Problem Set 4 Day 6-­‐Questions Questions 1. Consider the following information for inventory management. The item is demanded
50
weeks a year.
Item Cost
Order Cost
Annual holding cost (%)
Lead time
Annual Demand
$10.00
$250.00
33% of item cost
1 week
25,750
(a) State the order quantity and reorder point.
(b) Determine the annual holding and order costs.
ANSWER:
C = 10
S = 250
H = (.33) · C = 3.3
D = 25, 750
LT = 1/50 = 0.02
𝐸𝑂𝑄 =
(a)
!!"
!
= 1975.2
ROP = D · LT = 515
(b)
Annual Holding Cost
=
=
!"#
!
!"#
!
+ 𝐷 ∙ 𝐿𝑇 ∙ 𝐻 = 1502.6 ∙ 3.3 = 4958.6 if the buyer pays upon shipment
∙ 𝐻 = 987.6 ∙ 3.3 = 3259.1 if the buyer pays upon receipt
Annual Fixed Cost=(D/EOQ)xS=(13.0)(250)=3259.1
2. Quarter-inch stainless-steel bolts are consumed in a factory at a fairly steady rate of 60
per week. The bolts cost the plant two cents each. It costs the plant $12 to initiate an
order, and holding costs are based on an annual interest rate of 25 percent.
(a) Determine the optimal number of bolts for the plant to purchase and the time between
placement of orders.
(b) What is the yearly holding and setup cost for this item?
1 ANSWER
D = (60)(52) per year. S = 12. H = (0.02)(0.25).
(a) Optimal order Quantity
2𝑆𝐷
= 3869.9
𝐻
𝑞=
!
!
Frequency: !"# = 𝐷 ∙
!!"
= !"
!!
= 0.806 𝑡𝑖𝑚𝑒𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
Thus the order interval is the inverse of frequency, which is 1.24 times per year
(b)
Annual Holding Cost=(Q/2)H=9.67
Annual Order Cost=(frequency)S=9.67
3. Reconsider the bolt example in Question 2. Suppose that although we have estimated
demand to be 60 per week, it turns out that it is actually 120 per week (i.e., we have a 100
percent forecasting error).
(a) If we use the lot size calculated in the previous problem (i.e., using the erroneous
demand estimate), what will the setup plus holding cost be under the true demand
rate?
(b) What would the cost be if we had used the optimum lot size?
(b) What percentage increase in cost was caused by the 100 percent demand
forecasting error? What does this tell you about the sensitivity of the EOQ model
to errors in the data?
ANSWER:
(a) Let Q = 3869.9. Now let D = (120)(52) = 6240. Then, the ordering frequency is
D/Q = 1.61 times a year.
Annual Holding Cost = Q/2 · H = 9.67
Annual Order Cost = (frequency) · S = 19.34
Thus total cost is 29.02
(b) Here 𝐸𝑂𝑄 =
!!"
!
= 5472.8
2 Annual Holding Cost = EOQ/2 · H = 13.68
Annual Order Cost = D/EOQ · S = 13.68
Thus, the total cost is 27.36.
(c) Percentage increase = (29.02 − 27.36)/27.36 = 6.07%.
Thus, the EOQ model is pretty robust and still performs well
3