Last Name ______________________ First Name _________________________ ID ___________________________
Operations Management II 73-431 Winter 2008
Odette School of Business
University of Windsor
Midterm Exam II Solution
Thursday, January 31, 2:30 pm – 3:50 pm
Odette Building OB B04
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 min
Instructions:
 This exam has 20 pages including this cover page, four bank pages and 8 pages of tables.
 Please be sure to put your name and student ID number on each odd numbered page.
 Show your work.
 State results up to four decimal places.
 Do not return tables and formula sheet.
Grading:
Question
Marks:
1
/10
2
/13
3
/16
4
/13
5
/13
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (10 points) Circle the most appropriate answer
1.1 (i) Functional products include the staples that people buy in a wide range of retail outlets such as
grocery stores and gas stations. (ii) We should match functional products with a responsive
supply chain.
a. (i) true (ii) false
b. (i) false (ii) true
c. Both true
d. Both false
1.2 (i) Supply chain includes suppliers and their supplier, manufacturers and their manufacturers. (ii)
The Supply-Chain Management includes managing information, materials and services from rawmaterials suppliers through factories and warehouses to the end customer.
a. (i) true (ii) false
b. (i) false (ii) true
c. Both true
d. Both false
1.3 Suppose that the locations of warehouse = (0,0), customer 1 = (3,0) and customer 2 = (0,4).
What is savings (1,2)?
a. 2 Correct choice
b. 3
c. 4
d. 5
1.4 (i) Saving matrix method guarantees an optimal solution. (ii) Nearest neighbor method
guarantees an optimal solution.
a. (i) true (ii) false
b. (i) false (ii) true
c. Both true
d. Both false
1.5 For which of the following a single period model is the most appropriate?
a. pen
b. pencil
c. paper
d. computer
1.6 Suppose that cu  40 and co  80. If demand is Normally distributed with mean  , the order size
a. Q   Correct choice
b. Q  
c. Q  
d. Non of the above
2
Name:_________________________________________________
ID:_________________________
1.7 Notation n used to denote the expected number of units stock-out per
a. cycle or order
b. order or period
c. period or cycle
d. year
1.8 Consider the iterative procedure used to find an optimal Q, R  policy without service. The
iterative procedure stops when
a. Q  Q '
b. R  R'
c. Both
d. None
1.9 Type 2 service is
a. the proportion of demand not met from stock
b. the proportion of demand met from stock
c. the probability of no stockout
d. the probability of stockout?
1.10 Consider the procedure used to find an optimal Q, R  policy with Type I service. The optimal
order size
a. Q  EOQ
b. Q  EOQ
c. Q  EOQ
d. None of the above
Question 2: (13 points)
A large national producer of canned foods plans to purchase a combine that will be customized for
its needs. One of the parts used in the combine is a replaceable blade for harvesting corn. Spare
blades can be purchased at the time the order is placed for $130 each, but will cost $530 each if
purchased at a later time because a special production run will be required. It is estimated that the
number of replacement blades required by the combine over its useful lifetime can be closely
approximated by a normal distribution with mean 20 and standard deviation 5. The combine maker
agrees to buy back unused blades for $30 each. How many spare blades should the company
purchase with the combine?
cu  530-130=$400
a. (2 points) Compute the underage cost
co  130-30=$100
b. (2 points) Compute the overage cost
c. (6 points) How many spare blades should the company purchase with the combine?
cu
400
p

 0.8 , z  0.845, Q    z  20+0.84(5)=24.2
cu  co 400  100
d. (3 points) How would you change your answer to part c if the company purchases 4 combines?
How many spare blades should the company purchase with 4 combines?
 '  20(4)=80,  ' 5 4 =10, Q'   ' z '  80+0.84(10)=88.4
3
Name:_________________________________________________
ID:_________________________
Question 3: (16 points)
An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One
particular part, a popular brand of oil filter, is purchased by the warehouse for $3 each. It is estimated
that the cost of order processing and receipt is $25 per order. The company uses an inventory
carrying charge based on a 20 percent annual interest rate. The monthly demand for the filter follows
a normal distribution with mean 200 and standard deviation 25. Order lead time is assumed to be
four months. Assume that if a filter is demanded when the warehouse is out of stock, then the
demand is back-ordered, and the cost assessed for each back-ordered demand is $1.00. Determine
the average annual cost of holding, setup, and stock-out associated with this item assuming
Q  600, R  900.
  200(12)=2400,   200(4)=800,   25 4  50, h  Ic  0.20(3)=$0.60/unit/year
a. (4 points) Compute the average annual holding cost.
Q
600
h  R   h 
(0.60)+(900-800)(0.60)=180+60=$240
2
2
b. (2 points) Compute the average annual setup cost.
K 25(2400)

 $100
Q
600
c. (4 points) Compute the average annual stock-out cost.
R
900  800
 2, n  Lz   50(0.0085)=0.425

50
np 0.425(2400)1

 1.70
Q
600
z

d. (4 points) Compute the probability(no stock-out)
F z   0.9772
e. (2 points) Compute the fill rate (up to four decimal places)
  1
n
0.425
 1
 0.9993
Q
600
4
Name:_________________________________________________
ID:_________________________
Question 4: (13 points)
Consider Question 3 again. Find an Optimal Q, R  policy assuming no service constraint.
Iteration 1
2 K
2(25)( 2400)

 447.21
h
0.60
Qh 447.21(0.60)
Step 2: 1  F ( z ) 

 0.1118
p
1(2400)
z  1.22 (Table A-4)
R    z  800+1.22(50)=861
Step 3: L (z )  0.0538 (Table A-4)
n  L(z )  50(0.0538) = 2.69
Step 1: Q  EOQ 
2
np  K   2(2400) 2.69(1)  25  470.66 (not near 447.21, more iterations needed)
h
0.60
Qh 470.66(0.60)
Step 5: 1  F ( z ) 

 0.1177
p
1(2400)
z  1.185 (Table A-4)
R    z  800+1.185(50)=859.25
Step 4: Q 
Iteration 2
Step 3: L (z )  0.05785 (Table A-4)
n  L(z )  50(0.05785) = 2.8925
2
np  K   2(2400) 2.8925(1)  25  472.38 (near 470.6, may stop after finding R )
h
0.60
Qh 472.38(0.60)
Step 5: 1  F ( z ) 

 0.1181
p
1(2400)
z  1.185 (Table A-4)
R    z  800+1.185(50)=859.25
Step 4: Q 
Q and R converge. An optimal policy is Q=472 units, R=859 units
Question 5: (13 points)
The manager at Albertson’s, a grocery store selling on-line, has 5 orders that are to be delivered to
customers. The location and order size for each customer are shown below:
Warehouse
Customer 1
Customer 2
Customer 3
Customer 4
Customer 5
X-coordinate
0
0
7
2
4
9
Y-coordinate
0
5
1
10
5
2
5
Order size
50
60
70
80
40
Name:_________________________________________________
ID:_________________________
The Albertson’s fulfillment store has two trucks, each capable of carrying upto 220 units. Using the
savings matrix and nearest neighbor methods devise a suitable delivery schedule. If there is any
route that intersects itself, improve the route. State the route of each vehicle.
The distance matrix is shown below:
W
C1
C2
C3
C4
C5
W
0
C1
C2
C3
C4
C5
0
0
0
0
0
The savings matrix is shown below:
C1
C1
C2
C3
C4
C5
C2
C3
C4
C5
0
0
0
0
0
Rank savings: (2,5), (3,4), (1,3), …
Grouping: Vehicle 1: Vehicle 1: (2,5), Vehicle 2: (1,3,4)
Nearest neighbour tours: W-2-5-W, W-1-4-3-W (contains intersection, see plot below)
3
1
4
5
2
W
Eliminate intersection:
1. Remove (1,4), (3,W)
2. Reverse (4,3)
3. Add (1,3), (4,W)
Intersection free tours: W-2-5-W, W-1-3-4-W
6