OPRE 6302 on 20 March 2008 - The University of Texas at Dallas

Q3. UT Drill is a drill bit producer established by some UTD MBA students. UT Drill buys 5 cm long blank drill
bits and shapes them with drill patterns (like twist, masonry, lip, spur) by using a lathe. Then UT Drill packages
12 different drills in to a single box and sells them to the Lowe’s Home Improvement stores in Texas. UT Drill
requires 3000 blank drill bits every month and buys each bit at $0.05 and each box at $0.60. It costs $12 UTD
Drill to initiate an order from any of its suppliers. The holding costs are based on an annual interest rate of 12%.
[8pts] a) Determine the optimal number of drill bits that UT Drill should purchase and the time between these
purchases.
ANSWER: R= 3000/month. P = ∞. K=1200 cents. h = 5(0.01) = 0.05 cents. Then
2KR
EOQ =
h
=
2 · 1200 · 3000
=
0.05
√ 2 · 1200 · 3000 · 20 = √ 2 · 12 · 3 · 2 ∗ 1000 = 12, 000.
Time between orders is
Length of an Inventory Cycle = Q/R = 12000/3000 = 4 months.
[4pts] b) What is the annual holding and ordering cost for blank drill bits?
ANSWER:
Total monthly cost = C(Q = EOQ; P = ∞) =
1
EOQ h
2
+
KR
EOQ
Inventory holding cost per month Set up cost per month
= 1
1200 · 3000
12000 · 0.05 +
2 12000
= 300 + 300 = 600 cents,
or since optimal order is used, Total monthly cost= √ 2KRh = √ 2 · 1200 · 3000 · 0.05 = √ 1200 · 300 = √ 36 · 100 =
600. Then the annual cost is $72= 6 · 12.
[4pts] c) Determine the optimal number of package boxes that UT Drill should purchase.
ANSWER: R= 3000/12 per month. P = ∞. K=1200 cents. h = 60(0.01) = 12 · 0.05 cents. Then
EOQ =
2KR
h
=
2 · 1200 · 3000/12
12 · 0.05
= 1 √
2 · 1200 · 3000 · 20 =
12
1 √
2 · 12 · 3 · 2 ∗ 1000 = 1, 000.
12
[4pts] d) The forecaster at UT Drill has made a mistake in computing the monthly blank drill bit demand which
is actually 5000 per month. What is the annual holding and ordering cost for blank drill bits when the purchase
quantity in a) is used with the correct demand of 5000 per month? Basically, update your computations in b).
ANSWER:
Total monthly cost = C(Q = EOQ; P = ∞) =
1
EOQ h
2
+
KR
EOQ
Inventory holding cost per month Set up cost per month
= 1
1200 · 5000
12000 · 0.05 +
2 12000
= 300 + 500 = 800 cents.
Then the annual cost is $96= 8 · 12. Note that here we are computing the cost of ordering suboptimally in 12000
units. The formula √ 2KRh cannot be used when the order quantity is suboptimal.