smoothing (1 of 3)

Used when demand has no observable trend or seasonality

Systematic component of demand = level

Initial estimate of level, L0, assumed to be the average of all historical data

Simple Exponential Smoothing (2 of 3)

Given data for Periods 1 to n

Current forecast

Revised forecast using smoothing constant (0 < α < 1)

Thus

Simple Exponential Smoothing (3 of 3)

Supermarket data

F1 = L0 = 120.75

E1 = F1−D1 = 120.75−120 = 0.75

L1 = αD1+(1−α)L0

= 0.1×120+0.9 ×120.75=120.68

Trend-Corrected Exponential Smoothing (Holt’s Model) (1 of 4)

Appropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonality

Systematic component of demand = level + trend

Trend-Corrected Exponential Smoothing (Holt’s Model) (2 of 4)

Obtain initial estimate of level and trend by running a linear regression

Dt = at + b

T0 = a, L0 = b

In Period t, the forecast for future periods is

Ft+1 = Lt + Tt and Ft+n = Lt + nTt

Revised estimates for Period t

Trend-Corrected Exponential Smoothing (Holt’s Model) (3 of 4)

Smartphone player demand

D1 = 8,415, D2 = 8,732, D3 = 9,014, D4 = 9,808,D5 = 10,413, D6 = 11,961, α = 0.1, β = 0.2

Using regression analysis

L0 = 7,367 and T0 = 673

Forecast for Period 1

F1 = L0 + T0 = 7,367 + 673 = 8,040

Period 1 error

E1 = F1 – D1 = 8,040 – 8,415 = –375

Trend-Corrected Exponential Smoothing (Holt’s Model) (4 of 4)

Revised estimate

With new L1

F2 = L1 + T1 = 8,078 + 681 = 8,759

Continuing

F7 = L6 + T6 = 11,399 + 673 = 12,072

Trend- and Seasonality-Corrected Exponential Smoothing (1 of 2)

Appropriate when the systematic component of demand has a level, trend, and seasonal factor

Systematic component = (level + trend) × seasonal factor

Trend- and Seasonality-Corrected Exponential Smoothing (2 of 2)

After observing demand for period t + 1, revise estimates for level, trend, and seasonal factors

α = smoothing constant for level

β = smoothing constant for trend

γ = smoothing constant for seasonal factor

Winter’s Model (1 of 3)

L0 = 18,439 T0 = 524

S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67

F1 = (L0 + T0)S1 = (18,439 + 524)(0.47) = 8,913

The observed demand for Period 1 = D1 = 8,000

Forecast error for Period 1

= E1 = F1 – D1

= 8,913 – 8,000 = 913

Winter’s Model (2 of 3)

Assume α = 0.1, β = 0.2, γ = 0.1; revise estimates for level and trend for period 1 and for seasonal factor for Period 5

Winter’s Model (3 of 3)

Forecast demand for Period 2

F2 = (L1 + T1)S2 = (18,769 + 485)(0.68) = 13,093

Time Series Models

Forecasting Method	Applicability
Moving average	No trend or seasonality
Simple exponential smoothing	No trend or seasonality
Holt’s model	Trend but no seasonality
Winter’s model	Trend and seasonality

Summary of Learning Objective 3

Time-series methods for forecasting are categorized as static or adaptive. In static methods, the estimates of parameters are not updated as new demand is observed. Static methods include regression. In adaptive methods, the estimates are updated each time a new demand is observed. Adaptive methods include moving averages, simple exponential smoothing, Holt’s model, and Winter’s model. Moving averages and simple exponential smoothing are best used when demand displays neither trend nor seasonality. Holt’s model is best when demand displays a trend but no seasonality. Winter’s model is appropriate when demand displays both trend and seasonality.

Measures of Forecast Error (1 of 2)

Forecast errors contain valuable information and must be analyzed for two reasons:

Managers use error analysis to determine whether the current forecasting method is predicting the systematic component of demand accurately

All contingency plans must account for forecast error

Measures of Forecast Error (2 of 2)

Summary of Learning Objective 4

Forecast error measures the random component of demand. This measure is important because it reveals how inaccurate a forecast is likely to be and what contingencies a firm may have to plan for. The M S E, M A D, and M A P E are used to estimate the size of the fore- cast error. The bias and T S are used to estimate if the forecast consistently over- or under- forecasts or if demand has deviated significantly from historical norms.

Selecting the Best Smoothing Constant (1 of 2)

Figure 7-5 Selecting Smoothing Constant by Minimizing M S E

Selecting the Best Smoothing Constant (2 of 2)

Figure 7-6 Selecting Smoothing Constant by Minimizing M A D

Forecasting Demand at Tahoe Salt (1 of 10)

Moving average

Simple exponential smoothing

Trend-corrected exponential smoothing

Trend- and seasonality-corrected exponential smoothing

Forecasting Demand at Tahoe Salt (2 of 10)

Figure 7-7 Tahoe Salt Forecasts Using Four-Period Moving Average

Forecasting Demand at Tahoe Salt (3 of 10)

Moving average

L12 = 24,500

F13 = F14 = F15 = F16 = L12 = 24,500

σ = 1.25 × 9,719 = 12,148

Forecasting Demand at Tahoe Salt (4 of 10)

Figure 7-8 Tahoe Salt Forecasts Using Simple Exponential Smoothing

Forecasting Demand at Tahoe Salt (5 of 10)

Simple exponential smoothing

α = 0.1

L0 = 22,083

L12 = 23,490

F13 = F14 = F15 = F16 = L12 = 23,490

σ = 1.25 × 10,208 = 12,761

Forecasting Demand at Tahoe Salt (6 of 10)

Figure 7-9 Trend-Corrected Exponential Smoothing

Forecasting Demand at Tahoe Salt (7 of 10)

Trend-Corrected Exponential Smoothing

L0 = 12,015 and T0 = 1,549

L12 = 30,443 and T12 = 1,541

F13 = L12 + T12 = 30,443 + 1,541 = 31,984

F14 = L12 + 2T12 = 30,443 + 2 × 1,541 = 33,525

F15 = L12 + 3T12 = 30,443 + 3 × 1,541 = 35,066

F16 = L12 + 4T12 = 30,443 + 4 × 1,541 = 36,607

σ = 1.25 × 8,836 = 11,045

Forecasting Demand at Tahoe Salt (8 of 10)

Figure 7-10 Trend- and Seasonality-Corrected Exponential Smoothing

Forecasting Demand at Tahoe Salt (9 of 10)

Trend- and Seasonality-Corrected

L0 = 18,439 T0 =524

L12 = 24,791 T12 = 532

S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67

F13 = (L12 + T12)S13 = (24,791 + 532)0.47 = 11,902

F14 = (L12 + 2T12)S13 = (24,791 + 2 × 532)0.68 = 17,581

F15 = (L12 + 3T12)S13 = (24,791 + 3 × 532)1.17 = 30,873

F16 = (L12 + 4T12)S13 = (24,791 + 4 × 532)1.67 = 44,955

σ = 1.25 × 1,469 = 1,836

Forecasting Demand at Tahoe Salt (10 of 10)

Table 7-2 Error Estimates for Tahoe Salt Forecasting

Forecasting Method	M A D	M A P E (%)	T S Range
Four-period moving average	9,719	49	–1.52 to 2.21
Simple exponential smoothing	10,208	59	–1.38 to 2.15
Holt’s model	8,836	52	–2.15 to 2.00
Winter’s model	1,469	8	–2.74 to 4.00

The Role of Software Tools in Forecasting

Software is important

Large amounts of data

Frequency of forecasts

Importance of high-quality results

Can forecast demand by products and markets

Real time updates help firms respond quickly to changes in marketplace

Facilitates demand planning

Summary of Learning Objective 5

Given the repetitive nature of time-series forecasting methods, they can easily be modeled in Microsoft Excel with simple formulae that are copied across rows or columns. For regular forecasting at companies, however, it may be more effective to select among a wide variety of software packages available today.

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184 Chapter 7 • Demand Forecasting in a Supply Chain

We now describe one method for estimating the three parameters L, T, and S. As an example, consider the demand for rock salt used primarily to melt snow. This salt is produced by a firm called Tahoe Salt, which sells its salt through a variety of independent retailers around the Lake Tahoe area of the Sierra Nevada Mountains. In the past, Tahoe Salt has relied on estimates of demand from a sample of its retailers, but the company has noticed that these retailers always overestimate their purchases, leaving Tahoe (and even some retailers) stuck with excess inventory. After meeting with its retailers, Tahoe has decided to produce a collaborative forecast. Tahoe Salt wants to work with the retailers to create a more accurate forecast based on the actual retail sales of their salt. Quarterly retail demand data for the past three years are shown in Table 7-1 and charted in Figure 7-1.

In Figure 7-1, observe that demand for salt is seasonal, increasing from the second quarter of a given year to the first quarter of the following year. The second quarter of each year has the lowest demand. Each cycle lasts four quarters, and the demand pattern repeats every year. There is also a growth trend in the demand, with sales growing over the past three years. The company estimates that growth will continue in the coming year at historical rates. We now describe how each of the three parameters—level, trend, and seasonal factors—may be estimated. The following two steps are necessary to making this estimation:

1. Deseasonalize demand and run linear regression to estimate level and trend. 2. Estimate seasonal factors.

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10,000

50,000

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FIGURE 7-1 Quarterly Demand at Tahoe Salt

Table 7-1 Quarterly Demand for Tahoe Salt

Year Quarter Period, t Demand, Dt

1 2 1 8,000

1 3 2 13,000

1 4 3 23,000

2 1 4 34,000

2 2 5 10,000

2 3 6 18,000

2 4 7 23,000

3 1 8 38,000

3 2 9 12,000

3 3 10 13,000

3 4 11 32,000

4 1 12 41,000

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186 Chapter 7 • Demand Forecasting in a Supply Chain

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Note that in Equation 7.3, represents deseasonalized demand and not the actual demand in Period t, L represents the level or deseasonalized demand at Period 0, and T represents the rate of growth of deseasonalized demand or trend. We can estimate the values of L and T for the deseasonalized demand using linear regression with deseasonalized demand (see Figure 7-2) as the dependent variable and time as the independent variable. Such a regression can be run using Microsoft Excel (Data | Data Analysis | Regression). This sequence of commands opens the Regression dialog box in Excel. For the Tahoe Salt workbook in Figure 7-2, in the resulting dialog box, we enter

and click the OK button. A new sheet containing the results of the regression opens up. This new sheet contains estimates for both the initial level L and the trend T. The initial level, L, is obtained as the intercept coefficient, and the trend, T, is obtained as the X variable coefficient (or the slope) from the sheet containing the regression results. For the Tahoe Salt example, we obtain L ! 18,439 and T ! 524. For this example, deseasonalized demand for any Period t is thus given by

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Note that it is not appropriate to run a linear regression between the original demand data and time to estimate level and trend because the original demand data are not linear and the resulting linear regression will not be accurate. The demand must be deseasonalized before we run the linear regression.

ESTIMATING SEASONAL FACTORS We can now obtain deseasonalized demand for each period using Equation 7.4. The seasonal factor for Period t is the ratio of actual demand Dt to deseasonalized demand and is given as

(7.5)

For the Tahoe Salt example, the deseasonalized demand estimated using Equation 7.4 and the seasonal factors estimated using Equation 7.5 are shown in Figure 7-4.

Given the periodicity, p, we obtain the seasonal factor for a given period by averaging seasonal factors that correspond to similar periods. For example, if we have a periodicity of p ! 4, Periods 1, 5, and 9 have similar seasonal factors. The seasonal factor for these periods is obtained

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196 Chapter 7 • Demand Forecasting in a Supply Chain

as shown in Figure 7-5. The forecast shown in Figure 7-5 uses the resulting ! ! 0.54 and gives MSE ! 2,460, MAD ! 42.5 and MAPE ! 2.1 percent.

The smoothing constant can also be selected using Solver by minimizing the MAD or the MAPE at the end of 10 periods. In Figure 7-6, we show the results from minimizing MAD (cell G13). The forecasts and errors with the resulting ! ! 0.32 are shown in Figure 7-6. In this case, the MSE increases to 2,570 (compared to 2,460 in Figure 7-5) while the MAD decreases to 39.2 (compared to 42.5 in Figure 7-5) and the MAPE decreases to 2.0 percent (compared to 2.1 percent in Figure 7-5). The major difference between the two forecasts is in period 9 (the period with the largest error shown in cell D11), where minimizing MSE picks a smoothing constant that reduces large errors, while minimizing MAD picks a smoothing constant that gives equal weight to reducing all errors even if large errors get somewhat larger.

FIGURE 7-5 Selecting Smoothing Constant by Minimizing MSE

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Chapter 7 • Demand Forecasting in a Supply Chain 197

In general, it is not a good idea to use smoothing constants much larger than 0.2 for extended periods of time. A larger smoothing constant may be justified for a short period of time when demand is in transition. It should, however, generally be avoided for extended periods of time.

7.8 FORECASTING DEMAND AT TAHOE SALT

Recall the Tahoe Salt example earlier in the chapter with the historical sell-through demand from its retailers shown in Table 7-1. The demand data are also shown in column B of Figure 7-7. Tahoe Salt is currently negotiating contracts with suppliers for the four quarters between the second quarter of Year 4 and the first quarter of Year 5. An important input into this negotiation is the forecast of demand that Tahoe Salt and its retailers are building collaboratively. They have assigned a team consisting of two sales managers from the retailers and the vice president of

FIGURE 7-6 Selecting Smoothing Constant by Minimizing MAD

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