Lecture Principle of inventory and material management - Lecture 18

Lecture 18 - Forecasting (Continued). The contents of this chapter include all of the following: Compute three measures of forecast accuracy, develop seasonal indexes, conduct a regression and correlation analysis, use a tracking signal.

Forecasting (Continued)

Books

• Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming  College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M.  Clive, P.E., CFPIM, Fleming College

• Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005,  N.Y.: McGraw­Hill/Irwin.

• Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of  Business, Rollins College, Prentice Hall

þ Conduct a regression and correlation

analysis

þ Use a tracking signal

Mean Absolute Deviation (MAD)

n

Mean Squared Error (MSE)

n

Mean Absolute Percent Error (MAPE)

n

n

i = 1

Comparison of Forecast Error 

= 98.62/8 = 12.33 For α = .50

= 1,561.91/8 = 195.24 For α = .50

n

Comparison of Forecast Error 

Comparison of Forecast Error 

Ft =  α (At ­ 1) + (1 ­  α )(Ft ­ 1 + Tt ­ 1)

Tt =  β (Ft  ­ Ft ­ 1) + (1 ­  β )Tt ­ 1

Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt = Ft + Tt

Adjustment Example

ForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

Adjustment Example

ForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2

Adjustment Example

ForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

= 72 + 1.2 = 1.92 units

Step 2: Trend for Month 2

Adjustment Example

ForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

= 14.72 units

Step 3: Calculate FIT for Month 2

Adjustment Example

ForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

Actual demand (At)

Forecast including trend (FITt)with = 2 and = 4

Fitting a trend line to historical data points to 

project into the medium to long­range

Linear trends can be found using the least squares  technique

y = a + bx^

where y = computed value of the variable to be predicted (dependent variable)

Actual observation

(y value)

Trend line, y = a + bx^

1. We always plot the data to insure a

linear relationship

2. We do not predict time periods far

beyond the database

3. Deviations around the least squares

line are assumed to be random

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next year’s total demand

5. Divide this estimate of total demand by the number

of seasons, then multiply it by the seasonal index for that season

Steps in the process:

Seasonal index = average 2005-2007 monthly demand

average monthly demand

= 90/94 = 957

0.97

0.96 Seasonal Indices

Used when changes in one or more independent  variables can be used to predict the changes in the 

4.0 – 3.0 – 2.0 – 1.0 –

n = number of data points

n - 2

Computationally, this equation is 

considerably easier to use

We use the standard error to set up  prediction intervals around the point 

estimate

n - 2

4.0 – 3.0 – 2.0 – 1.0 –

[νΣξ2 − (Σξ)2][νΣψ2 − (Σψ)2]

r = -1

y = 1.80 + 30x1 - 5.0x2^

In the Nodel example, including interest rates in the model gives the new  equation:

An improved correlation coefficient of r = .96 means this model does a better  job of predicting the change in construction sales

Sales = 1.80 + .30(6) ­ 5.0(.12) = 3.00 Sales = $3,000,000

Tracking Signal

in period i)

( |Αχτυαλ − Φορεχαστ|/ν) ∑

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptable range

Cumulative

-10/10 = -1 -15/7.5 = -2 0/10 = 0 -10/10 = -1 +5/11 = +0.5 +35/14.2 = +2.5

The variation of the tracking signal between ­2.0 and +2.5 is within 

acceptable limits

It’s possible to use the computer to 

continually monitor forecast error and adjust  the values of the  α  and  β  coefficients used in  exponential smoothing to continually 

minimize forecast error

This technique is called adaptive smoothing

Developed at American Hardware Supply, focus  forecasting is based on two principles:

1. Sophisticated forecasting models are not

always better than simple ones

2. There is no single technique that should be

used for all products or services

This approach uses historical data to test multiple forecasting models for  individual items

The forecasting model with the lowest error is then used to forecast the next  demand

absolute value of the individual forecast errors divided 

by the number of periods

from the cumulative forecast.

Seasonal Index =   period average demand

avg. demand for all periods

End of Lecture 18