Problems l. he number of bushels of apples sold at a roadside fruit stand over a
ID: 3119471 • Letter: P
Question
Problems l. he number of bushels of apples sold at a roadside fruit stand over a 12-day period were as follows: Number Sold 25 a. If a two-period moving average had been used to forecast sales, what would the daily forecasts have been starting with the forecast for Day 3? b. If a four-period moving average had been used, determine what the forecasts would have been for each day, starting with Day 5. c. Use a three-period weighted moving average with wr 2, wh 3, and ws .5 and forecast sales for the seventh and eighth days. d. Plot the original data and each set of forecasts on the same graph. Which forecast has the greater tendency to smooth? Which forecast has the better ability to respond quickly to changes? e. What does use of the term sales instead of the term demand imply? 2. If exponential smoothing with a .4 had been used to forecast daily sales for apples in the preceding problem, determine what the daily forecasts would have been. Then, plot the original data, the exponential forecasts, and a set of naive forecasts on the same graph. Based on a visual comparison, can you say that the naive would have been more accurate or less accurate than the exponential smoothing method, or would they have been about the same? 3 jeweler wants to forecast sales of one-carat diamond rings. Sales data for the previ- ous 15 weeks have been obtained: Week 1 2 3 4 5 6 7 8 9 10 12 13 15 a. Develop a series of forecasts, beginning in Week 4, that would have resulted if a three-period moving average forecast had been used. b. Using a starting forecast for Week 4 of 23 rings, develop the forecasts that would have resulted if an exponential smoothing model with a .20 had been used. 4. An electrical contractor's records during the last five weeks indicate the number of job requests: Predict the number of requests for Week 6 using each of these methods: a. Naive. b. A four-period moving average. c. A four-period weighted moving average with wh .1, w, .2, ws 3, and w 4 d. Exponential smoothing with a 30, Determine the forecast using the naive method for Weeks 2 through 5 and com- pute MAPE and MPE values.Explanation / Answer
1)a)
Moving average for day 3 = ( 25 + 31) /2 = 28
Moving average for day 4 = ( 31 + 29) /2 = 30
Similarly, calculated for all days
b)
Moving average for day 5 = ( 25 + 31 + 29 + 33) /4 = 29.5
Moving average for day 6 = ( 31 + 29 + 33 + 34) /4 = 31.75
Similarly, calculated for all days
c)
38.1
Weighted moving average for day 7 = 33 * .2 + 34 * .3 + 37 * .5 = 35.3
Weighted moving average for day 8 = 34 * .2 + 37 * .3 + 35 * .5 = 35.4
3)
a)
Moving average for week 4 = ( 25 + 19 + 24) /3 = 22.67
Moving average for week 5 = ( 19 + 24 + 28) /3 = 23.67
similarly, calculated for other weeks
b)
forecast for week 5 (f5) = f4 + alpha * ( actual 4 - f4)
= 23 + 0.2 * ( 28 - 23)
= 24
forecast for week 6 (f6) = f5 + alpha * ( actual 5 - f5)
= 24 + 0.2 * ( 30 - 24)
= 25.20
Similarly, calculated for all weeks.
Day Number sold 2 yr. moving avg. 1 25 2 31 3 29 28 4 33 30 5 34 31 6 37 33.5 7 35 35.5 8 32 36 9 38 33.5 10 40 35 11 37 39 12 32 38.5Related Questions
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