# production control

Pages: 14 (785 words) Published: July 31, 2014
1) The manager of an automobile repair shop hopes to
achieve a better allocation of inventory control efforts by
adopting an A-B-C approach to inventory control.
a) Given monthly usages in the following table, classify the items in A, B and C categories according to dollar usage:
Item Usage Unit Cost
4021 90
\$1,400
9402 300 12
4066 30
700
6500 150 20
9280 10
1,020
4050 80
140
6850 2,000 10
3010 400 20
4400 5,000 5

a) In descending order:
Item
Usage x Cost
4021
\$126,000

Category
A

4400
4066
6850

25,000
21,000
20,000

B
B
B

4050
9280
3010
9402
6500

11,200
10,200
8,000
3,600
3,000
228,000

C
C
C
C
C

b) Determine percentage of items in each
category and percentage of total cost for each
category.
Category Percent of
Items

Percent of Total
Cost

A

11.1%

57.8%

B

33.3%

30.2%

C

55.6%

11.9%

2) A large bakery buys flour in 25-pound bags. The
bakery uses an average of 4,860 bags a year.
Preparing an order and receiving a shipment of
flour involves a cost of 10\$ per order. Annual
carrying costs are 75\$ per bag.
a) Determine the economic order quantity.
b) What is the average number of bags on hand?
c) How many orders per year will there be?
d) Compute the total cost of ordering and carrying
flour.
e) If ordering costs were to increase by 1\$ per
order, how much would that affect the minimum
total annual cost?

D = 4,860 bags/yr.
S = \$10
H = \$75
DS
a) Q = 2H = 2(4,860)10 = 36 bags
75
b) Q/2 = 36/2 = 18 bags
c) D = 4,860 bags = 135 orders

Q

36 bags / orders

TC = Q / 2H +

d)
e) Q =
TC =

D
S
Q

=

36
4,860
(75) +
(10) = 1,350 + 1,350 = \$2,700
2
36

2(4,860)(11)
= 37.757
75

37.757
4,860
(75) +
(11) = 1,415.89 + 1,415.90 = \$2,831.79
2
37.757

Increase by [\$2,831.79 – \$2,700] = \$131.79

3) A manager receives a forecast for next year. Demand is
projected to be 600 units for the first half of the year and 900 units for the second half. The monthly holding cost is
2\$ per unit, and it costs an estimated 55\$ to process an
order.
a) Assuming that monthly demand will be level during each
of the six-month periods covered by the forecast(e.g., 100
per month for each of the first six months), determine an
order size that will minimize the sum of ordering and
carrying costs for each of the six-month periods.
b) Why is it important to be able to assume that demand will be level during each six-month period?
c) If the vendor is willing to offer a discount of 10\$ per order for ordering in multiples of 50 units (e.g., 50,100,150),
offer in either period? If so, what order size would you
recommend?

H = \$2/month
S = \$55
D1 = 100/month (months 1–6)
D2 = 150/month (months 7–12)

a.

Q0 =

2DS
H

D1 : Q 0 =
D2 : Q0 =

2(100)55
= 74.16
2
2(150)55
= 90.83
2

b. The EOQ model requires this.

c. Discount of \$10/order is equivalent to S – 10 = \$45 (revised ordering cost)
1–6
TC74 =\$148.32
50
100
( 2) +
( 45) = \$140 *
2
50
100
100
( 2) +
( 45) = \$145
=
2
100

TC 50 =
TC100

7–12 TC91 =

\$181.66

TC 50 =

50
150
(2) +
(45) = \$185
2
50

TC100 =

100
150
(2) +
(45) = \$167.5 *
2
100

TC150 =

150
150
(2) +
(45) = \$195
2
150

4) A chemical firms produces sodium bisulfate in 100pound bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50 tons
per day. Setup costs 100\$, and storage and handling
costs are 5\$ per ton a year. The firm operates 200
days a year. (Note: 1 ton=2000 pounds.)
a) How many bags per run are optimal?
b) What would the average inventory be for this lot size?
c) Determine the approximate length of a production
run in days.
d) About how many runs per year would there be?
e) How much could the company save annually if the
setup cost could be reduced to 25\$ per run?

p = 50/ton/day
u = 20...