Homework 4 | OPM 101 | Due Monday, April 7th, 2025
(Please submit your HW to CANVAS)
Full Name: ___ _______________________ CSUS Email: _____
_____________________________
****Show all work to get a chance for partial credit.
1. Find the file “OPM 101_Homework 4_Data” on CANVAS. This file contains 20 samples collected
from a cosmetic manufacturing line. The data indicates the skin sensitivity level to a hair color.
The Excel file also has the A2, D3, D4, and d2 table on the second sheet. Please write “see
attachment” in the answer space if you do graphics in Excel file and you want to attach it to
your homework. Please try to use Excel, otherwise you may have to do a lot of computation by
hand.
(a) Construct an X-bar chart for this manufacturing line:
16,0000
X-bar
14,0000
12,0000
10,0000
8,0000
6,0000
4,0000
2,0000
0,0000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
X-bar Chart
i. Is this process “in control”? ii. Do you notice any problems despite your answer to Part i?
___This process is in control because all of the data is inside the control limits meaning that
this process is stable. The process does fluctuate a bit and it seems like the process is going
below the lower control limit towards the end but, this shouldn’t be a problem because the
process stays within the control limits the whole
time._______________________________________________________________________
___________________________________________________________________________
(b) Construct an R-Chart for this manufacturing line:
R-bar
12,0000
10,0000
8,0000
6,0000
4,0000
2,0000
0,0000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
R-Chart
i. Is this process “in control”? ii. Based on your calculation for the X-Bar Chart and R-Chart,
compare your answers regarding the “in control” question? Do the charts result differently? Why
or Why Not?
_This process for represented by the R-bar chart is not in control. At points 14,17, and 20 the
process goes above the upper control limit and it seems like it continues to go up beyond point
20.__This process for the variability (range) is not in control as the process goes outside the
control limits. The last process for the mean, represented by the x bar chart was in control
because the process stayed in the control limits. Overall this would mean that the mean(X-bar)
is
stable
however
the
variability(R-bar)
is
not
stable.______________________________________________________________________
_
___________________________________________________________________________
___________________________________________________________________________
2. You have been the inventory manager at Malmart Distribution Center. You have estimated that
the annual demand for passenger car tires is 200,000 units. Placing an order costs $300. Cost
to hold a tire is $3 per year. Cost per tire is $70.
(a) How much (Q*) and how often do you need to order and fulfill the demand?
Demand (D) = 200000
Cost of placing order (S) = $300
Cost to hold order (H) = 3
Q* = sqrt (2DS)/H = 2* 200000 *300/ 3 = 6324.56
How often to order = T* = Q*/D
T*= 6324.56/ 200000 = .0316228 * 365 = 11.54 days
Q*: __6324.56_______ T*: ___11.54 days______
(b) At the end of your first year of managing, you realize that the demand is variable. However,
the average annual demand is still 200,000 with a standard deviation of 5.6 tires per day.
The tires supplier cannot deliver the products on the same day. The average lead time is
now 20 days with a standard deviation of 4.1 days. You consider a 95% Service Level to
satisfy customers. What is the Reorder Point (ROP)?
D= 200000/ 365 = 547.95 tires/day (D-bar)
L bar or e- bar = 20 days
σe= 4.1 days
Z score for 95 percent service level = 1.645 (ZSL)
ROP= 547.95 * 20 + 1.645√20 * 5.62 + 547.952 * 4.12 = 14654.88
ROP: ___14654.88______
(c) You also want to test OUT model. The review process, T, is 30 days. Assume that the onhand
inventory is 18,000 tires. What is the OUT inventory level and the Order Quantity (Q)?
(Hint: Use the information in Part b to find the value for the remaining parameters.)
T= 30 days
Average lead time (E-bar) =20 days
On hand inventory = 18000 tires
OUT = 547.95* (20 + 30) + 1.645 √(20 +30) * 5.62 + 547.952 * 4.12 = 31093.72
Q = OUT – on hand inventory = 31093.72 – 18000 =
OUT: _31093.72________Q: ____13093.72_____