Case Study 4: Due February 26, 2013
1. Problem 8 on p 309 of the tex parts a and b only.
2. Economic Order Quantity with Defects
In An economic order quantity model with defective items and shortages by Eroglu and
Azdemir, (International Journal of Production Economics, Vol XXXXXXXXXX)), the authors
investigate the EOQ model in which 100% of the items received are not perfect. In it,
they de ne the following:
D demand rate in units per time h holding cost/unit/unit time
y order size for each cycle backorder cost/unit/unit time
w maximum backorder level allowed percentage of scrap items
in the defective items
k xed order cost x screening rate in units per time
c unit variable cost d unit screening cost
p percentage of defective items in y t1 time to build up a backorder
level of w units
s unit selling price of good items t2 time to eliminate the
backorder level of t2 units
v unit selling price of t3 time to screen y units per cycle
imperfect quality items v
cs unit disposal cost for scrap items t cycle length
In their model, the expected total pro t per unit time is given as
E(TPU) = sD+
vD(1 ?? )E(p)
E1
??
D(c + d + csE(p))
E1
??
kD
yE1
??
hE4y
2E1
+hw??
(h + )E2w2
2yE1
where,
E1 = 1 ?? E(p)
E2 = E(
1 ?? p
1 ?? p ?? D=x
)
E3 = E((1 ?? p ?? D=x)2)E4 =
D(2 ?? D=x)
x
+ E3
Given a company orders a product and expects the defective fraction, E(p), to be
5%. Demand is 15,000 units annually and they screen at a rate of 60,000 units annually
(think of this as the QC check which is done much quicker than demand arrives). Order
cost is $400 per order, holding cost per year is $4 per unit and shortage cost per year is
$6 per unit. Unit purchase, screening and disposal costs are $35, $1 and $2, respectively.
Selling price of good items is $60 and sell price of imperfect items is $25. The portion of
1
scrap items in the defective items is 20% (so that the portion of scrap items in lot size y
is XXXXXXXXXXy).
Optimum order quantity is given as
y =
r
2kD(h + )
h
and optimum maximum backorder allowed is
w =
hy
h +
ASSIGNMENT:
a)Calculate the expected total pro t per unit.
b)What is the e ect of di erent defective rates on optimal order quantity, backorder
quantity and expected total pro t per unit? Please display your results graphically as
well as a brief description.
2