ch 12 solution

(c)
D 2500
Number of orders 10
orders /y ear
Q 250
D
Annual order cost S 10(18.75) $187.50
Q
Q D
(d) TC H S 187.50 187.50 $375/ year
2 Q
(e)
working days
Time between orders
( DQ / )
250
25 days
10
(f) ROP dL 10(2) 20 units (where 10 daily demand)
2500
d 10
250
DS QH
12.14 (a) Total cost order cost + holding cost
Q 2
1,200 252524 For Q 25: $1,500
25 2
1,200 254024 For Q 40: $1,230
40 2
1,200 25 50 24
For Q 50: $1,200
50 2
1,200 25 60 24
For Q 60: $1,220
60 2
1,200 25 100 24
For Q 100: $1,500
100 2
As expected, small variations in order quantity will
not have a significant effect on total costs.
(b) Economic Order Quantity:
2DS 21,20025 Q 50 units
H 24
where: D annual demand, S setup or order cost,
H holding cost
12.15 (a) The EOQ assumptions are met, so the optimal order
quantity is
2DS 2(250)20
EOQ 100
units
H 1
(b) Number of orders per year D/Q 250/100 2.5
orders per year.
Note that this would mean in one year the company
places 3 orders and in the next it would only need
2 orders since some inventory would be carried over
from the previous year. It averages 2.5 orders per year.
(c) Average inventory Q/2 100/2 50 units
(d) Given an annual demand of 250, a carrying cost of
$1, and an order quantity of 150, Patterson Electronics
must determine what the ordering cost would have
to be for the order policy of 150 units to be optimal.
To find the answer to this problem, we must solve the
traditional economic order quantity equation for the
ordering cost. As you can see in the calculations that
follow, an ordering cost of $45 is needed for the order
quantity of 150 units to be optimal.
CHAPTER 12 I NVENTORY M ANAGEMENT 187
2DS
Q
H
2 H
S Q
2D
2
(150) (1)
=
2(250)
22,500
= $45
500
12.16 Production Order Quantity, noninstantaneous delivery:
Q
2DS
1 d
H
p
2 10,000 200
50
1.001 200
2309.4 or 2,309 units
where: D annual demand, S setup or order cost, H holding
cost, d daily demand rate, p daily production rate
12.17 Production order quantity, noninstantaneous delivery.
(a) D 12,000/yr.
H $.10/light-yr.
S $50/setup
P $1.00/light
p 100/day
12,000/yr.
d
300 days/yr.
40 /d ay
2DS 2(12,000)50
Q
d 40
H 1 .101 p
100
4,472 lights per run
Q d
(b) Average holding cost /y ear 1 H
2 p
4,472 40
$26,832
1 (.10)
$134.16
2 100
200
D 12,000
(c) Average setup cost /y ear S 50
Q 4,472
$134.16
(d) Total cost (including cost of goods)
PD $134.16 $134.16
($1 12,000) $134.16 $134.16
$12,268.32/year
12.18 (a) Production Order Quantity, noninstantaneous delivery:
Q
2DS
H 1d p
2 10,000 40
50
0.601 500
1217.2 or 1,217 units
where: D annual demand, S setup or order cost,
H holding cost, d daily demand rate, p daily
production rate
d
(b) Imax Q1
1,095
p