Assignment 4: Part (A)
Problem 1: A toy manufacturer uses approximately 32000 silicon chips
annually. The Chips are used at a steady rate during the 240 days a year
that the plant operates. Annual holding cost is 60 cents per chip, and
ordering cost is $24. Determine
a) How much should we order each time to minimize our total cost
b) How many times should we order
c) what is the length of an order cycle (working days 288/year)
d) What is the total cost
What is the Optimal Order Quantity
2 DS
EOQ 
H
D = 32000, H = .6, S = 24
2(32000)( 24)
EOQ 
 1600
.6
How many times should we order
Annual demand for a product is 9600
D = 32000
Economic Order Quantity is 1600
EOQ = 1600
Each time we order EOQ
How many times should we order ?
D/EOQ
32000/1600 = 20
what is the length of an order cycle
working days = 240/year
32000 is required for 240 days
1600 is enough for how many days?
(1600/32000)(240) = 12 days
What is the Optimal Total Cost
The total cost of any policy is computed as
TC  (Q / 2) H  ( D / Q ) S
The economic order quantity is 1600
TC  .6(1600 / 2)  24(32000 / 1600)
TC  480  480
TC  960
This is the total cost of the optimal policy
Assignment 4: Part (B)
A small manufacturing firm uses approximately 3400 pounds of
chemical dye per year. Currently the firm purchases 300 pounds per
order and pays $3 per pound.
The ordering cost is $100 and inventory carrying cost is 51 cents per unit
per year.
D= 3400, S= 100, H=.51
a) The supplier has just announced that orders of 1000 pounds and more
will be filled at a price of $2 per pound. Determine the order size that
will minimizes the total cost.
b) If the supplier offered a discount at 1500 pounds instead of 1000
pounds, what order size will minimize total cost?
Ordering and Carrying Costs
Annual Cost
The Total-Cost Curve is U-Shaped
Q
R
TC  H  S
2
Q
Ordering Costs
QO (optimal order quantity) Order Quantity
(Q)
Cost
Total Cost
Adding Purchasing cost
doesn’t change EOQ
TC with PR
TC without PR
PR
0
EOQ
Quantity
Cost
Price Discount
p1
p2
0
Quantity
Cost
Total Cost Including Purchasing Cost
p1
p2
0
EOQ
Quantity
Cost
Total Cost Including Purchasing Cost
0
EOQ
Quantity
Cost
Total Cost Including Purchasing Cost
0
Q
Quantity
Cost
Total Cost Including Purchasing Cost
0
EOQ
Quantity
The Problem
A small manufacturing firm uses approximately 3400 pounds of
chemical dye per year. Currently the firm purchases 300 pounds per
order and pays $3 per pound.
The ordering cost is $100 and inventory carrying cost is 51 cents per unit
per year.
D=3400, S= 100, H=.51
a) The supplier has just announced that orders of 1000 pounds and more
will be filled at a price of $2 per pound.
2SD
2(100)(3400)
EOQ 

 1155
H
.51
Q
0-999
≥1000
P
3
2
The Problem
A small manufacturing firm uses approximately 3400 pounds of
chemical dye per year. Currently the firm purchases 300 pounds per
order and pays $3 per pound.
The ordering cost is $100 and inventory carrying cost is 51 cents per unit
per year.
D=3400, S= 100, H=.51
b) Determine the order size that will minimizes the total cost.
If the supplier offered a discount at 1500 pounds instead of 1000 pounds,
what order size will minimize total cost?
EOQ  1155
Q
0-...
≥1500
P
3
2
Assignment
b) If the supplier offered a discount at 1500 pounds instead of 1000
pounds, what order size will minimize total cost?
D= 3400, S=100, H= .51
EOQ  1155
Q
0-...
≥1500
P
3
2
TC = HQ/2 + SD/Q + PD
TC ( Q = 1155 , P = 3) = .51(1155)/2 + 100(3400)/1155 + 3(3400)
TC = 294.5 + 294.5 + 10200 = 10789
TC ( Q = 1500 , P = 2) = .51(1500)/2 + 100(3400)/1500 + 2(3400)
TC = 382.5+226.7 +6800 = 7409.2