Problem Set 4
Solve problems 5-12, 5-14, and 5-18. Save your responses in a Word file.
Develop a four-month moving average forecast for Wallace Garden Supply and compute the MAD. A three-month moving average forecast was developed in the section on moving averages in Table 5.3.
see attached for data
Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a three-year moving average to forecast sales. Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other two years are each given a weight of 1. Which method do you think is best?
Year Scale Fertilizer Demand
Sales of Cool-Man air conditioners have grown steadily during the past five years:
The sales manager had predicted, before the business started, that year 1's sales would be 410 air conditioners. Using exponential smoothing with a weight of 􏰅 = 0.30, develop forecasts for years 2 through 6
Problem Set 5
Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year.
(a) How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost? (b) How many orders per year would be placed?
What would the annual ordering cost be? (c) What would the average inventory be? What
would the annual holding cost be?
Attached in the file are the detailed step-by-step and guided instruction on solving the problems. Please study them and you can quickly answer similar management worded problems that you will encounter.
5-12 Four Month Moving average
Month Actual SHED Sales Four-month moving average
May 19 =(10+12+13+16)/4 12.75
June 23 =(12+13+16+19)/4 15.00
July 26 =(13+16+19+23)/4 17.75
August 30 =(16+19+23+26)/4 21.00
September 28 =(19+23+26+30)/4 24.50
October 18 =(23+26+30+28)/4 26.75
November 16 =(26+30+28+18)/4 25.50
December 14 =(30+28+18+16)/4 23.00
January =(28+18+16+14)/4 19.00
5-14 Three (3) period moving averages without Weights
Year Demand Formula Forecast Error Absolute error
4 5 (4+6+4)/3 4.67 0.33 0.33
5 10 (6+4+5)/3 5.00 5.00 5
6 8 (4+5+10)/3 6.33 1.67 1.67
7 7 ...
This solution contains step-by-step solution to forecasting problems and Economic Order Quantity (EOQ). The forecasting method discussed are the moving average with and without weights, and forecasting using exponential smoothing method.
Control charts, PERT network, Forecasting (using linear trend equation, moving average, Exponential smoothing, optimal order quantity
Problem 1. The perfect Circle Company manufactures bushings. Once each hour a sample of 125 finished bushings is drawn from the output; each bushing is examined by a technician. Those which fail are classified as defective; the rest are satisfactory. Here are data on ten consecutive samples taken in one week:
Sample no. 1 2 3 4 5 6 7 8 9 10
Defective 15 13 16 11 13 14 20 25 30 45
a. What type of control chart should be used here?
b. What is the centerline of the chart?
c. What is the lower and upper control limits (LCL and UCL) based on 99.7% confidence level?
d. What statistic should be plotted on the control chart?
e. Draw the control chart and plot using Excel.
f. Is this system under control?
g. What should the quality control engineer do?
Problem 2. A project consists of 8 activities, lettered A through H below. For each activity, the preceding activity is given, and a probabilistic estimate of the time required to complete it. Times are in days.
Preceding Optimistic Most Likely Pessimistic
Activity Activity Time Time Time
A -- 2 days 4 days 6 days
B A 3 6 9
C A 2 5 11
D -- 2 10 12
E C, 4 8 15
F B,E 2 4 12
G D 3 4 11
H F,G 1 1 1
a. Determine the expected time for each activity assuming it satisfies the beta distribution.
b. Determine the variance for each activity assuming beta distribution.
c. Draw the PERT network for this project, with the activities on the arrows.
d. List all possible paths through the network (from beginning to end).
e. What is the expected duration of each path?
f. What is the variance of each path?
g. What is the critical path(s) based on the expected durations?
h. What is the probability to finish the project in 17 days?
Problem 3. National Mixer, Inc., sells can openers. Monthly sales for a seven-month period were as follows:
Month (000 units)
Feb. . . . . . . . . . 19
Mar. . . . . . . . . . 18
Apr. . . . . . . . . 15
May . . . . . . . . . 20
Jun. . . . . . . . . . 18
Jul. . . . . . . . . . . 22
Aug. . . . . . . . . . 20
a. Plot the monthly data using Excel.
b. Forecast September sales volume using each of the following:
(1) A linear trend equation.
(2) A five-month moving average.
(3) Exponential smoothing with a smoothing constant equal to .20, assuming a February forecast of 19(000).
(4) The naïve approach.
(5) A weighted average using .60 for August, .30 for July, and .10 for June.
Problem 4. The manager of a car wash received a revised price list from the vendor who supplies soap, and the promise of a shorter lead time for deliveries. Formerly the lead time was four days, but now the vendor promises a 25% reduction in the lead time. Annual usage of soap is 4,500 gallons. The car wash is open 360 days a year. Assume that daily usage follows the normal distribution, and that it has a standard deviation of 2 gallons per day. The ordering cost is $30 and annual carrying cost is 25% of the purchasing price. The revised price list (cost per gallon) is shown in the table.
Quantity Unit Price
a. What order quantity is optimal?
b. What ROP is appropriate if the acceptable risk of a stockout is 1.5 percent?
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