Assignment 7 Solutions
12.9
Annual Demand in Units
Setup Cost for Each Order
Holding Cost per Unit per Year
Lead Time for a New Order in Days
D = 1,500
S = $150
H = $45
L=6
a)
Q* =
b)
Annual Holding Cost = (Q / 2) H = (100 / 2) $45 = $2,250
2  1,500  $150
2DS
=
= 100
$45
H
The economic order quantity is 100 units per order.
The cost of holding the component in inventory is $2,250 per year.
c)
Annual Ordering Cost = (D / Q) S = (1,500 / 100) $150 = $2,250
The cost of ordering the component is $2,250 per year.
d)
ROP = dL = (1,500 / 300) 6 = 30 units
A new order should be placed when there are 30 units left in inventory.
12.23 Annual Demand in Units
Setup Cost for Each Order
Holding Cost Percentage
D = 100
S = $45
I = 20%
We evaluate the economic order quantity for each level of quantity discount:
9 sheets or less. Unit Price P = $18.00
Q* =
2DS
=
IP
2  100  $45
= 50 units
0.2  $18.00
10 to 50 sheets. Unit Price P = $17.50
Q* =
2DS
=
IP
2  100  $45
= 50.7 units (ie 51 units)
0.2  $17.50
More than 50 sheets. Unit Price P = $17.25
Q* =
2DS
=
IP
2  100  $45
= 51.1 units (ie 52 units)
0.2  $17.25
Now, what answer do we give? There are two approaches possible:
Approach #1: Calculate the total cost for each alternative.
TC1
TC2
TC3
= (D / Q) S + (Q / 2) H + PD = (100 / 50)$45 + (50 / 2)(0.2)$18 + (100)$18
= $1,980
= (D / Q) S + (Q / 2) H + PD = (100 / 51)$45 + (51 / 2)(0.2)$17.50 + (100)$17.50
= $1,927.48
= (D / Q) S + (Q / 2) H + PD = (100 / 52)$45 + (52 / 2)(0.2)$17.25 + (100)$17.25
= $1,901.24
Option three has the lowest total costs, so this is the choice we should recommend.
Approach #2: Common Sense
Both quantity one (50) and quantity two (51) put the company in the range where the 50
and over discount will apply anyways. Calculations of total cost for these quantities are
inappropriate because the supplier will not sell at the given costs for the economic order
quantity. Hence quantity three (52) is the one to choose.
13.3
Note that we cannot quantify all costs for this plan (such as the cost of production), but
we will evaluate the costs for the information given. We can determine the following
costs:




Stockout ($100 per unit)
Inventory Holding ($20 per unit per month)
Hiring ($5,000 per 100 units)
Firing ($7,500 per 100 units)
These costs also suggest the we should be keeping track of inventory from month to
month and thus also production and demand from month to month. The way I read the
question is:



Under this plan, we produce this month what was demanded last month – in
this case ‘demand’ is the aggregate demand forecast provided in the table;
Inventory levels will therefore fluctuate because production this month does
not match demand this month; and,
If inventory is exhausted and demand is greater than production, a stockout
cost will be incurred.
We prepare the following chart to evaluate the plan:
Period
1
2
3
4
5
6
7
8
Totals
Expected
Demand
1400
1600
1800
1800
2200
2200
1800
1400
Beginning
Inventory
200
400
200
0
0
0
0
400
Production
1600
1400
1600
1800
1800
2200
2200
1800
Ending
Inventory
400
200
0
0
0
0
400
800
1800
Stockout
Hiring
Firing
0
0
0
0
400
0
0
0
400
0
0
200
200
0
400
0
0
800
0
200
0
0
0
0
0
400
600
So the costs that we can measure for this problem are:
Inventory Carrying = 1800 x $20
Stockout
= 400 x $100
Hiring
= 800 / 100 x $5,000
Firing
= 600 / 100 x $7,500
Total Costs (excluding production)
= $36,000
= $40,000
= $40,000
= $45,000
= $161,000
How this was marked: yes, this was an obtusely-worded question. You received full marks on this question for identifying and
accurately calculating at least two of the above four costs. Just don’t expect me to be nearly so nice on the final exam.
13.9
Plan A:
Period
1
2
3
4
5
6
Total
Demand
1000
1200
1400
1800
1800
1600
Production
1000
1000
1000
1000
1000
1000
Subcontracting
0
200
400
800
800
600
2800
Subcontracting Cost = 2800 x $60 = $168,000
Total Costs (excluding production) = $168,000
Plan B:
Period
1
2
3
4
5
6
Total
Demand
1000
1200
1400
1800
1800
1600
Production
1300
1000
1200
1400
1800
1800
Hire
0
200
200
400
0
0
800
Fire
300
0
0
0
0
200
500
Hiring Cost = 800 / 100 x $3000
= $24,000
Firing Cost = 500 / 100 x $6,000
= $30,000
Total Costs (excluding production) = $54,000
Why are there no inventory carrying or stockout costs here? Note the subtle difference
between this plan and the plan in question 13.3. Question 13.3 says ‘chase strategy’ but
then explicitly states that production in a month should equal demand in the prior month,
causing inventory carrying or stockout costs. Conversely, this plan states that workforce
will be varied to meet demand in the current month, and this is the generally accepted
definition of a ‘chase strategy’ plan. Once again feeling generous, you will not be marked
down for including inventory carrying or stockout costs in your analysis of this plan, but
be wary of this point on the final exam.
We would select Plan B, which has a lower cost.
14.11 a) To develop a Gross Requirements Plan for item C, we note from the diagram that one
of item C is used in Assembly A and another is used in Assembly H. Note that existing
inventories aren’t taken into account in a gross requirements plan. Our plan should thus show
requirements for all three components:
Item
A Gross Req
Order Rel
H Gross Req
Order Rel
C Gross Req
Order Rel
1
2
3
4
5
6
7
8
100
100
100
100
9
10
50
50
100
100
100
50
100
50
11
12
150
150
50
50
50
50
150
150
b) Our net requirements plan does taken into account existing inventories and provides us with
some more detailed quantities. Once again, it should show items A, H, and C:
Item
A Gross Req
On Hand
Net Req
Planned Receipt
Planned Release
H Gross Req
On Hand
Net Req
Planned Receipt
Planned Release
C Gross Req
On Hand
Net Req
Planned Receipt
Planned Release
1
2
3
4
5
6
7
8
100
9
100
100
100
50
50
50
50
50
50
100
100 100
50 50 0
50 100
50 100
100 50 50
10
50
50
50
150
50
100
100
50
50
50
0
50
50
150
50
50
0
50
50
20” Fan
Frame
Grills (2)
Handle
Supports (2)
Hub
Fan
Assembly
Blades (5)
Electrical
Motor
Knob
Switch
12
150
150
150
50
100
14.13 a) The product structure diagram is:
Housing
11
150
0
0
150
150
b) The time-phased product structure is:
Frame
Support
Handle
Housing
Grills
Fan
Hub
Fan Assembly
Blades
Motor
Switch
Knobs
1
2
3
c) The net material requirements plan is:
4
Elec
5
6
7
Lot Size
Lead Time
1
1
2
3
1
2
On Hand
100
100
200
150
Item ID
20” Fan
Housing
Grills
Fan
Assembly
Electrical
Unit
Frame
1
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
2
3
4
5
6
900
900
100
800
800
800
1800
200
1600
1600
1600
900
150
750
750
750
900
900
900
900
800
800
800
800
7
1000
100
900
900
Lot Size
Lead Time
1
1
On Hand
50
400
1
100
2
1
Supports
Handle
Hub
Blades
1
12
Item ID
Motor
20
Switch
1
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
Gross Requirements
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
2
3
4
5
1600
50
1550
1550
6
7
50
50
1550
800
400
400
400
400
750
750
750
750
3750
50
50
3750
3800
3800
900
900
900
900
900
20
880
888
888
8
Lot Size
25
Lead Time
1
On Hand
Item ID
Knob
1
Gross Requirements
Scheduled Receipt
Projected On Hand
Net Requirements
Planned Order Receipts
Planned Order Releases
2
3
4
5
900
200
200
200
700
700
200
700
6
7