DS 412 SP 06 - D8 412 Operations Management Spring 2006 ‘...

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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 take-home part of the exam. 2. Use MS Excel to answer the question. 3. Your computer printouts must be turned in along with your in-class exam. 4. Please bring this question sheet to your in-class 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 SQmVDUI-wa—i dd—h—h—L mAwM-a 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 MQY'WS mfloaze lamina] —go\eCQ}-‘Ll : {in .‘Qfm ‘Ff I Mao , ”37”“““ "”1”“ ‘ Q5+5QWQ+I9¢$+QQQ5+¥IC :LI-‘L- 3C ‘ 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 Y-intercept 'a' represent estimated sales? 3-:0 o-;z.'/q+<tssb\ Forecast sales in March 200 regression equation. 7 = [email protected]) =. lOW-b’ (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 off-peak hours. Compute the mean seasonal factors. I?“— %%-: ms: 0 'iOLi cue Tires reqc vu+ -'-I"Lb= C) 99% — qu-ns- ,____.__.-——..—_.. 1+ ’3an mac“ , o€o+‘Lo°e-H‘?.%+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 QLLQ-maich . €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+73-9+20~3+16-l+ 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; Nah-1006,30 7: é7+1~5xlf: ’04-‘53? $.MI5500 Bmkbué’ _‘(o.7o4o« 63/1: o-é‘l wak (1-70 +1-72) I; 21.72.. Dam (0-99 +1-07)/1 = 1-03 ofiflfuwk, (gel—r 0«->"3f)/2_;0-57 >1 3-5—0)! 1&6.— 350 X30 I“‘2$ox45’ +onzo — 260 x30 b- £14150): 3750x 0.25- +5750xo.45+375oxo»3:37~53' ‘ 5:14-16?) = 3650 x045 +3 900 xo-451-390-ox0-3 : .3837“? H1170); 35:50 xo-zs- +3801? x 0-45 +4050x 0.3: 381m” flaw/W; iéf Aim)- 5v; $3837.51» E~ E gxfmlfisEl/zlJf - @EV = 0- 8x 1-4 + 0.2404: 1.94 @Ev: 0-.8x3+o.>.x(~z) ; 2f?— [D [0,7e’F/MVE’5EV:JaJ_ . . ‘ '4“ B ‘2“; zflaM’jEV:$fiMp&-A ...
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