Course title
Term
Assignment
Due Date
Total Marks
:
:
:
:
:
Operations Management
IV (Fall 2011)
Two
November 30, Wednesday
70
1. Rabindra Sharma, operations manager at Furniture Kingdom, has received the
following estimates of demand requirements:
May
Jun
Jul
Aug
Sep
Oct
1,200
1,400
1,800
1,800
1,000
800
Assuming production costs at $40/unit, stockout costs for lost sales of $90/unit,
inventory carrying costs of $30 per unit per month, and zero ending inventory,
evaluate the below two plant:
Plan A: Produce at a steady rate (equal to minimum requirements) of 1000 units per
month and subcontract additional units at a $70 per unit premium cost.
Plan B: Vary the workforce, which performs at a current production level of 1,300 units
per month. The cost of hiring additional workers is $4,000 per 100 units produced.
The cost of layoff is $8,000 per 100 units cut back.
(10)
ANS:
Stock out cost= $90 per unit
Inventory Carrying cost =$30 per unit per month
Zero Ending inventory
Cost of production per unit = $40
Plan A: Produce at constant rate of 1000 units per month
Cost of subcontracting per unit = $70
Firing is done in the first month to bring production down to 1000 units/month from 1300
units/month
Cost
Exp
Production Sub
Prod
Sub
Inv
Firing
@1000
Total
Con
cost
Con
Hold
Cost
Month Demand
units
Cost
cost
cost
$80
per month
unit
$40
@70
@30
pu
May
1200
1000
200 40000
14000
0
24000 78000
Jun
1400
1000
400 40000
28000
0
0
68000
Jul
1800
1000
800 40000
56000
0
0
96000
Aug
1800
1000
800 40000
56000
0
0
96000
Sep
1000
1000
0
40000
0
0
0
40000
Oct
800
1000
0
40000
0
6000
0
46000
240000 154000
6000
24000 424000
If you have taken the minimum requirement i.e. 800 as your production rate (since I made a
mistake in the question), the following will be the calculation of costs.
Exp
Month Demand
May
Jun
Jul
Aug
Sep
Oct
1200
1400
1800
1800
1000
800
Sub
Prod
Sub
Cost
Firing
Con
cost
Con
Cost
per month
unit
$40
800
800
800
800
800
800
400
600
1000
1000
200
0
32000
32000
32000
32000
32000
32000
192000
cost
@70
28000
42000
70000
70000
14000
0
224000
$80
pu
40000
0
0
0
0
0
24000
Production
@1000
units
Total
Cost
100000
74000
102000
102000
46000
32000
456000
Plan B: Vary workforce
Cost of hiring = $40 per unit
Cost of layoff =$80 per unit
Exp
Month Demand
May
Jun
Jul
Aug
Sep
Oct
1200
1400
1800
1800
1000
800
Prod
Rate
per
month
1200
1400
1800
1800
1000
800
Hire
Units
Fire
Units
0
200
400
0
0
0
100
0
0
0
800
200
Cost
Prod
Hiring Firing
cost
Cost
Cost
$40
$80
$40
pu
pu
48000
0
8000
56000 8000
0
72000 16000
0
72000
0
0
40000
0
64000
32000
0
16000
320000 24000 88000
Total
Cost
56000
64000
88000
72000
104000
48000
432000
Total Cost of Plan B = $432000
Thus plan A is better (if you have taken 1000 units as monthly production rate) or else
plan B is better.
2. Technodrive Pvt Ltd needs an aggregate plan for January through June for its Airconditioner production. The company has developed the following data:
Holding cost
Subcontracting
Regular-time labor
Overtime labor
8 hours/worker/day
Hiring cost
Layoff cost
Stockout cost
Costs
$7/ ac /month
$70/ ac
$10/hour
$15/hour for hours above
$50/ ac
$80/ ac
none
Other Data
Current workforce (December)
Labor hours/ ac
Workdays/month
Beginning inventory
Ending inventory
8 people
4 hours
25 days
400 ac’s
0 ac’s
Demand
Jan.
Feb.
March
April
May
June
Forecast
600
750
950
1100
1200
850
What will each of the following strategies cost?
Strategy A: Produce exactly what is demanded per month with no excess production
or under production (Chase Strategy) through hiring and firing of workers as and
when needed.
Strategy B: Use a constant workforce of 10 people and vary only overtime. Assume
that there is no limit on the capacity by having workers work overtime.
Strategy C: Produce at the minimum demand level i.e. 600 units per month and
subcontract the rest.
(15)
ANS:
Strategy A: Chase Strategy
Cost of hiring = $50 per unit
Cost of firing = $80 per unit
Current production capacity with 8 ppl = 8 ppl * 8 hrs per day * 25 days per month =
1600 hours or 400 units (4 hours equivalent to one unit)
Production cost = 10*4 = $40/unit
Beginning inventory = 400 units
Assuming all inventory used up in first month
Cost
Exp
Month
Demand
Jan
Feb
Mar
Apr
May
Jun
600
750
950
1100
1200
850
Prod
Rate
200
750
950
1100
1200
850
Prod
cost
@$40
per unit
8000
30000
38000
44000
48000
34000
202000
Hiring
0
550
200
150
100
0
Hiring
cost
@$50
per
unit
0
27500
10000
7500
5000
0
50000
Firing
200
0
0
0
0
350
Firing
cost
@$80
per unit
Total
Cost
16000
0
0
0
0
28000
44000
24000
57500
48000
51500
53000
62000
296000
Total Cost of Strategy A = $296000
Strategy B: Level Strategy (10 workers) with overtime
Current production capacity with 10 ppl = 10 ppl * 8 hrs per day * 25 days per month
=2000 hours or 500 units (4 hours equivalent to one unit)
OT cost = $15 * 4 hrs = $60/unit
Initially there will also be a hiring cost since we have increased the production capacity
from 400 units to 500 units. Thus hiring cost will be 100*50=$5000.
Cost
Month
Exp
Demand
Prod
Rate
Jan
Feb
Mar
Apr
May
Jun
600
750
950
1100
1200
850
500
500
500
500
500
500
Prod cost
@$40
per unit
20000
20000
20000
20000
20000
20000
120000
Inv
300
50
0
0
0
0
Inv cost
@$7
per unit
2100
350
0
0
0
0
2450
OT
0
0
400
600
700
350
OT cost
@$60
per unit
Total
Cost
0
0
24000
36000
42000
21000
123000
22100
20350
44000
56000
62000
41000
245450
Total Cost of Strategy B = $245450+5000 = $250,450.
Strategy C: (Level Strategy 600 units per month) with subcontracting
Initially there will also be a hiring cost since we have increased the production capacity
from 400 units to 600 units. Thus hiring cost will be 200*50=$10000.
Subcontract cost = $70 per unit
Cost
Month
Exp
Demand
Prod
Rate
Sub
Con
Units
Jan
Feb
Mar
Apr
May
Jun
600
750
950
1100
1200
850
600
600
600
600
600
600
0
0
100
500
600
250
SubCon
cost
@$70
per unit
24000
0
24000
0
24000
7000
24000 35000
24000 42000
24000 17500
144000 101500
Prod
cost
@$40
per unit
Inv
400
250
0
0
0
0
Inv cost
@$7
per
unit
Total
Cost
2800
1750
0
0
0
0
4550
26800
25750
31000
59000
66000
41500
250050
Total Cost of Strategy C = $250050+10000 = $260050.
So if we were to choose among the three, strategy B would be the best in terms of
minimum cost.
3. Krishi Udyan Pvt Ltd has received the following price schedules from one two of its
suppliers of an underground control valve. Annual usage is 2400 valves; ordering cost
is $10 per order and annual inventory holding costs are $3.33 per unit.
Vendor A
Quantity
Vendor B
Price
Quantity
Price
1-99
$34.50
100-199
34.25
100-199
33.75
200-399
33.00
200-399
32.50
400+
31.00
400+
31.10
Which vendor should be selected and what order quantity is best?
Calculation for EOQ: S = $10, H = $3.33, D = 2,400
EOQ = SQRT ((2*2400*10)/3.33) = 120.06 units
Qty
Price
1-99
100199
200399
400+
100199
200399
400+
EOQ
P/B qty
$34.50
120.06
-
not
feasible
$33.75
120.06
120.06
feasible
$32.50
120.06
200
not
feasible
$31.10
120.06
400
not
feasible
$34.25
120.06
120.06
feasible
$33.00
120.06
200
not
feasible
$31.00
120.06
400
not
feasible
Working out the total costs as below:
Vendor
A
B
(15)
Qty
Price
Holding
Ordering
Purchase
Total
120.06
$33.75
$199.90
$199.90
$81,000.00
$81,399.80
200
$32.50
$333.00
$120.00
$78,000.00
$78,453.00
400
$31.10
$666.00
$60.00
$74,640.00
$75,366.00
120.06
$34.25
$199.90
$199.90
$82,200.00
$82,599.80
200
$33.00
$333.00
$120.00
$79,200.00
$79,653.00
400
$31.00
$666.00
$60.00
$74,400.00
$75,126.00
Vendor
A
Vendor
B
Thus the lowest cost is incurred if the order quantity is 400 units and vendor B is a
better option.
4. As the production schedules for an exercise equipment manufacturer, you are to
schedule an order for 100 treadmills, which are to be shipped in week 10. Assume lotfor-lot ordering. Below is information about the treadmills.
Item
Treadmill
A
B
C
D
E
F
Lead
Time On Hand Inv
2
20
2
25
2
30
3
20
1
5
2
10
2
15
Components
A(1), B(2), C(3)
D(3), F(1)
E(2), F(2)
D(3), E(2)
a. Develop a product structure tree.
b. Develop a net material requirements plan for all the components.
(15)
ANS:
Product Structure for Ultimate Steppers
Treadmill, S
A (1)
D (3)
F (1)
B (2)
F (2)
E (2)
C (3)
E (2)
D (3)
Net material Requirement Planning for all items
Week
Lot
Size
Lead
time
(weeks
)
On
Hand
Item
LotforLot
2
20
Tread
mill, S
1
2
10
A
2
30
B
3
10
C
5
6
7
8
9
2
0
2
0
20
20
20
20
20
20
20
0
80
80
80
80S
2
5
2
5
25
25
25
25
25
0
0
0
0
0
0
0
55
55
55
160
S
3
0
3
0
30
30
30
30
30
0
130
130
13
0
Gross
Requirement
Scheduled
Receipt
Projected
20
on Hand
Net Requirement
Planned Order
10
100
Gross
Requirement
Scheduled
Receipt
Projected
30
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
LotforLot
4
Gross
Requirement
Scheduled
Receipt
Projected
25
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
Lotfor Lot
3
Gross
Requirement
Scheduled
Receipt
Projected
20
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
LotforLot
2
240
S
2
0
2
0
20
20
20
20
20
0
220
220
Receipt
Planned Order
Release
220
Week
Lot
Size
Lead
time
(weeks
)
On
Hand
Item
LotforLot
1
15
D
1
2
5
E
2
20
F
4
5
5
5
5
655
Gross
Requirement
Scheduled
Receipt
Projected
10
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
LotforLot
3
Gross
Requirement
Scheduled
Receipt
Projected
5
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
LotforLot
2
1
0
1
0
10
43
0
10
5
6
660C
165A
0
0
655
165
655
165
8
9
10
0
0
0
0
0
0
0
0
0
0
0
0
165
440C
260B
0
0
430
260
430
260
260
260B
+55A
Gross
Requirement
Scheduled
Receipt
Projected
15
on Hand
Net Requirement
Planned Order
Receipt
Planned Order
Release
7
1
5
1
5
15
15
15
0
300
300
300
5. Spike, a maker of outstanding running shoes, keeps the soles of its size -11 running
shoes in inventory for one period at a cost of $0.20 per unit. The setup costs are $45.
Beginning inventory is 45 and lead time is 2 weeks. Shown below are the gross
requirements per period.
Period
1
Net Requirements
2
3
4
5
6
7
8
9
10
11
35
40
35
0
20
40
20
0
30
40
Determine Spike’s cost based on
a. EOQ.
b. Lot-for-lot.
c. Part period balancing (PPB).
(15)
ANS:
Annual Demand, D = 260 x 52 / 11 ≈ 1229 units
Holding cost, H = $10.4 per unit per year ($0.20 per unit per week x 52)
Setup cost, S = $45 per order
Beginning Inventory = 45 units
Lead time, L = 2 weeks
(a) MRP Lot-Sizing: EOQ
1
Gross Requirement
0
Scheduled Receipt
Projected on Hand 45 45
Net Requirement
0
Planned Order Receipt
Planned Order Release 104
Q* =
2 DS
H
=
2
35
3
40
4
35
5
0
6
20
7
40
8
20
9
0
10
30
10
0
74
30
104
39
0
39
0
19
0
83
21
104
63
0
63
0
33 97
0
7
0 104
104
2 * 1229 * 45
10.4
11
40
104
≈ 104 units
Actual Total Cost
= Setup Cost + Holding Cost
= 3 x $45 + 565 x $0.20
= $135 + $113 = $248
(b) MRP Lot-Sizing: Lot-for-lot
Gross Requirement
Scheduled Receipt
Projected on Hand 45
Net Requirement
Planned Order Receipt
1
2
35
3
40
4
35
5
0
6
20
7
40
8
20
9
0
10
30
11
40
45
10
0
30
30
0
35
35
0
0
0
0
20
20
0
40
40
0
20
20
0
0
0
0
30
30
0
40
40
Planned Order Release
Total Cost
30
35
0
20
40
20
0
30
40
= Setup Cost + Holding Cost
= 7 x $45 + 55 x $0.20
= $315 + $11 = $326
(c) MRP Lot-Sizing: Part-period balancing
Economic part period (EPP) = Setup cost/ Holding cost = $45/$0.20 = 225
Trail Lot
Size
Period
Combined
(Cumulative
Net Req.)
Part Periods
3
30
0
= 30x0
3,4
65
35 = 0 + 35x1
3,4,5
65
35 = 35 + 0x2
3,4,5,6
85
95 = 35 + 20x3
3,4,5,6,7
125
255 = 95 + 40x4
(Combine periods 3 through 7; 255 is as close to EPP of 225
units)
8
20
0
= 20x0
8,9
20
0
= 0 +0x1
8,9,10
50
60 = 0 + 30x2
8,9,10,11
90
180 = 60 + 40*3
(Combine periods 8 through 11; EPP not yet reached)
1
Gross Requirement
Scheduled Receipt
Projected on Hand 45 45
Net Requirement
Planned Order Receipt
Planned Order Release 125
Total Cost
MRP technique
EOQ
Lot-for-Lot
PPB
2
35
3
40
4
35
5
0
6
20
7
40
8
20
9
0
10
30
11
40
10
0
95
30
125
60
60
40
0
70
20
90
70
40
0
90
= Setup Cost + Holding Cost
= 2x 45 + 490 x$0.20
= $90 + $98 = $188
Total Cost
$ 248
$ 326
$ 188
Thus PPB offers the most cost-effective lot-sizing technique.