MGT 3110: Exam 2 Study Guide
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22.
What is aggregate planning? What is its purpose?
What are demand options for aggregate planning? Give examples and discuss the effects
of each.
Why is there a need for aggregate planning?
Briefly discuss the advantages and disadvantages of each of these planning strategies:
a. Maintain a level rate of output and let inventories absorb fluctuations in demand.
b. Vary the size of the workforce to correspond to predicted changes in demand
requirements.
c. Maintain a constant workforce size, but vary hours worked to correspond to predicted
demand requirements.
What is Master Production Schedule?
What are the inputs to master scheduling? What are the outputs?
Define independent and dependent demand items.
What is Bill of Materials?
What is Low-Level coding and what how is it used?
What are the benefits of MRP?
What are the inputs required for MRP?
What is “Lot Sizing” in MRP?
What are the reasons for using a lot sizing method other than Lot-for-lot?
What is the objective of ABC analysis?
Describe the thumb rule used in ABC classification.
List the assumptions needed for developing the EOQ formula.
What costs are included in the total cost for the EOQ model?
The EOQ formula consists of three numbers, D, S, and H. Increasing which of these three
will result in increase in the value of EOQ.
If annual demand were to double, would the value of EOQ also double? Why or why not?
Which of the assumptions required for developing the EOQ formula is not necessary for
the Economic Production Quantity Model?
For the Economic Production Quantity to be valid, production rate “p” must be greater
than the demand rate “u”. Explain the reasons for this.
What costs are included in the total cost if quantity discount is allowed?
PROBLEMS
1.
Wormwood, Ltd., produces a variety of furniture products. The planning committee wants
to prepare an aggregate plan for the next five months. Demand forecast as given below.
Demand
1
150
2
170
3
180
4
160
5
160
Cost of production per unit using regular time is $50, using overtime it is $75, and using
subcontracting it is $80. Inventory holding cost per unit per period is $5. Backorder cost is
$60 per unit. Hiring cost is $150 per worker. Firing cost is $200 per worker.
Currently there are 12 workers and each can produce 15 units per period. Workers can be
hired or fired, but at most only 12 workers can be on the roll. Overtime capacity is 30 units
per period and subcontracting capacity is 10 units per period. Beginning inventory is zero.
No backorder is allowed at the end of period 5.
When computing number of workers needed, make sure you round the number up to a
whole number.
a. Develop a “chase” and determine the cost.
b. Develop a “level” and determine the cost.
c. An image of the spreadsheet Solver model is give below. Fill out the formulas in the
appropriate cells.
d. Fill out the Solver parameters in the table below.
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
B
C
D
E
F
G
Solver model
Capacity
No. of workers
Production/worker/period
Capacity/period
Overtime capacity
Subcontracting capacity
Initial inventory
Safety stock
Costs
Output cost per unit
Regular time
Overtime
Subcontracting
Inventory/unit/period
Backorder/unit
Hiring cost/worker
Firing cost/worker
Period
Forecast
Workers
Beginning workers
Hires
Fires
Workers available
12
15
30
10
0
0
$10
$16
$20
$2
$25
$150
$200
1
150
2
170
3
180
4
160
5
160
Total
820
1
2
3
4
5
Total
30
31
32
33
34
35
36
37
38
39
40
Output
Regular time
Overtime
Subcontracting
Total output
Output-Forecast
1
2
3
4
5
Total
Inventory
Beginning
Available
1
2
3
4
5
Total
1
2
3
4
5
Total
41 Ending
42 Average
43 Backlog
44
45 Costs
46 Output
47
Regular time
48
Overtime
49
Subcontracting
50 Inventory
51 Backorder
52 Hiring cost
53 Firing cost
54 Total
Solver parameters
Set Target Cell
Changing cells
Constraints
2.
The forecast is 30 units for each of the first two periods and 40 units for each of the next
four periods. The starting inventory is 50 units. The lot size of 60 units. Develop the
master schedule and available to promise given the following committed customer orders.
Week
1
2
3
4
5
6
3.
Customer order
35
25
10
5
3
1
A Bill of Materials is desired for a bracket (A) that is made up of a base (B), two springs
(C) and four clamps (D). The base is assembled from one clamp (D) and two housings (E).
Each clamp has one handle (F) and one casting (G). Each housing has two bearings (H)
and one shaft (I).
a. Develop a product structure tree.
b. The lead time for the parts are given below. Develop a time-phased product structure.
c. The available inventory for each part is given in the table below. Determine the net
requirement quantities of all parts required to assemble 50 units of bracket A.
Item
A
B
C
D
E
F
G
H
I
4.
Available
5
5
10
20
50
150
50
5
0
A product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and
three fasteners (F). The lead time, current on-hand inventory and scheduled receipts are
given below. All components are lot for lot. The Master Schedule requires 100 units of
product A be available in week 4 and 150 in week 6. Produce the MRP for the upcoming
six weeks. Produce a list of all planned order releases.
Part
A
B
C
P
F
5.
Lead time
1
2
3
2
1
2
1
1
2
Lead time
1
1
3
2
3
On-hand
20
100
30
0
0
Scheduled receipts
None
50 in week 1
20 in week 1, 30 in week 2
50 in week 1
30 in week 1, 40 in week 3
A company has 12 items in its inventory. Using the data given below classify the items
into A, B, and C classes.
SKU
D120
E111
C140
E151
B180
B120
E149
A180
E110
A155
F120
B150
Annual usage (units)
6850
371
1292
62
12667
9625
7010
5100
258
862
1940
967
Unit $ value
1.20
8.60
13.18
91.80
3.20
10.18
1.27
0.88
62.25
18.10
0.38
2.20
6.
Herbert Adams sells bicycles. One particular model is highly popular with annual sales of
2,000 units per year. The cost of one such bicycle is $800.00. Annual holding costs are
25% of the item's cost, and the ordering cost is $40. The store is open 250 days a year.
a.
What is the economic order quantity?
b. What is the average number of orders per year?
c.
What is the average cycle time in days?
d. What is the annual total costs?
7.
Montegut Manufacturing produces a product for which the annual demand is 10,000.
Production averages 100 per day, while demand is 40 per day. Holding costs are $1.50 per
unit per year; set-up costs $200.00. If they wish to produce this product in economic
batches, what size batch should be used? What is the maximum inventory level? What is
the time between orders? What is the time to producing a lot? How many order cycles are
there per year? Determine the total annual inventory cost?
8.
The annual demand, ordering cost, and the inventory carrying cost rate for a certain item
are D = 600 units, S = $10/order and holding cost is 30% of item price. Price is established
by the following quantity discount schedule. What should the order quantity be in order to
minimize the total annual cost?
Quantity
Unit price
1 to 49
$5.00
50 to 249
$4.50
250 and up
$4.10
Answers to discussion questions:
1.
What is aggregate planning? What is its purpose?
Aggregate planning involves developing a general plan for employment, output, and
inventory levels. The goal is to develop a plan which makes efficient use of the resources
of an organization. Planners attempt to determine the best way to meet forecasting demand
requirements within the constraints imposed by long-term decisions.
2.
What are demand options for aggregate planning? Give examples and discuss the effects
of each.
Demand options are techniques used to even out fluctuations in demand. Following are
some examples.
 Back ordering during high- demand periods (Effective if substitute products are not
available, but may result in loss of customer orders to competition and lost customer
good will)
 Counter-seasonal product mix (effective in reducing huge ups and downs in demand ,
but may lead to products or services outside the company’s areas of expertise
 Economic incentives such as discounts (loss of profit)
3.
Why is there a need for aggregate planning?
The need for aggregate planning is to begin to translate long-term decisions into shortterm operating plans. Aggregate planning constitutes the intermediate step in this process.
4.
Briefly discuss the advantages and disadvantages of each of these planning strategies:
a. Maintain a level rate of output and let inventories absorb fluctuations in demand.
b. Vary the size of the workforce to correspond to predicted changes in demand
requirements.
c. Maintain a constant workforce size, but vary hours worked to correspond to predicted
demand requirements.
a.
b.
c.
Maintaining a constant workforce has the advantage of making estimation of labor
costs relatively easy, is good for morale, and minimizes hiring and layoff costs.
However, inventory carrying costs tend to be high.
Since labor force has to be continually adjusted, hiring and layoff costs tend to be
high. Due to the instability of the labor force, employee morale is low. However, the
inventory carrying costs are very low because production is matched with demand,
resulting in little or no inventory.
Varying the workforce can cause morale problems. Moreover, working overtime
generally is less productive, increases quality problems, and increases the risk of
accidents.
5.
What is Master Production Schedule?
Master Production Schedule specifies production quantities of each Independent Demand
item for a planning horizon of 12 to 15 weeks. Total of MPS quantities must be in
accordance with the aggregate production plan.
6.
What are the inputs to master scheduling? What are the outputs?
The master schedule has three inputs: the beginning inventory, forecasts for each period of
the schedule, and customer orders. Its outputs are projected inventory, production
requirements, and uncommitted (available-to-promise) inventory.
7.
Define independent and dependent demand items.
Finished products whose demand is independent of production decisions are called
“Independent demand” items. Items for which demand can be directly calculated from
production decisions are called “Dependent demand” items. These are raw-materials and
parts required for the production of the finished goods.
8.
What is Bill of Materials?
Bill of materials is structured list of components, ingredients, and materials needed to
make an end product. Items needed to produce a given part are called components or
“children”. The part into which the components go us called “Parent”. The BOM also
gives the number of units of a child item needed to produce one unit of the parent item.
9.
What is Low-Level coding and what how is it used?
A level code starting from zero at the top of the BOM tree and incremented by 1 going
down each level of the BOM tree is assigned. Then, the lowest level at which an item
appears is called Low-Level code. The MRP computations are processed one level at a
time, starting from level zero.
10.
What are the benefits of MRP?
 Better response to customer orders
 Faster response to market changes
 Improved utilization of facilities and labor
 Reduced inventory levels
11.
What are the inputs required for MRP?

Master Production Schedule

Bill of Materials

Inventory status
12.
What is “Lot Sizing” in MRP?
The process of combining net requirements into production lots is called lot sizing.
13.
What are the reasons for using a lot sizing method other than Lot-for-lot?


Lot-for-lot often requires too many lots that may not be economically justifiable
Sometime lot-for-lot generates absurdly small lots
14.
What is the objective of ABC analysis?
The objective of ABC analysis is to identify the inventory items with (i) the largest
annual dollar expenditure (class A), (ii) least annual dollar investment (class C), and
(iii) all other items that fall in between (class B).
15.
Describe the thumb rule used in ABC classification.
 Class A: 10 to 20% of items, 60 to 70% annual $ usage
 Class B: intermediate items
 Class C: 50 to 60% of items, <= 15% annual $ usage
16.
List the assumptions needed for developing the EOQ formula.
 Only one product is involved.
 Annual demand requirements are known.
 Demand is spread evenly throughout the year so that the demand rate is reasonably
constant.
 Lead time is known and constant.
 Each order is received in a single delivery.
 There are no quantity discounts.
17.
What costs are included in the total cost for the EOQ model?
Annual holding cost and annual ordering cost
18.
The EOQ formula consists of three numbers, D, S, and H. Increasing which of these three
will result in increase in the value of EOQ.
D and S are in the numerator of the EOQ formula. Therefore increasing these two
values will result in higher value for EOQ.
19.
If annual demand were to double, would the value of EOQ also double? Why or why not?
No. The annual demand is inside square-root.
20.
Which of the assumptions required for developing the EOQ formula is not necessary for
the Production Lot Size Model?
The assumption that each order is received in a single delivery is not necessary.
21.
For the Production Lot Size to be valid, production rate “p” must be greater than the
demand rate “u”. Explain the reasons for this.
If p < u, a negative number will result inside the square-root. If p = u, a zero will
result in the denominator. These two cases represent situations where the production
needs to be continuous without a stop, i.e. there is no determinable batch size.
22.
What costs are included in the total cost if quantity discount is allowed?
Annual holding cost, annual ordering cost, and annual item cost
Answers to problems
1.
(a) Chase:
2.
Period
Forecast
Output
Regular time
Overtime
Subcontracting
Total output
Output-Forecast
Period
Workers
Hires
Fires
Inventory
Period
Beginning
Available
Ending
Average
1
150
2
170
3
180
4
160
5
160
Total
820
150
0
0
150
0
170
0
0
170
0
180
0
0
180
0
160
0
0
160
0
160
0
0
160
0
820
0
0
820
0
1
10
2
12
2
3
12
4
11
5
11
Total
2
1
0
150
0
0
2
3
1
2
0
170
0
0
3
0
180
0
0
4
0
160
0
0
5
0
160
0
0
Total
0
820
0
0
Backlog
0
0
0
0
0
Period
Costs
Output
Regular time
Overtime
Subcontracting
Hiring cost
Firing cost
Inventory
Backorder
Total
1
2
3
4
5
$7,500
$0
$0
$0
$400
$0
$0
$7,900
$8,500
$0
$0
$300
$0
$0
$0
$8,800
$9,000
$0
$0
$0
$0
$0
$0
$9,000
$8,000
$0
$0
$0
$200
$0
$0
$8,200
(b) Level:
Average demand =
Number of workers =
Period
Workers
Hires
Fires
Costs
Period
Output
Regular time
Overtime
Total
$8,000 $41,000
$0
$0
$0
$0
$0
$300
$0
$600
$0
$0
$0
$0
$8,000 $41,900
164
10.93 or 11
Period
Forecast
Output
Regular time
Overtime
Subcontracting
Total output
Output-Forecast
Inventory
Period
Beginning
Available
Ending
Average
Backlog
0
1
150
2
170
3
180
4
160
5
160
Total
820
164
164
164
164
164
164
14
164
-6
164
-16
164
4
164
4
820
0
0
820
0
1
11
2
11
3
11
4
11
5
11
Total
0
1
1
1
2
3
4
5
Total
0
164
14
7
0
14
178
8
11
0
8
172
0
4
8
0
164
0
0
4
0
164
0
0
0
22
1
2
3
4
5
Total
$8,200
$0
$8,200
$0
$8,200
$0
$8,200
$0
$8,200
$0
41000
0
22
22
12
Subcontracting
Hiring cost
Firing cost
Inventory
Backorder
Total
$0
$0
$200
$35
$0
$8,435
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
$0
$0
$0
$55
$0
$8,255
$0
$0
$0
$20
$480
$8,700
B
$0
$0
$0
$0
$240
$8,440
$0
$0
$0
$0
$0
$8,200
C
0
0
200
110
720
$42,030
D
E
F
G
Solver model
Capacity
No. of workers
Production/worker/period
Capacity/period
Overtime capacity
Subcontracting capacity
Initial inventory
Safety stock
12
15
=B4*B5
30
10
0
0
Costs
Output cost per unit
Regular time
Overtime
Subcontracting
Inventory/unit/period
Backorder/unit
Hiring cost/worker
Firing cost/worker
$10
$16
$20
$2
$25
$150
$200
Period
Forecast
Workers
Beginning workers
Hires
Fires
Workers available
Output
Regular time
Overtime
Subcontracting
Total output
1
2
3
4
5
150
170
180
160
160
Total
820
1
2
3
4
5
Total
=B4
=B29
=COPY
=SUM(B27:F27)
Changing cells
=B26+B27-B28
COPY
1
2
=B29*$B$5
3
4
5
Total
=SUM(B32:F32)
Changing cells
=SUM(B32:B34)
=SUM(B27:F27)
36
37
38
39
40
=B35-B23
Output-Forecast
Inventory
Beginning
Available
1
=B9
=B39+B35
41 Ending
=MAX(0,B40-B23)
42 Average
=(B39+B41)/2
43 Backlog
=MAX(0,B23-B40)
44
45 Costs
46 Output
47
Regular time
48
Overtime
49
Subcontracting
2
3
4
5
Total
=B41
=MAX(0,C40(C23+B43))
=MAX(0,(C23+B43)C40)
1
=SUM(B43:F43)
2
3
4
5
Total
=SUM(B47:F47)
=B32*$B14
=B42*$B17
50 Inventory
51 Backorder
=B27*$B19
52 Hiring cost
63 Firing cost
54 Total
=SUM(B45:B51)
=SUM(B54:F54)
Solver parameters
Set Target Cell
=G54 MINIMIZE
Changing cells
B27:F28, B33:F34
Constraints
B33:F33 <= B7
B34:F34 <= B8
G43 = 0
B33:F33 = INT
B34:F34 = INT
#2.
Fixed order quantity
Period
Forecast
Customer orders - committed
Projected on-hand inventory
60
50
1
30
35
15
2
30
25
45
3
40
10
5
4
40
5
25
5
40
3
45
6
40
1
5
MPS
Available to promise
0
15
60
25
0
60
55
60
56
0
#3. (a)
A
B
C2
D1
F
D4
E2
G
H2
F
I
G
(b) Lead time = 7 weeks
F
D
G
B
H
E
I
C
A
F
D
G
1
2
3
4
5
(c)
Part
A
B
C
D
E
F
G
Gross
50
1 x A = 45
2 x A = 2 x 45 = 90
4 x A + 1 x B = 4 x 45 + 40 = 220
2 x B = 80
1 x D = 200
1 x D = 200
Available
5
5
10
20
50
150
50
Net
50 – 5 = 45
45 – 5 = 40
90 – 10 = 80
220 – 20 = 200
80 – 50 = 30
200 – 150 = 50
200 – 50 = 150
6
7
H
I
2 x E = 2 x 30 = 60
1 x E = 30
60 – 5 = 55
30 – 0 = 30
5
0
#4.
Item A
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Planned receipts
Planned order releases
20
1
2
20
0
0
20
0
0
Item B
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Planned receipts
Planned order releases
100
1
0
50
100
0
0
2
0
150
0
0
Item C
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Planned receipts
Planned order releases
30
1
0
20
30
0
0
2
0
30
50
0
150
Item P
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Planned receipts
Planned order releases
0
1
0
50
0
0
0
2
0
50
0
30
Lead time =
3
20
0
80
Lead time =
3
80
150
0
0
Lead time =
3
80
80
0
0
Lead time =
3
0
50
0
0
Item F
Lead time =
Week
1
2
3
Gross requirement
0
0
0
Scheduled receipts
30
40
Projected on-hand
0
0
30
30
Planned receipts
0
0
0
Planned order releases
170
0
0
Action report: Order 170 units of F; Exception: None
1
4
100
5
6
150
20
80
0
0
0
150
0
150
0
4
0
5
150
6
0
70
0
80
70
80
0
0
0
0
4
0
5
150
6
0
0
0
0
0
150
0
0
0
0
4
80
5
0
6
0
50
30
0
0
0
0
0
0
0
4
240
5
0
6
0
70
170
0
0
0
0
0
0
0
1
3
2
3
5.
Annual
usage
(units) Unit $ value
10.18
9625
3.20
12667
13.18
1292
62.25
258
18.10
862
1.27
7010
1.20
6850
91.80
62
0.88
5100
8.60
371
2.20
967
0.38
1940
No. SKU
1 B120
2 B180
3 C140
4 E110
5 A155
6 E149
7 D120
8 E151
9 A180
10 E111
11 B150
12 F120
Annual Dollar
volume
Dollar %
97,982.50
40,534.40
17,028.56
16,060.50
15,602.20
8,902.70
8,220.00
5,691.60
4,488.00
3,190.60
2,127.40
737.20
220565.66
44.4%
18.4%
7.7%
7.3%
7.1%
4.0%
3.7%
2.6%
2.0%
1.4%
1.0%
0.3%
100%
6.
D = 2000, No. of days = 250, H = 25% x $800 = $200, S = $40
a.
EOQ =
Cum. % Cum. % for
for $ no. of items
44.4%
8.3%
62.8%
16.7%
70.5%
25.0%
77.8%
33.3%
84.9%
41.7%
88.9%
50.0%
92.6%
58.3%
95.2%
66.7%
97.3%
75.0%
98.7%
83.3%
99.7%
91.7%
100.0%
100.0%
b.
2(2000)40
 28
200
N = D/Q = 2000/28 = 70.7
c.
u = D/No. of days per year = 2000/250 = 8, T = Q/u = 28/8 = 3.5 days
d.
Annual total cost = (D/Q)S + (Q/2)H = (2000/28)40 + (28/2)200 = $5,657
7.
D = 10,000, H = $1.50, S = $200, p = 100/day, u = 40/day
2𝐷𝑆
EPQ = √
𝐻
𝑝
2(10000)200
√𝑝−𝑢 = √
1.50
100
√
100−40
= 2108
Imax = (Q/p)(p - u) = (2108/100)(100 - 40) = 1264.80
Average number of orders per year = D/Q = 10000/2108 = 4.74
Cycle time (Time between orders) = Q/d = 2108/40 = 52.7 days
Production time = Q/p = 2108/100 = 21.08 days
Annual holding cost = (Imax/2) x H = (1264.80/2) x 1.50 = $948.60
Class
A
A
B
B
B
B
C
C
C
C
C
C
Annual setup cost = (D/Q) x S = (10000/2108) x 200 = $948.77
Total cost = 948.60 + 948.77 = $1,897.37
8.
D=
Q
600
Price
S=
Holding
cost
10
Holding cost =
Formula Q
1 - 49
5.00
1.50
89
50 - 249
250 &
above
4.50
1.35
94
4.10
1.23
99
Q
1 – 49
50 - 249
>= 250
EOQ =
Candidate
Price
Q
5.00
4.50
94
4.10
250
250 @ P = $4.10
30%
Candidate Q
Formula Q > upper limit -not a candidate
Formula Q is within range, =
Candidate Q = Formula Q
Formula Q < lower limit,
Candidate Q = lower limit
Ordering cost
Holding cost
63.83
24.00
63.45
153.75
94
250
Item cost
Total cost
2700
2460
2827.28
2637.75