Homework (due Monday, March 28)
Page 140-141, Problem 4.1, 4.6 (not b-5), Problem 4.7 (calculate MAD and MSE)
Problem 4.1 page 140
a. forecast demand for week of Oct. 12 using 3-week moving
average
Oct. 12 forecast = Oct 5 demand + September 28 demand + September 21 demand
3
Oct. 12 forecast = 374 + 368 + 381
3
Oct. 12 forecast = 374.33
b. 3-week moving average with weights of .1 .3 and .6. Forecast
demand for Oct. 12
Oct. 12 forecast = Oct 5 demand (.6) + September 28 demand (.3) + September 21 demand (.1)
Oct. 12 forecast = 374 (.6) + 368 (.3) + 381 (.1)
Oct. 12 forecast = 224.40 + 110.40 +38.10
Oct. 12 forecast = 372.90
c. compute forecast for week of Oct 12. using exponential
smoothing with a forecast for Aug.31 of 360 and alpha=.2
Next forecast = Previous forecast + (Actual demand from previous period – Previous forecast)
Oct. 12 forecast = Oct. 5 forecast + (374 - Oct. 5 forecast)
Hmmmmm. How do you get the Oct 5 forecast with the information given?….that is, with only the Aug. 31
forecast?
FIRST, you must go back and calculate the exponentially smoothed forecast for each week, beginning with
the week of Sept. 7 and working your way up to the Oct. 5 forecast.
1
Sept. 7 forecast = Aug. 31 forecast + alpha (Aug. 31 demand- Aug. 31 forecast)
Sept. 7 forecast = 360 + .20 (360-360)
Sept. 7 forecast = 360 + .20 (0)
Sept. 7 forecast = 360 + 0
Sept. 7 forecast = 360
Sept. 14 forecast = Sept. 7 forecast + alpha (Sept. 7 demand - Sept. 7 forecast)
Sept. 14 forecast = 360 + .20 (389 - 360)
Sept. 14 forecast = 360 + .20(29)
Sept. 14 forecast =360 + 5.8
Sept. 14 forecast =365.80
Sept. 21 forecast = Sept. 14 forecast + alpha (Sept. 14 demand - Sept. 14 forecast)
Sept. 21 forecast = 365.80 + .20 (410-365.80)
Sept. 21 forecast = 365.80 + .20 (44.2)
Sept. 21 forecast =365.80 + 8.84
Sept. 21 forecast =374.64
Sept. 28 forecast = Sept. 21 forecast +alpha (Sept. 21 demand - Sept. 21 forecast)
Sept. 28 forecast =374.64 + .20( 381-374.64)
Sept. 28 forecast =374.64 + .20 (6.36)
Sept. 28 forecast =374.64 + 1.27
Sept. 28 forecast =375.91
October 5 forecast = Sept. 28 forecast + alpha(Sept. 28 demand - Sept. 28 forecast)
October 5 forecast =375.91 +.20(368-375.91)
October 5 forecast =375.91 + .20( -7.91)
October 5 forecast =375.91 +(-1.58)
October 5 forecast =374.33
Now we have the information to actually calculate the original question: what is the Oct. 12 exponentially
smoothed forecast?
Oct. 12 forecast = Oct. 5 forecast + (374 - Oct. 5 forecast)
Oct. 12 forecast = 374.33 + .20 ( 374 - 374.33)
Oct. 12 forecast = 374.33 + .20 ( -.33)
Oct. 12 forecast = 374.33 +(-.066)
Oct. 12 forecast = 374.26
*** This is a great example of the “problem” with exponential smoothing forecasts - you must know where to
begin! You have to always read the problem carefully to know where to get the previous period’s forecast. I
could have told you to use a 4-week moving average for Oct. 5, or I could have simply given you a forecast
for Oct. 5, or in this case, you had to use the data you were give and work forward to get an Oct. 5 forecast.
With exponential smoothing, read the problem very carefully so you know where to begin.
2
Problem 4.6 Page 141
Month Sales
Jan 20
Feb 21
March 15
April 14
May 13
June 16
July 17
Aug 18
Sept 20
Oct 20
Nov 21
Dec 23
a. Plot the demand data. WHY? We said the answer 10 times in class! You must know the underlying
pattern of your demand data so you can select a forecasting technique that can mimic the pattern of demand.
Sales/Demand
30 |
28 |
26 |
24 |
22 |
20 |
18 |
16 |
14 |
12 |
10 |
8 |
6 |
4 |
2 |
|
__________________________________________________________________________________
_
| | | | | | | | | | | |
Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
Time in Months
3
b. Forecast January Sales using each of the following
1. Naive
January Forecast = Dec. demand
January Forecast = 23
2. 3-month moving average forecast
January Forecast = December demand + November demand + October demand
3
January Forecast = 23 + 21+ 20
3
January Forecast = 21.33
3. 6-month moving average using .1 .1 .1 .2 .2 & .3
January Forecast = Dec. demand (.3) + Nov. (.2) + Oct. (.2) + Sept. (.1) + Aug. (.1) + July (.1)
January Forecast = 23 (.3) + 21 (.2) + 20 (.2) + 20 (.1) + 18 (.1) + 17 (.1)
January Forecast = 6.9 + 4.2 + 4 + 2 + 1.8 + 1.7
January Forecast = 20.6
4. Exponential Smoothing using alpha=.3 and Sept. forecast of
18.
January Forecast = Dec. forecast + alpha (Dec. demand - Dec. Forecast)
Hmmmmm. The problem is that we don’t have a Dec. forecast to plug into our equation. We were, however,
given a Sept. forecast of 18. Can you use that Sept. forecast and work your way up to a Dec. Forecast? I think
you can!
Oct. Forecast = Sept. forecast + alpha (Sept. demand - Sept. forecast)
Oct. Forecast = 18 +.30(20-18)
Oct. Forecast =18 + .30(2)
Oct. Forecast =18 + .6
Oct. Forecast =18.6
Nov. Forecast = Oct. forecast + alpha (Oct. demand - Oct. forecast)
Nov. Forecast = 18.6 + .30 ( 20- 18.6)
Nov. Forecast = 18.6 + .30 (1.4)
Nov. Forecast = 18.6 + .42
Nov. Forecast = 19.02
4
Dec. Forecast = Nov. forecast + alpha (Nov. demand - Nov. forecast)
Dec. Forecast = 19.02 +.30(21-19.02)
Dec. Forecast =19.02 +.30 (1.98)
Dec. Forecast =19.02 + .594
Dec. Forecast =19.61
Now, we have enough information to answer the original question:
January Forecast = Dec. forecast + alpha (Dec. demand - Dec. Forecast)
January Forecast = 19.61 +.30( 23-19.61)
January Forecast = 19.61 +.30(3.39)
January Forecast =19.61 +1.017
January Forecast =20.63
Page 141 Problem 4.7 MAD & MSE
Year Demand Forecast from Error Absolute value error Error2
Marketing (demand-forecast)
1 167,325 170,000 -2,675 2,675 7,155,625
2 175,362 170,000 5,362 5,362 28,751,044
3 172,536 180,000 -7,464 7,464 55,711,296
4 156,732 180,000 23,268 23,268 541,399,824
5 176,325 165,000 11,325 11,325 128,255,625
(sum of the absolute values of errors) (sum of the errors squared)
MAD & MSE for the Forecast created by the VP of Marketing
MAD = Actual demand – forecasted demand
n 5
MSE = (Actual demand – Forecasted demand)2 = 761,273,414 = 190,318,353.5
n-1 4
Year Demand Forecast from Error Absolute value error Error2
Operations (demand-forecast)
1 167,325 160,000 7,325 7,325 53,655,625
2 175,362 165,000 10,362 10,362 107,371,044
3 172,536 170,000 2,536 2,536 6,431,296
4 156,732 175,000 -18,268 18,268 333,719,824
5 176,325 165,000 11,325 11,325 128,255,625
5
(sum of the absolute values of errors) (sum of the errors squared)
MAD & MSE for the Forecast created by the VP of Operations
MAD = Actual demand – forecasted demand
n 5
MSE = (Actual demand – Forecasted demand)2 = 629,433,414 = 157,358,353.5
n-1 4
***Which forecast is better, the forecast from the VP of Marketing or the forecast from the VP of Operations?
What makes a forecast “better” (hint: greater accuracy, less error). Since MAD and MSE are measures of
forecast error, we should pick the forecast with the lower values of MAD and MSE because that forecast has
less error. The forecast by the VP of Operations has less error (and is therefore “better”!) as indicated by the
lower values of MAD & MSE.
