Production and Operations Management
MID-TERM EXAM – SPRING 2012
This is a TAKE-HOME Exam. The exam consists of six questions on 2 pages. You are required to answer ALL the questions. Answer each question thoroughly and show all your calculations. Give clear explanations for your answers where necessary. Completed exams are due on Thursday, March 4th by Midnight. You may use regular e-mail or the drop-box to submit your completed exam.
EACH STUDENT IS EXPECTED TO ABIDE BY THE SENTIMENTS CONTAINED IN THE FOLLOWING HONOR STATEMENT
TAKE-HOME EXAM HONOR STATEMENT:
I did not request or receive assistance in preparing the answers to this exam. (Clarifications that you seek from the instructor will not be counted as assistance).
Question 1. (35 points)
The Multifaceted Garden Store uses two forecasting techniques to predict annual national sales of their lawnmowers at their various franchises. The actual sales and the corresponding forecasts for techniques 1 & 2 for the period spring 2010 to spring 2011 are given below:
| |Spring 10 |Summer 10 |Fall 10 |Winter 10 |Spring 11 | |Actual |17178 |11452 |6106 |1527 |18183 | |Forecast 1 |16948 |11250 |6308 |1604 |18007 | |Forecast 2 |17453 |12102 |6006 |1445 |18504 |
a. Calculate the MAD, the MAPE, the MSE and the tracking signal for Forecast 1.
b. Calculate the MAD, the MAPE, the MSE and the tracking signal for Forecast 2.
c. Compare the results obtained in parts (a) and (b).
There is a significantly smaller amount of error in the forecast for Part A. The large error for the summer 10 and spring 11 for forecast is exploited by looking at the large MSE for those two periods. The tracking signals show that on average forecast 1 underestimates the actual results and forecast 2 overestimates the actual results. d. The company is interested in developing forecasts for their lawnmower sales during the summer of 2011. Which of the two forecasting techniques (1 or 2) would you recommend that they use, and why? I would recommend that they use forecast technique 1 because it has a smaller MAD, MAPE, MSE, and TS. e. Actual sales figures for the previous two years (2009 and 2010) are given below: | |Spring |Summer |Fall |Winter |Total | |2009 |16095 |10730 |5300 |1327 |33452 | |2010 |17178 |11452 |6106 |1527 |36263 |
Can you suggest an appropriate technique (regression, smoothed moving average, exponential smoothing, etc.) that might yield reasonable forecasts for this time series? Justify your answer. In this case I would suggest a time series decomposition model. The seasonal forecasting method would be most appropriate since there is obvious seasonality in the data. The chart below illustrates the major differences in MAD using four of the forecasting techniques. Regression was not included due to obvious seasonality in the data.
|4- Period Models |MAD | |Simple Moving Average |5458 | |Weighted Moving Average |6028 | |1-.2,2-.3,3-.3,and 4-.2 | | |Exponential SC=.6 |6550 | |Seasonal Quarterly |205 |
Question 2. (20...