Quantitative Methods

?le^p- Do A,. !rd?*^, Lg (b) What is the MAD for this model? (c) Computc the RSFE and tracking signals. Arc

they within acceptable lirnits?

5-30 IIow would lhc (orecast iirl wcck 2-5 ol thc prcvious prohlem change if the initial fbrecast was 40 instead of 50'l llow would the lbrecast for weck 25 chan-ee if the tbrecast for week I were assumed to be 60'l Consulting income at Kate l&'alsh Associates for the

MONTH INCOME ($t,000s)

February

March

April

Ma.v

Junc

July

Use exponential srnoothinc t0 August's in- come. Assume that the initial for February is

DrscussroN QUESTToNS AND PROBLEMS 183

(a) Compute seasonal indices for each quarler based onaC

ize the data op a trend line on the zed.

(c) Use the line to the sales for each quarter ol'

(d) Use the indi to adjust the forecasts the final forecasts.fbund in part (c)

$: s-:+ Usin-e the data in 5-33. develop a multiple resression model to sales (both trend and

dummy variables to into the model. Use

this model to ct sales for quarter of the next year. C on the ol'this nrodel.

$: s-:s Trevor Harty. an fvid mountajn bike\always wanted to start a business sellin-g top-of-t\-line moun- tain bikcs and othcr outdoor supplics. A littlc ovcr 6 years ago, hp and a silcnt partncr opcr-rcd a storc called Haie {nd Harty Trail Bikes and Supplies. Growth was fapid in the flrst 2 years, but since that

in sales has slowcd a bit, as cxpected. The quarterlv sales (in $1,000s) for the past 4 years are shown in the table below:

T'EAR 1 YEAR2 YEAR3 YEAR4

(b)

S: s-l

QUARTER 1

QUARIER 2

QUARTER 3

QUARTER4

211

112

130

162

(a) Develop a Use this to

282

178

1:16

168

282

182

13,1

296

210

i58

i82

ine using data in the table.

which srnoothing provides better forecast? -$:s-:6 The

$: s-:: A major souree of is a state sales tax on certain ty of goods and rvices. Data are cclmpiled l're state comptrol uses them to ploJect particular

lbr the statc of goods is classifi as Retail YEAR

Trade. Four of quarterly data (in ions) fbr Unemployment

rare (%) ar area of southeast Texas

QUARTER 1 YEAR2 YEAR3 1'EAR4

sales for quarter of year 5. What does the of line indicate?

(b) Usc thc rnultiplic tion rnodel 1r'r incorporatc both into tht: fbrecast. indicate'l

scasonal componcnts the slope ol-this line

(c) Compare the slope t0 the slope in the tion model that

wh-v these are so different and explain one is best to use.

a 1 0-year Usc exponen tbr ncxl vear- 0.6, and 0.8.

34 5678910 6.2 5.5 5.3 5.5 6.1 '7.1 6.8 6.i

70.0

68.5

(r4.tl

11 a

$65,000. The snroothing

5-32 Resolve Problem 5-31

21 8 225 247 254 243 255 292 299

lectcd is a : 0. l. 3. Using MAD,

250

283

289

356

on0

Quantitative Analysis for Manawment, Twelfth Edition, by Barry Render, Ralph M. Stair, Copyright O 201 5 by Pearson Education, lnc.

5-37 Management of Davis's Departnrent Store has used time-series extrapolation to forecast retail sales ibr thc next lirur quarters. The sales estinratcs urc SI00.000, $120,000. $140,000, and $160.000 for' the respectivc qriarters bcfore adjusting for seasonal- ity. Seasonal indices fbr the four quarters have been

Michael E. Hanna, and Trevor S. Hale- Published by Prentice Hall.

1

2

3

4

f 1/

265

264

-727

.. : -q-29@ter Park. Florida's 911 system, Ibr the past 24 weeks are as {ollows:

45

35

20

30

1l

22

23

24

(a) Cornpute the exponentially smoothed forecast of calls for each week. Assume an initial tbrecast of -50 calls in thc flrst wcck and usc t-l : 0.L What is thc forecast for the 2-5th week?

(b) Rcibrecast cach period using a : 0.6. (c) Actual calls during thc 25th wcck w'ere 85. Which

snoothins constanf provides a superior fbrecast?

WEEK CALLS WEEK CALLS

935 r0 20 lt 15 t?. .10 13 55 14 35 15 25 16 55

ratcs in thc United States during are given in the following table.

smoothing to find the best forecast sc smoothing constants ol 0.2, 0.4, Lich onc had tl.rc lowcsl- MAI)'l

trend line in part (a) for the decomposi- the deseasonalized

L)nc