Name (print, please) _______________________________________________ ID ___________________________
Operations Management I 73-331 Fall 2001
Faculty of Business Administration
University of Windsor
Midterm Exam II Solution
Wednesday, November 21, 5:30 – 6:50 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 min
Instructions:
 This exam has 11 pages including this cover page and 2 pages of tables.
 Please be sure to put your name and student ID number on each page.
 Show your work.
Grading:
Question
Marks:
1
/15
2
/10
3
/10
4
/10
5
/10
6
/20
Total:
/75
Name:_________________________________________________
ID:_________________________
Question 1: (1 point  15 questions = 15 points)
1.1 The following are the two major inventory control decisions:
a. how to count and when to count
b. how much to order and when to order
c. how to estimate holding/ordering/stock-out costs and when to compute EOQ
d. how to estimate holding/ordering/stock-out costs and when to compute EPQ
1.2 The loss of profit resulting from ordering less than the demand is a part of
a. holding cost
b. ordering cost
c. setup cost
d. stock-out cost
e. none of the above
1.3 The EOQ model assumes that the on-hand inventory level increases
a. instantaneously from zero to Q at time t  0
b. at the rate P at time t  0
c. at the rate P   at time t  0
d. at the rate   P at time t  0
1.4 The EPQ model assumes that the on-hand inventory level increases
a. instantaneously from zero to Q at time t  0
b. at the rate P at time t  0
c. at the rate P   at time t  0
d. at the rate   P at time t  0
1.5 The annual holding cost is the same as the annual ordering cost
a. for any order quantity
b. for Q  EOQ, but not for Q  EPQ
c. for Q  EPQ, but not for Q  EOQ
d. for Q  EOQ and for Q  EPQ
1.6 The total annual holding and setup costs are ______________ to changes in order quantity for
Q  EOQ
a. sensitive
b. insensitive
c. none of the above
1.7 The total annual holding and setup costs are ______________ to changes in order quantity for
Q  EPQ
a. sensitive
b. insensitive
c. none of the above
2
Name:_________________________________________________
ID:_________________________
1.8 The rotation cycle policy
a. is applicable when the budget is limited
b. is applicable when space is limited
c. is assumed when several products are produced in a single facility
1.9 The rotation cycle policy
a. assumes that in each production cycle there is only one setup for each product, and
the products are produced in the same sequence in each production cycle
2K i  i
b. dictates that Qi* 
for the i -th product when the space is limited
hi  2wi
c. dictates that Qi*  mEOQi for the i -th product when the budget is limited
1.10
a.
b.
c.
In a single-period inventory model it is assumed that the ending inventory
is salvaged
is salvaged and transferred to the next period
of one period is the beginning inventory of the next period
1.11
a.
b.
c.
In a multi-period inventory model it is assumed that the ending inventory
is salvaged
is salvaged and transferred to the next period
of one period is the beginning inventory of the next period
1.12 If the shortages are back-ordered, then the annual number of units purchased does not
depend on Q, R 
a. True
b. False
1.13
a.
b.
c.
d.
What is reorder level?
The time between arrival of successive orders
The time between placing order and arrival of the order
The number of units ordered
The number of units on hand when the order is placed
1.14
a.
b.
c.
The standardized loss function is denoted by
F z 
z 
L(z)
1.15 The standardized loss function is used to compute
a. the probability of not stocking out during the lead time
b. the proportion of demands that are met from the stock
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Name:_________________________________________________
ID:_________________________
Question 2: (10 points)
Suppose that Item A has a unit cost of $10.00, an ordering cost of $50, and a monthly demand of 25
units. It is estimated that cost of capital is approximately 25 percent per year. Storage cost amounts
to 3 percent and breakage to 2 percent of the value of the each item.
a. (2 points) Compute holding cost per unit per year.
I  0.25  0.03  0.02  0.30
h  Ic  0.3010  $3 per unit per year
b. (2 points) Compute annual demand.
  2512  300 units per year
c. (3 points) Compute EOQ of Item A.
EOQ=
2 K

h
250300
 100 units
3
d. (3 points) Suppose that both Items A and B should be purchased and there is only $1800
available for buying Items A and B. The unit cost of Item B is $5 and the EOQ of Item B is 200
units. What is the optimal order quantity of Item A?
Fund required by the EOQ order quantity of Item A = 100(10) = $1000
Fund required by the EOQ order quantity of Item B = 200(5) = $1000
Total fund required by the EOQ order quantities of Items A and B = 1000+1000 = $2,000 (1 point)
Fund available = $1,800
Hence, m =
fund available
1,800

 0.90 (1 point)
fund required
2,000
Therefore, the optimal order quantity of Item A = m  EOQA = 0.90(100) = 90 units (1 point)
4
Name:_________________________________________________
ID:_________________________
Question 3: (10 points)
Suppose that Item A has a production rate of 400 items per year. The cost and demand information
of Item A are the same as those stated in Question 2. That is, Item A has a unit cost of $10.00, an
ordering cost of $50, and a monthly demand of 25 units. It is estimated that cost of capital is
approximately 25 percent per year. Storage cost amounts to 3 percent and breakage to 2 percent of
the value of the each item.
a. (2 points) Compute EPQ of Item A.
EOQ=
2 K

h'
2 K

 
h1  
 P
250300
 200 units
 300 
31 

 400 
b. (2 points) What is the cycle time of Item A?
T
Q* EPQ 200


 0.6667 years


300
Item C has a production rate of 2400 items per year, a unit cost of $20.00, an ordering cost of $75,
and a monthly demand of 40 units.
c. (4 points) What is the cycle time if both Items A and C are produced in a single facility?
T* 


2 K j
 h'
j
j

2K1  K 2 

h'1 1  h'2  2
250  75

 2 
 300 
31 
300  Ic2 1   2
P2 
 400 

2125

0.75  300  4.8  480
250  75
  
  
h1 1  1 1  h2 1  2  2
P1 
P2 


250  75
480 

 300 
31 
480
300  0.30201 
 400 
 2,400 
250

225  2,304
250
= 0.3144 years
2,529
d. (2 point) What is the optimal order quantity of Item A?
Q*  T *  0.3144300  94.322 units
5
Name:_________________________________________________
ID:_________________________
Question 4: (10 points)
Irwin sells a particular model of fan, with most of the sales being made in the summer months. Irwin
makes a one-time purchase of the fans prior to each summer season at a cost of $30 each and sells
each fan for $50. Any fans unsold at the end of summer season are marked down to $20 and sold in
a special fall sale.
a. (2 points) What is the underage cost per unit?
cu  Selling price – purchase price = 50-30 = $20/unit
b. (2 points) What is the overage cost per unit?
co  Purchase price – salvage value = 30-20 = $10/unit
c. (3 points) If the demand is uniformly distributed between 200 and 800 units, find the optimal order
quantity.
For the optimal order quantity Q , Probability(demand  Q ), p 
cu
20

 0.6667
cu  co 20  10
Hence, Q*  a  pb  a   200  0.6667800  200  600 units
d. (3 points) If the demand is normally distributed with a mean of 500 and a standard deviation of
100, find the optimal order quantity.
For the optimal order quantity Q , Probability(demand  Q ), p 
cu
20

 0.6667
cu  co 20  10
Find the standard normal z -value for which cumulative area on the left, F z   0.6667 . (1 point)
Since Table A-1 gives area between z  0 and positive z -values, find z -value for which Table A-1
area is 0.6667-0.50 = 0.1667. Hence, z  0.43 (1 point)
Q*    z  500  0.43  100  543 units (1 point)
6
Name:_________________________________________________
ID:_________________________
Question 5: (10 points)
Comptek Computers wants to reduce a large stock of personal computers it is discontinuing. It has
offered the University Bookstore a quantity discount pricing schedule if the store will purchase the
personal computers in volume, as follows:
Quantity
Price
1-9
$940
10-49
920
50+
900
The annual inventory holding cost is 20%, the ordering cost is $150, and annual demand for this
particular model is estimated to be 120 units. Compute the optimal order size.

First, consider the cheapest price level of c3  $900 per unit. h3  Ic3  0.20  900  $180 /unit/year
EOQ3 
2 K

h3
2150120
 14.142 units (1 point for EOQ computation)
180
Since the price level of c3  $900 is not available for an order quantity Q  EOQ3 = 14.142 units,
EOQ3 is infeasible and a candidate for optimal order quantity is Q3  50 , because 50 is the
minimum order quantity for the price level of c3  $900 (1 point)

Now, consider the next price level, c2  $920 per unit. h2  Ic2  0.20  920  $184 /unit/year
EOQ2 
2 K

h2
2150120
 13.988
184
Since the price level of c2  $920 is available for an order quantity Q  EOQ2 = 13.988 units,
EOQ2 is feasible and a candidate for optimal order quantity is Q2  13.988  14. (1 point)

It’s not necessary to consider the other price level.

Now, compute total cost for each candidate for optimal order quantity:
j
3
(1 point)
(1 point)
(1 point)
(1 point)
Candidate
Holding cost
Ordering cost
Cost of item
Total cost
Qj
h jQ j
c j
2
K
Qj
Holding cost +
Ordering cost +
Cost of item
180  50
 4,500
2
150  120
 360
50
900  120  108,000
$112,860
184  14
 1,288
2
150  120
 1,285.7
14
920  120  110,400
$112,973.71
Q3  50
(1 point)
2
Q2  13.988
(1 point)

Conclusion: The total cost is minimum, $112,860 for Q3  50 . Therefore, an optimal order
quantity is Q3  50 . (1 point)
7
Name:_________________________________________________
ID:_________________________
Question 6: (20 points)
The home appliance department of a large department store is using a lot size-reorder point system
to control the replenishment of a particular model of FM table radio. The store sells an average of
600 radios each year. The annual demand follows a normal distribution with a standard deviation of
50. The store pays $25 for each radio, which it sells for $70. The holding cost is 30 percent per year.
Fixed costs of replenishment amount to $250. If a customer demands the radio when it is out of
stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about
$15 per radio. Replenishment lead time is three months. Currently, the store is using Q  210 and
R  190 . Compute
a. (2 points) the mean and standard deviation of the lead time demand

3
3
3
 0.25 years,     600  150 units, (1 point)      50
 25 units (1 point)
12
12
12
b. (1 point) the annual holding cost per unit
h  Ic  0.3  25  $7.5 per unit per year
c. (1 point) the stock-out cost per unit
p = loss of profit + good will = (70-25) +15 =$60 per unit
d. (1 point) the safety stock
R    190  150  40 units
e. (3 points) the expected number of units stock-out per cycle
z
R   190  150

 1.6 (1 point)

25
Lz   0.0232 (1 point)
n  Lz   250.0232  0.58 units per cycle (1 point)
(Continued…)
8
Name:_________________________________________________
ID:_________________________
f. (2 points) the annual holding cost
hQ
7.5  210
 h R    
 7.5190  150  787.50  300  $1,087.50 (1 point for each part)
2
2
g. (2 points) the annual ordering cost
K 250  600

 $714.29
Q
210
h. (2 points) the annual stock-out cost
np 0.58  60  600

 $99.43
Q
210
i.
(1 point) the total annual holding, ordering and stock-out cost
1,087.50  714.29  99.43  $1,901.22
j.
(3 points) the probability of not stocking out during the lead time
z
R   190  150

 1.6 (1 point)

25
Table A-4: The probability of not stocking out during the lead time = F z  1.6
= 0.9460
Table A-1: The probability of not stocking out during the lead time
= the area on the left of z  1.6 (1 point)
= P   z  1.6  P   z  0  P0  z  1.6
= 0.50  P0  z  1.6  0.5  0.4452  0.9452 (1 point)
k. (2 points) the fill rate, up to four decimal places
  1
n
0.58
 1
 0.9972  99.72%
Q
210
9