For all the problems, to receive full score, you must show your complete and accurate work, i.e., show
how you calculated the numbers you use. If you only provide the final answers without computations,
you will not receive a full score even if the answer you provided is correct (and will miss the
opportunity of partial credits if your answer is not correct). The computations should show all the
steps you use. Note that, if you use Excel and Excel formulas/tools (e.g., average function or regression
tool in Data Analysis) to come up with solutions, your solution steps will be included in the Excel file.
The points from the bonus question in this homework will count towards your Homework 1 score.
Problem 1. (10 points)
A manager recorded the number of gallons of ice cream sold for the past six periods. He asked you to choose
a forecasting model to predict the demand for gallons of ice cream in Period 7. You consider applying a
two–period moving average model and a two–period weighted moving average model with weights of 0.6
and 0.4.
a) Which model is better for this data set (hint: show all your work including forecasts for each period and
calculations using measures of forecast accuracy)? (9 points)
b) What is the forecast of demand for period 7 considering the best model? (1 point)
Period Demand
1 650
2 700
3 810
4 800
5 900
6 700
Problem 2. (22 points)
An assembly line is to operate eight hours per day with a desired output of 240 units per day. The
following table contains information on this product’s task times and precedence relationships:
TASK
TASK TIME
(SECONDS)
IMMEDIATE
PREDECESSOR
A 75 —
B 48 A
C 40 A
D 40 A
E 27 B, C
F 48 C, D
G 72 E, F
H 90 G
a. Draw the precedence diagram. (5 points)
b. What is the workstation cycle time required to produce 240 units per day? (2 points)
c. Balance this line using the longest task time. Use largest number of following tasks as a secondary
(tiebreaker) rule. You need to show all the assignments to the workstations and the order in which
you assign tasks. (10 points)
d. What is the efficiency of your line? (5 points)
Problem 3. (18 points)
The following data were collected for 12 months using a company’s sales reports. The report shows, for
each month, the amount of money the company spent for advertising (x) and the amount of sales (y) made
after those advertising expenditures. Both the advertising and sales dollars are in units of thousand dollars.
The Chief Executive Officer of the company is interested in the impact of the advertising spending on the
actual sales.
Month x y
1 90 8,400
2 116 9,980
3 138 12,640
4 150 14,100
5 166 16,420
6 164 13,800
7 156 13,180
8 130 12,280
9 108 9,280
10 102 9,760
11 68 6,850
12 84 7,720
(a) Provide the scatter plot for advertising vs sales dollars with the trend line. (4 points)
(b) Obtain a linear regression line for the data. (Hint: You need to calculate a and b to get the linear
regression equation: y= a + bx) (8 points) You need to show all the work in Excel or manually
when you computed the line equation.
(c) Predict the sales figures in months 13 and 14 if the advertising budgets allocated for months 13
and 14 are $120,000 and $118,000, respectively. (6 points)
Bonus Problem (6 points) (Bonus points will be added to your homework score).
a) A supplier of instrument gauge clusters uses a Kanban system to control material flow. The gauge cluster
housings are transported five at a time. A fabrication center produces approximately 18 gauges per hour.
It takes approximately two hours for the housing to be replenished. Due to variations in processing times,
management has decided to keep 35 percent of the needed inventory as safety stock. How many Kanban
card sets are needed? (3 points)
b) Transmissions are delivered to the fabrication line six at a time. It takes 180 minutes for transmissions
to be delivered. Approximately eighteen vehicles are produced each hour, and management has decided
that 20 percent of expected demand should be maintained as safety stock. How many Kanban card sets
are needed? (3 points)