CHAPTER 13: Role of Inventory Management
1. The Goodstone Tire Company produces a brand of tire called the Rainpath. The annual demand at its
distribution center is 12,400 tires per year. The transport and handling costs are $2600 each time a
shipment of tires is ordered at the distribution center. The annual carrying cost is $3.75 per tire.
a. Determine the optimal order quantity and the minimum total annual cost.
b. The company is thinking about relocating its distribution center, which would reduce transport and
handling costs to $1900 per order but increase carrying costs to $4.50 per tire per year. Should the
company relocate based on inventory costs?
2. The Olde Town Microbrewery makes Townside beer, which it bottles and sells in its adjoining
restaurant and by the case. It costs $1700 to set up, brew, and bottle a batch of the beer. The annual
cost to store the beer in inventory is $1.25 per bottle. The annual demand for the beer is 21,000 bottles
and the brewery has the capacity to produce 30,000 bottles annually.
a. Determine the optimal order quantity, total annual inventory cost, the number of production runs per
year, and the maximum inventory level.
b. If the microbrewery has only enough storage space to hold a maximum of 2500 bottles of beer in
inventory, how will that affect total inventory costs?
3. The bookstore at Tech purchases jackets emblazoned with the school name and logo from a vendor.
The vendor sells the jackets to the store for $38 apiece. The cost to the bookstore for placing an order is
$120, and the annual carrying cost is 25% of the cost of a jacket. The bookstore manager estimates that
1700 jackets will be sold during the year. The vendor has offered the bookstore the following volume
discount schedule:
What is the bookstore’s optimal order quantity, given this quantity discount information?
4. Determine the optimal order quantity of jackets and total annual cost in Problem 13-23 if the carrying
cost is a constant $8 per jacket per year.
5. The weekly demand for a company’s product follows the probability distribution below:
Weekly Demand
Probability
100
0.20
125
0.15
150
0.40
175
0.25
a. Determine the expected value, or average, weekly demand.
b. Use the following random numbers to simulate the product’s demand for the next five weeks: 72, 27,
93, 17, 47.
i. If the first random number interval begins with 1. Determine the total demand for the simulated five
week period.
ii. If the first random number interval begins with 1. Determine the average weekly demand for the
simulated five week period.
Solutions
1.
a.
D  12, 400
Cc  $3.75
Co  $2,600
2  2, 600 12, 400 
2Co D

 4146.6
Cc
3.75
Q
TC 

Co D CcQ

Q
2
 2, 60012, 400
4,912.03
 $15,549.92
b. Co  $1,900

 3.75 4,912.03
2
Cc  $4.50
Q
TC 

2 1,900 12, 400 
2Co D

 3235.9
Cc
4.50
Co D CcQ

Q
2
1,90012, 400 
3,833.19
 14,561.59

 4.50 3,833.19 
2
Select the new location.
2.
Co  $1, 700
Cc  $1.25
D  21, 000 / yr.
P  30, 000 / yr.
a.
Q
2 1, 700  21, 000 
 13, 798.55
 21, 000 
1.25 1 

 30, 000 
1, 700  21, 000   1.25  13, 798.55   1  21, 000 
TC 



13, 798.55
2

  30, 000 
 5,174.46
D
21, 000
Number of production runs  
 1.52
Q 11, 062.62
 d
Maximum inventory level  Q 1  
p

 21, 000 
 13, 798.55 1 

 30, 000 
 4,139.57
b. Maximum inventory level  2,500
3.
 21, 000 
2,500  Q 1 

 30, 000 
2,500  Q .3
Q  8,333.33
1,700 21,000  1.25  8,333.33  1  .70
TC 



8,333.33
2


 $5,846.50
D  1, 700
Co  $120
Cc   0.25 $38  $9.50
Q
2 120 1, 700 
2Co D

 207
Cc
 9.5
120 1, 700    9.50  207  
 381, 700 
207
2
 $66,568.76
Q  300 :
120 1, 700   9.31 300  37.24 1, 700
TC 



300
2
 $65,384.80
Q  500 :
120 1, 700   9.12  500  36.48 1, 700
TC 



500
2
 $64, 704
Q  800 :
120 1, 700    9.025 800  36.10 1, 700
TC 



800
2
 $65, 235
Select Q  500; TC  $64, 704.
TC 
4.
Q
TC 
2 120 1, 700 
8
 226
120 1, 700   8 226  
226
 $66, 406.65
Q  300 :
2
 381, 700 
120 1, 700   8300  
 37.24 1, 700 
300
2
 $65,188
Q  500 :
120 1, 700   8500   36.48 1, 700
TC 



500
2
 $64, 424
Q  800 :
120 1, 700   8800   36.10 1, 700
TC 



800
2
 $64,825
Select Q  500; TC  $64, 424.
TC 
5.
a.
b.
i.
ii.
142.50.
700
140