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Unformatted text preview: D8 412 Operations Management Spring 2006
‘ Midterm Exam 1 ~ Part 1 Prof Uday 1212191 I. This is the takehome part of the exam.
2. Use MS Excel to answer the question. 3. Your computer printouts must be turned in along with your inclass exam.
4. Please bring this question sheet to your inclass exam. A call center records the following daily volume of calls over a three week period. m Call Volume ‘ 1 413
2 536
3 495
4 451
5 480
6 400
7 525
8 490
9 492
10 519
11 1 402
12 616
13 485
14 527
15 461 a. Use the method of Moving Averages with N = 5 to forecast Call Volume for 
periods 6 through 15. I). Use Simple Exponential Smoothing with smoothing constant alpha = 0.3 to
forecast Call Volume for periods 2 through 15. Obtain a printout of your forecasts. Day SQmVDUIwa—i dd—h—h—L
mAwMa Forecasting With Excel Call Voiume
413
536
495
451
480
400
525
490
492
519
402
616
485
527
461 .MA #N/A
#N/A
#NIA
#N/A
475
472.4
470.2
469.2
477.4
485.2
485.6
503.8
502.8
509.8
498.2 SES #N/A
413
449.9
463.43
459.701
465.7907
446.05349
469.737443
475.8162101
480.6713471
492.1699429
465.11 89601
5101383272
502.7682904
51 0.0378033 I FEM an . 53’ "I , 4 I F r 7.293 5 ' “ta“ OWL C t
:LH. n. ' ' f
,. ~ \'
Pr,“ ezﬁ’ r), 1. (18 points) Refer to your take home exam. Use the computer printout provided to answer the
following questions. a. Complete the following error table (use one decimal). Ex oonential Smoothin ; b. Based on days 6 through l0, compute the MAD for each forecast method. Which method Is better, and why? u
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‘ 5 SEE Q5‘%+q%.q+Qo.‘5+IC ‘L+'3%3 .2 “33 M“ 9 ’ 5  belly.
EXCEL Output Use moving Wmﬁe ‘3 .‘ (12 points) Monthly Online Sales Y (in thousands of dollars) of Savannah Corporation has been showing an increasing trend, which is represented by the following regression equation:
Y = 67 + 2.5t, where t represents the month and t = l for Jan 2005. What is the estimated increase in sales per month, based on egression equation? For which time period (month and "yearj‘rdbes t e Yintercept 'a' represent estimated sales? 3:0 o;z.'/q+<tssb\ Forecast sales in March 200 regression equation. 7 = [email protected])
=. lOWb’ (18 points) The number of customers visiting Mandy's fast food outlet on Berger Street on a typical
day varies based on the time of day, and the same kind of pattern repeats every day. The number of
customers therefore has a seasonal pattern. To assess the seasonal effects, a day may be broken down
into four blocks of time: breakfast, lunch, dinner, and offpeak hours. Compute the mean seasonal
factors. I?“—
%%: ms: 0 'iOLi cue Tires reqc
vu+ 'I"Lb= C) 99% — quns ,____.__.——..—_.. 1+ ’3an mac“ , o€o+‘Lo°eH‘?.%+Ci+ ”(Lg Jr N
. ‘ '  If \ ‘L
p03“ \7 (1.9 . ’ QR
) /""
')’5
(28 points) One of the lines of business of Chao Enterprises is to sell Christmas trees over the holiday
season. Each tree is purchased from a farm at a cost of $30. The trees are sold to customers at a price Wee. Any trees leﬁ over at the end of the holiday season are sold to a lumber yard at a price of $20/tree. From past experience, the ﬁrm anticipates that demand for trees during the holiday season is likely to be 250, 260, or 270, with respective probabilities of 0.25, 0.45, and 0.3. The ﬁrm would like
to determine the number of trees to purchase from the farm, in order to maximizejhe expected value of the proﬁt. (3935 i mist} C
Set up the payoff table.
What is the best decision?
gm“ (‘1
QLLQmaich . €1.59 Q60 Q3933“)
I a
9.50 '5 ‘?5‘ O 6899/ ..,..(_;~ ' _. ' )
/~~‘~ \. (1,59. 9'? (32 points) Hansen, Inc. has recently decided to begin manufacturing its product in Europe. It must
decide what size plant to build. The ﬁrm assumes the plant will have a lifetime of 10 years. It is
considering two options: a large plant or a small Iant. Demand in Europe is assumed to be either high
or low, with probabilities (mm If demand is high, the ﬁrm can expan‘ths small
plant to a large plant after two years. TEE: cost of building the plant is $5 million for ﬂarge plaﬁt; and
$1 million for a small 1:19:11.“er the small plant is expanded to a large p153: aﬁer two years, e
additional cost will $3 millig. If the ﬁrm builds a large plant, the proﬁts generated over the 10—year
period will be gmjﬂonyith high‘demand, and $4million with low demand. If the ﬁrm builds a small
plant, the proﬁts over the ﬁrst—two years will be $0.4 million with high demand and $0.3 million with
low demand. If it decides not to expand, the proﬁts over the next 8 years will be $1.2 million with high
demand and 30.9 with low demand. On the other hand, if it expands after two years, the proﬁts over
the next 8 years will be $6 million. (All proﬁts and costs are given in terms of present values). Draw the decision tree, label it completely, and indicate all the payoffs. Solve the decision tree to determine the best decisions to maximize the net proﬁts. 1 hi8h(0°§.l 3 “4H3,
a 2.0..
b.
C. Ex  onentiai Smoothin
_m—— am we I SES : MAD =(6S 9+739+20~3+16l+ sang/5: 1,3: 9
MA M; 45am) .091th .L 15—ch HA1). 7m 1.; 77:». MJ '5, 4'25w/@JL.
Dec 4100:} @mdw) f=l5 1.4; Nah1006,30 7: é7+1~5xlf: ’04‘53? $.MI5500 Bmkbué’ _‘(o.7o4o« 63/1: oé‘l
wak (170 +172) I; 21.72..
Dam (099 +107)/1 = 103
oﬁﬂfuwk, (gel—r 0«>"3f)/2_;057 >1 35—0)! 1&6.— 350 X30 I“‘2$ox45’ +onzo
— 260 x30 b £14150): 3750x 0.25 +5750xo.45+375oxo»3:37~53'
‘ 5:1416?) = 3650 x045 +3 900 xo451390ox03 : .3837“?
H1170); 35:50 xozs +3801? x 045 +4050x 0.3: 381m”
ﬂaw/W; iéf Aim) 5v; $3837.51» E~ E gxfmlﬁsEl/zlJf 
@EV = 0 8x 14 + 0.2404: 1.94
@Ev: 0.8x3+o.>.x(~z) ; 2f?— [D [0,7e’F/MVE’5EV:JaJ_ . . ‘
'4“ B ‘2“; zflaM’jEV:$ﬁMp&A ...
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