Class Notes (811,170)
MSCI 432 (10)
Lecture

Assignment #2 - Solution Winter 2010

6 Pages
370 Views

School
University of Waterloo
Department
Management Sciences
Course
MSCI 432
Professor
Binyamin Mantin
Semester
Fall

Description
MSCI 432.001/633: Production and Service Operations Management, Winter 2010 Assignment # 2  Due by Friday, February 12, 2010, at noon time. Drop your solutions in the MSci432/633 slot of the metal box located in front of CPH 2367 (2nd floor, where CPH building meets E2 building). No late submissions.  Individual submissions. You must indicate whether you have collaborated/cooperated on this assignment with other students. Also indicate whether you are 432.001 or 633.  As a rule, type your solution for all text-dominated so lutions. Save paper, submit double-sided and please no fancy marginalia. 1. [6 marks] The number of students spotted at the Grad House in each of the last six weeks has been: t 1 2 3 4 5 619 0 Students t 83 10695 91 110 108 a. Use a two-week moving average to forecast the number of students in each of weeks 7 and 10. Also compute the MSE based on the # of students and forecasts for period 1 to 6. To initialize assume x-1x =000 (i.e., your prediction for the first period is 100). b. A consultant suggests the use of simple (single) exponential smoothing with α=0.1. Use such a procedure to develop forecasts of # of students in weeks 7 and 10. Initialize with F=100. Alst compute MSE and MAD. c. Without redoing all the computations, what would be the forecast of students in week 7 using exponential smoothing if F wert 90 instead of 100? a. [2 marks] xt,2 xt  xt1/2  and  at xt,2 x t,t at Now using these three formulas, we obtain,    110108 /2 109 x6,7 x6,10 a6 Now developing the whole table; t 1 2 3 4 5 619 0 xˆt1,t 100 91.5 94.5 100.5 93 100.5 109 109 109 109 xt 83 10695 91 110 108 x - 1714.50.5 9.5 17 7.5 t xt1,t (xt- xt1,t 289.10.25 0.25 90.25 289.00 56.25 The MSE = the sum of the last row divided by 6 = 155.83. b. [2 marks] In simple exponential smoothing, we have; aˆt xt 1 at1 here  0.1 xˆ  aˆ t,t t Using these formula, the following table is developed. T 1 2 3 4 5 61 870 xt1,t 100 98.3 99.1 98.7 97.9 99.1 100 100 xt 83 106 95 91 110 108 xt-xˆt1,t 17 7.7 4.1 7.7 12.1 8.9 2 (xt-xt1,t 289.00 59.29 16.81 59.29 146.41 79.21 MAD = 9.6, and MSE = 108.34, which is better than moving average. c. [2 marks] x6,7 a6  x6 1 a5  x6 1  x 5 1  a4 2  x6  x5   a4 Continuing in this manner, we get 6 6 New x6,7Old x6,7   new a0 1  old a0 6    new a0  oldaˆ0  0.9690100  5.3 New x6,7 old x6,75.3 100.05.3 94.7 2. [6 marks] Union Gas reports the following (normalized) figures for gas consumption by households in a metropolitan area of Ontario: Jan. Feb. Mar. Apr. May June July Aug. Sept.Oct. Nov. Dec. 200179619617310575 39 13 20 37 73 108191 200282721719711088 51 27 23 41 40 107172 200291621819312099 59 33 37 59 95 128201 20228 a. Using a simple (single) exponential smoothing model (with α=0.1), determine the forecast for consumption in (1) February 2010 and (2) June 2012. b. Do the same using the Winters seasonal smoothing model with α=0.2, β=0.05, and δ=0.1. Use the first two years of data for initialization purposes. c. Plot the demand data and the two sets of forecasts. (i) Does there appear to be a point of abrupt change in the demand pattern? (ii) Assess the performance of the Winters model briefly for the different months (without calculating any error measures). (iii) Which method is preferred? a. Assuming initial forecast is 196, we have the following predictions as in the last column of the table below. i. The forecast for February, 2010, is 124.2 ii. Single exponential smoothing assumes no trend or seasonal factors. Thus, the forecast for June, 2012 is also 124.2. b. Refer to the table below to see the initialization using the first two years and updating thereafter. i. The forecast for February, 2010, is 247.8 ii. The forecast for June, 2012 is (161.81+1.86*29)*0.53=114.98, since June 2012 is 29 months away from January 2010, and we are using S and G from that month and the best factor available for June. Lin.  exponential  Demand  Reg.  Ct  Average Ct  Winter  smoothing  Use first two years (24 obs.) for initial  Jan‐07  1  196  127.49  1.54  estimates (linear reg.)  196  Feb‐07  2  196  125.56  1.56 slope ‐1.93391 196 Mar‐07  3  173  123.62  1.40 intercept 129.4239 196 Apr‐07  4  105  121.69  0.86 193.7 May‐07  5  75  119.75  0.63 184.8 Jun‐07  6  39  117.82  0.33 173.8 Jul‐07  7  13  115.89  0.11 160.4 Aug‐07  8  20  113.95  0.18 145.6 Sep‐07  9  37  112.02  0.33 133.1 Oct‐07  10  73  110.08  0.66 123.5 Nov‐07  11  108  108.15  1.00 118.4 Dec‐07  12  191  106.22  1.80 1.67 1.43 117.4 Jan‐08  13  227  104.28  2.18 1.87 1.60 124.7 Feb‐08  14  217  102.35  2.12 1.76 1.51 135.0 Mar‐08  15  197  100.42  1.96 1.41 1.21 143.2 Apr‐08  16  110  98.48  1.12 0.87 0.75 148.5 May‐08  17  88  96.55  0.91 0.62 0.53 144.7 Jun‐08  18  51  94.61  0.54 0.33 0.28 139.0 Jul‐08  19  27  92.68  0.29 0.23 0.20 alpha= 0.2  130.2 Aug‐08  20  23  90.75  0.25 0.29 0.25 beta= 0.05  119.9 Sep‐08  21  41  88.81  0.46 0.56 0.48 delta= 0.1  110.2 Oct‐08  22  40  86.88  0.46 0.73 0.63 103.3 Nov‐08  23  107  84.94  1.26 1.53 1.31 G S F  97.0 Dec‐08  24  172  83.01  2.07 2.12 1.82 ‐1.93 83.01  115.92
More Less

Related notes for MSCI 432

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.