Resolve Problem 4.19 with α = .1 and β =.8. Using MSE, determine which smoothing constants provide a better
To determine: Compute MSE using the given smoothing constants and find the better forecasting smoothing constants using trend-adjusted exponential smoothing method.
Introduction: A sequence of data points in successive order is known as time series. Time series forecasting is the prediction based on past events which are at uniform time interval. Moving average method and trend projections are two of the time series methods which use weights to prioritize past data.
Answer to Problem 20P
On comparing MSE from two smoothing constants (refer to equations (1) and (2)), it can be inferred that smoothing constant with α=0.1 and β=0.8 provides better forecast because it minimizes the error.
Explanation of Solution
Given information:
Time period | Month | Income ($ in thousands) |
1 | February | 70 |
2 | March | 68.5 |
3 | April | 64.8 |
4 | May | 71.7 |
5 | June | 71.3 |
6 | July | 72.8 |
Formula to calculate the MSE &forecasted demand
Where,
Calculation of FIT and MSE usingα=0.1 andβ=0.2:
Time period | Month | Income ($ in thousands) | Ft ($ in thousands) | Tt | FIT | Error | Sq. Error |
1 | February | 70 | 65 | 0 | 65 | 5 | 25 |
2 | March | 68.5 | 65.500 | 0.100 | 65.600 | 2.9 | 8.41 |
3 | April | 64.8 | 65.890 | 0.158 | 66.048 | -1.25 | 1.56 |
4 | May | 71.7 | 65.923 | 0.133 | 66.056 | 5.64 | 31.85 |
5 | June | 71.3 | 66.621 | 0.246 | 66.867 | 4.43 | 19.66 |
6 | July | 72.8 | 67.310 | 0.335 | 67.644 | 5.16 | 26.58 |
Total | 113.05 | ||||||
MSE | 18.84 |
Table 1
Excel worksheet:
Calculation of FIT for February:
To calculate FIT for February, compute F1 and T1. The forecast F1 is $ 65 and trend T1 is 0. The sum of both values gives FIT, which is equal to $ 65.
Calculation of FIT for March:
To calculate FIT for February, compute F2 and T2. The forecast F2 is $ 65.5 and trend T2 is 0.1. The sum of both values gives FIT, which is equal to $ 65.60.
Calculation of FIT for April:
To calculate FIT for March, compute F3 and T3. The forecast F3 is $ 65.890 and trend T3 is 0.158. The sum of both values gives FIT, which is equal to $ 66.048.
Calculation of FIT for May:
To calculate FIT for May, compute F4 and T4. The forecast F4 is $ 65.923 and trend T4 is 0.133. The sum of both values gives FIT, which is equal to $ 66.056.
Calculation of FIT for June:
To calculate FIT for June, compute F5 and T5. The forecast F5 is $ 66.621 and trend T5 is 0.246. The sum of both values gives FIT, which is equal to $ 66.867.
Calculation of FIT for July:
To calculate FIT for July, compute F6 and T6. The forecast F6 is $ 67.310 and trend T6 is 0.335. The sum of both values gives FIT, which is equal to $ 67.644.
Calculation of MSE:
MSE is obtained by dividing the summation value of the square of the difference between actual and forecasted sales with the number of years n; n=6.
Table 1provides the values for square of the difference between actual and forecasted sales.
MSE using α=0.1 and β=0.2 is 18.84.
Calculation of FIT and MSE using α=0.1 and β=0.8:
Time period | Month | Income ($ in thousands) | Ft ($ in thousands) | Tt | FIT | Error | Sq. Error |
1 | February | 70 | 65 | 0 | 65 | 5 | 25 |
2 | March | 68.5 | 65.500 | 0.400 | 65.900 | 2.6 | 6.76 |
3 | April | 64.8 | 66.160 | 0.608 | 66.768 | -1.968 | 3.87 |
4 | May | 71.7 | 66.571 | 0.451 | 67.022 | 4.678 | 21.89 |
5 | June | 71.3 | 67.490 | 0.825 | 68.314 | 2.986 | 8.91 |
6 | July | 72.8 | 68.613 | 1.064 | 69.677 | 3.123 | 9.76 |
Total | 76.19 | ||||||
MSE | 12.70 |
Table 2
Excel worksheet:
Calculation of FIT for February:
To calculate FIT for February, compute F1 and T1. The forecast F1 is $ 65 and trend T1 is 0. The sum of both values gives FIT, which is equal to $ 65.
Calculation of FIT for March:
To calculate FIT for February, compute F2 and T2. The forecast F2 is $ 65.5 and trend T2 is 0.4. The sum of both values gives FIT, which is equal to $ 65.90.
Calculation of FIT for April:
To calculate FIT for March, compute F3 and T3. The forecast F3 is $ 66.160 and trend T3 is 0.608. The sum of both values gives FIT, which is equal to $ 66.786.
Calculation of FIT for May:
To calculate FIT for May, compute F4 and T4. The forecast F4 is $66.571 and trend T4 is 0.451. The sum of both values gives FIT, which is equal to $ 67.022.
Calculation of FIT for June:
To calculate FIT for June, compute F5 and T5. The forecast F5 is $ 67.490 and trend T5 is 0.825. The sum of both values gives FIT, which is equal to $ 68.314.
Calculation of FIT for July:
To calculate FIT for July, compute F6 and T6. The forecast F6 is $ 68.613 and trend T6 is 1.064. The sum of both values gives FIT, which is equal to $ 69.677.
Calculation of MSE:
MSE is obtained by dividing the summation value of the square of the difference between actual and forecasted sales with the number of years n=6.
Table 2provides the values for square of the difference between actual and forecasted sales.
MSE using α=0.1 and β=0.8 is 12.70.
On comparing MSE from two smoothing constants (refer to equations(1)&(2)), it can be inferred that smoothing constant with α=0.1 and β=0.8 provides better forecast because it minimizes the error.
Want to see more full solutions like this?
Chapter 4 Solutions
Principles Of Operations Management
- Under what conditions might a firm use multiple forecasting methods?arrow_forwardScenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. Is Ben Gibson acting legally? Is he acting ethically? Why or why not?arrow_forwardScenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. As the Marketing Manager for Southeastern Corrugated, what would you do upon receiving the request for quotation from Coastal Products?arrow_forward
- Scenario 4 Sharon Gillespie, a new buyer at Visionex, Inc., was reviewing quotations for a tooling contract submitted by four suppliers. She was evaluating the quotes based on price, target quality levels, and delivery lead time promises. As she was working, her manager, Dave Cox, entered her office. He asked how everything was progressing and if she needed any help. She mentioned she was reviewing quotations from suppliers for a tooling contract. Dave asked who the interested suppliers were and if she had made a decision. Sharon indicated that one supplier, Apex, appeared to fit exactly the requirements Visionex had specified in the proposal. Dave told her to keep up the good work. Later that day Dave again visited Sharons office. He stated that he had done some research on the suppliers and felt that another supplier, Micron, appeared to have the best track record with Visionex. He pointed out that Sharons first choice was a new supplier to Visionex and there was some risk involved with that choice. Dave indicated that it would please him greatly if she selected Micron for the contract. The next day Sharon was having lunch with another buyer, Mark Smith. She mentioned the conversation with Dave and said she honestly felt that Apex was the best choice. When Mark asked Sharon who Dave preferred, she answered, Micron. At that point Mark rolled his eyes and shook his head. Sharon asked what the body language was all about. Mark replied, Look, I know youre new but you should know this. I heard last week that Daves brother-in-law is a new part owner of Micron. I was wondering how soon it would be before he started steering business to that company. He is not the straightest character. Sharon was shocked. After a few moments, she announced that her original choice was still the best selection. At that point Mark reminded Sharon that she was replacing a terminated buyer who did not go along with one of Daves previous preferred suppliers. Ethical decisions that affect a buyers ethical perspective usually involve the organizational environment, cultural environment, personal environment, and industry environment. Analyze this scenario using these four variables.arrow_forwardScenario 4 Sharon Gillespie, a new buyer at Visionex, Inc., was reviewing quotations for a tooling contract submitted by four suppliers. She was evaluating the quotes based on price, target quality levels, and delivery lead time promises. As she was working, her manager, Dave Cox, entered her office. He asked how everything was progressing and if she needed any help. She mentioned she was reviewing quotations from suppliers for a tooling contract. Dave asked who the interested suppliers were and if she had made a decision. Sharon indicated that one supplier, Apex, appeared to fit exactly the requirements Visionex had specified in the proposal. Dave told her to keep up the good work. Later that day Dave again visited Sharons office. He stated that he had done some research on the suppliers and felt that another supplier, Micron, appeared to have the best track record with Visionex. He pointed out that Sharons first choice was a new supplier to Visionex and there was some risk involved with that choice. Dave indicated that it would please him greatly if she selected Micron for the contract. The next day Sharon was having lunch with another buyer, Mark Smith. She mentioned the conversation with Dave and said she honestly felt that Apex was the best choice. When Mark asked Sharon who Dave preferred, she answered, Micron. At that point Mark rolled his eyes and shook his head. Sharon asked what the body language was all about. Mark replied, Look, I know youre new but you should know this. I heard last week that Daves brother-in-law is a new part owner of Micron. I was wondering how soon it would be before he started steering business to that company. He is not the straightest character. Sharon was shocked. After a few moments, she announced that her original choice was still the best selection. At that point Mark reminded Sharon that she was replacing a terminated buyer who did not go along with one of Daves previous preferred suppliers. What should Sharon do in this situation?arrow_forwardScenario 4 Sharon Gillespie, a new buyer at Visionex, Inc., was reviewing quotations for a tooling contract submitted by four suppliers. She was evaluating the quotes based on price, target quality levels, and delivery lead time promises. As she was working, her manager, Dave Cox, entered her office. He asked how everything was progressing and if she needed any help. She mentioned she was reviewing quotations from suppliers for a tooling contract. Dave asked who the interested suppliers were and if she had made a decision. Sharon indicated that one supplier, Apex, appeared to fit exactly the requirements Visionex had specified in the proposal. Dave told her to keep up the good work. Later that day Dave again visited Sharons office. He stated that he had done some research on the suppliers and felt that another supplier, Micron, appeared to have the best track record with Visionex. He pointed out that Sharons first choice was a new supplier to Visionex and there was some risk involved with that choice. Dave indicated that it would please him greatly if she selected Micron for the contract. The next day Sharon was having lunch with another buyer, Mark Smith. She mentioned the conversation with Dave and said she honestly felt that Apex was the best choice. When Mark asked Sharon who Dave preferred, she answered, Micron. At that point Mark rolled his eyes and shook his head. Sharon asked what the body language was all about. Mark replied, Look, I know youre new but you should know this. I heard last week that Daves brother-in-law is a new part owner of Micron. I was wondering how soon it would be before he started steering business to that company. He is not the straightest character. Sharon was shocked. After a few moments, she announced that her original choice was still the best selection. At that point Mark reminded Sharon that she was replacing a terminated buyer who did not go along with one of Daves previous preferred suppliers. What does the Institute of Supply Management code of ethics say about financial conflicts of interest?arrow_forward
- The Pro Apparel company manufactures baseball-stylecaps with various team logos. The caps come in an assort-ment of designs and colors. The company has had monthlysales for the past 24 months as follows:Develop a forecast model using the method you believe best,and justify your selection using a measure (or measures) offorecast accuracy.arrow_forwardWeekly income for Quiet Mental Breakdown, an online psychology firm, is provided below. Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average gives a better forecast. Week Income 1 980 2 1040 3 1120 4 1050 5 960 6 990 7 1030 8 1260 9 1240 10 1100 Group of answer choices Both the four-period & three-period simple moving averages have the same forecast accuracy in terms of their MSE There is not enough information to determine the answer The four-period simple moving averages gives a better forecast because it has the smallest MSE The three-period simple moving average gives a better forecast because it has the smallest MSEarrow_forwardDaily high temperatures in st. Louis for the last week were as follows: 33,33,38,36,43,23,28(yesterday).Calculate the mean absolute deviation based on a 3 day moving average?In my text book it say that you need the actual forecast however, the problem never gives me the real temp thus creating a problem to calculate mean absolute deviation? any help would be greatly appreciatedarrow_forward
- Explain what are the benefits of exponential smoothing over moving average forecasting ?arrow_forwardUse the sales data in the table ( attached Image) and apply the same forecast method when α = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1. What is the best value for α? What does the best value of α indicate or show in regards to the forecast model? (Hint: Use Microsoft Excel to solve the question)arrow_forwardThe following monthly sales (in thousands of AUS dollars) of chocolate boxes have been recorded for January, February, March, and April, respectively: 8, 8, 5, 9. Focusing on sales forecast accuracy for the month of April only, explain which of the following forecasting method would you recommend: the Naïve method, the Average method, or the Simple exponential smoothing method (assuming alpha=0.8 and initial state of 7)?arrow_forward
- Contemporary MarketingMarketingISBN:9780357033777Author:Louis E. Boone, David L. KurtzPublisher:Cengage LearningMarketingMarketingISBN:9780357033791Author:Pride, William MPublisher:South Western Educational PublishingPurchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage Learning