Operations
Management
Capacity Planning
Supplement 7
7-1
Outline
Capacity.
Utilization.
 Efficiency.

Managing Demand and Capacity.
Break-Even & Crossover Analysis.
Net Present Value.
7-2
Capacity Planning
Capacity planning answers:
 How much long-range capacity is needed?

Add or remove facilities or equipment.
 How much intermediate-range capacity is
needed?

Add or remove personnel, equipment or shifts;
Use or build inventory; Subcontract.
7-3
Definition and Measures of Capacity
Capacity:
The maximum output of a system in a given
period.
Design Capacity:
The maximum capacity that can be achieved
under ideal conditions.
Example: 200/day
Effective capacity:
The expected capacity given the current
operating environment and constraints;
may be viewed as a percentage of design
capacity.
Example: 180/day or 90%
7-4
Utilization & Efficiency
 Utilization = Percent of design capacity achieved.
Utilization =
Actual output
Design capacity
 Efficiency = Percent of effective capacity achieved.
Actual output
Efficiency =
Effective capacity
7-5
Utilization & Efficiency Example
 Design capacity = 120/day.
 Effective capacity = 100/day.
 Actual output = 80/day.
Utilization =
Actual output
= 80/120 = 67%
Design capacity
Actual output
= 80/100 = 80%
Efficiency =
Effective capacity
7-6
Anticipated Output
 Anticipated output
= Design Capacity x Effective Capacity % x Efficiency
 Example:



Design capacity = 150 units per day
Effective capacity = 80%
Efficiency = 90%
 Anticipated output = 150 x 0.80 x 0.90 = 108 per day.
 Efficiency = 90%; Utilization = 108/150=72%
7-7
Capacity Planning Process
 Forecast demand accurately.
 Compute needed capacity.
 Develop alternative plans.

Understand technology and capacity increments.
 Evaluate capacity plans.

Quantitative & Qualitative factors.

Build for change.
 Select and implement best capacity plan.
7-8
Managing Existing Capacity
To make capacity match demand, either:
 Adjust demand = Demand management.
 Adjust capacity = Capacity management.
 Use or build inventory.
 Find complementary products for
seasonal demands.
7-9
Managing Existing Capacity
Demand Management
Capacity Management
 Vary prices.
 Vary staffing.
 Vary promotion.
 Change equipment
& processes.
 Backorder.
 Offer complementary
products.
 Change methods.
 Redesign the product/service
for faster processing.
7-10
Complementary Products
Sales (Units)
5,000
4,000
3,000
2,000
1,000
0
Total
Snowmobiles
Jet Skis
J M M J S N J M M J S N J
Time (Months)
7-11
Capacity Expansion Options

Advantages:
Expected Demand
Demand
 1. Add capacity in advance
of increasing demand.
Can capture market.
 Discourage competition.
New Capacity

Small expansions
Disadvantages:
Expensive and risky.
 Demand may not materialize.
 Size of needed expansion
relies on forecast.

Demand

Time in Years
New Capacity
Expected Demand
Time in Years
7-12
Large expansion
Capacity Expansion Options
(cont.)
 Add new capacity after
demand materializes.
Expected Demand
Advantages:
Lower cost.
 Less risk.
 Size of expansion known.


Disadvantages:

Demand

New Capacity
Time in Years
May be too late to market.
7-13
Small expansions
Break-even Analysis
 To evaluate process & equipment alternatives.
 Objective:
Find the point ($ or units) at which total cost equals
total revenue, -or Find the range of output over which different
alternatives are preferred.

 Assumptions:
Revenue & costs are related linearly to volume.
 All information is known with certainty.
 No time value of money.

7-14
Break-even Analysis - Costs
Fixed costs: Costs independent of the
volume of units produced.

Depreciation, taxes, debt, mortgage payments, etc.
Variable costs: Costs that vary with the
volume of units produced.

Labor, materials, portion of utilities, etc.
7-15
Break-even Chart
Dollars
Total revenue line
Profit
Variable cost
Loss
Total cost line
Fixed cost
Volume (units/period)
Breakeven point
Total cost = Total revenue
7-16
Break-even Equations
F = Fixed cost per unit time.
V = Variable cost per unit produced.
x = Number of units produced per unit time.
P = Revenue (price) per unit
TC = Total costs per unit time = F + Vx
TR = Total revenue per unit time = Px
Profit = TR - TC
At break-even point: Total Cost = Total Revenue
7-17
Break-even Example 1
A firm produces radios with a fixed cost of $7,000 per
month and a variable cost of $5 per radio. If radios sell
for $8 each:
1a) What is the break-even point?
TR = TC so 8x = 7000 + 5x
x = 7000/3 = 2,333.333 radios per month
1b) What output is needed to produce a profit of
$2,000/month?
Profit = 2000/month so
TR - TC = 8x - (7000 + 5x) = 2000
x = 9000/3 = 3,000 radios per month
7-18
Break-even Example 1 - continued
1c) What is the profit or loss if 500 radios are produced each
week?
First, get monthly production:
50052/12 = 2,166.6667 radios per month
Then calculate profit or loss
TR - TC = 82166.6667 - (7000 + 52166.6667)
= $-500 per month
($500 loss per month)
7-19
Break-even Example 2
A firm produces radios with a fixed cost of $7,000 per month and
a variable cost of $5 per radio for the first 3,000 radios
produced per month. For all radios produced each month after
the first 3,000 the variable cost is $10 per radio (for added
overtime and maintenance costs). If radios sell for $8 each:
2a) What are the break-even point(s)?
Now TC has two parts depending on the level of production:
For x  3000/month: TC = 7000 + 5x
For x > 3000/month: TC = 7000 + 5(3000) + 10(x-3000)
= -8000 + 10x
For any x: TR = 8x
7-20
Break-even Example 2 - continued
For x  3000/month: TC = 7000 + 5x
For x > 3000/month: TC = -8000 + 10x
For any x: TR = 8x
For x  3000/month: 7000 + 5x = 8x so x = 2,333.33/month
This is < 3000/month, so it is a valid break-even point.
For x > 3000/month: -8000 + 10x = 8x so x = 4000/month
This is > 3000/month, so it is also a valid break-even point.
7-21
Dollars (Thousands)
Break-even Example 2
40
Total revenue line
32
24
Total cost line
16
Break-even
points
8
1000
2000
3000
4000
Volume (units/month)
7-22
Break-even Example 3
A firm produces radios with a fixed cost of $7,000 per month and
a variable cost of $5 per radio for the first 2,000 radios
produced per month. For all radios produced each month after
the first 2,000 the variable cost is $10 per radio (for added
overtime and maintenance costs). If radios sell for $8 each:
3a) What are the break-even point(s)?
Again TC has two parts depending on the level of production:
For x  2000/month: TC = 7000 + 5x
For x > 2000/month: TC = 7000 + 5(2000) + 10(x-2000)
= -3000 + 10x
For any x: TR = 8x
7-23
Break-even Example 3 - continued
For x  2000/month: TC = 7000 + 5x
For x > 2000/month: TC = -3000 + 10x
For any x: TR = 8x
For x  2000/month: 7000 + 5x = 8x so x = 2,333.33/month
This is not < 2000/month, so it is not a break-even point!!
For x > 2000/month: -3000 + 10x = 8x so x = 1500/month
This is not > 2000/month, so it is not a break-even point!!
THERE ARE NO BREAK-EVEN POINTS!
7-24
Dollars (Thousands)
Break-even Example 3
40
32
24
Total cost line
Total revenue line
16
8
1000
2000
3000
4000
Volume (units/month)
7-25
Dollars (Thousands)
Other Break-even Possibilities
40
32
24
Total cost line
Total revenue line
16
8
1000
2000
3000
4000
Volume (units/month)
7-26
Crossover Chart
Process A: Low volume, high variety
Process B: Repetitive
Process C: High volume, low variety
Process A
Process B
Process C
7-27
Lowest cost
process
Crossover Example
Consider three production processes with different fixed and
variable costs:
Process A: FA = $5000/week VA = $10/unit
Process B: FB = $8000/week VB = $4/unit
Process C: FC = $10000/week VC = $3/unit
Over which range of output is each process best?
First write total cost expressions:
A: 5,000 + 10x
B: 8,000 + 4x
C: 10,000 + 3x
7-28
Crossover Example
A: 5,000 + 10x
B: 8,000 + 4x
C: 10,000 + 3x
1. At x = 0, A is best (since 5000 < 8000 < 10000).
2. As x gets larger, either B or C may become better than A:
B < A when 8000 + 4x < 5000 + 10x or x > 500/week
C < A when 10000 + 3x < 5000 + 10x or x > 714.28/week
So A is best only for x < 500/week and
B is best starting at x > 500/week
7-29
Crossover Example
A: 5,000 + 10x
B: 8,000 + 4x
C: 10,000 + 3x
3. Eventually, C will become better than B (note that C has a lower
variable cost than B).
C < B when 10000 + 3x < 8000 + 4x or x > 2000/week
so B is best for 500/week < x < 2000/week and
C is best starting at x > 2000/week
7-30
Crossover Example
Summary:
A is best for output of 0-500 units per week.
B is best for output of 500-2000 units per week.
C is best for output greater than 2000 units per week.
0
2000
500 714
A<B
A<C
B<C
A<B
B<A
A<C
A<C
B<C
B<C
A<B<C B<A<C
B<A
C<A
B<C
B<C<A
7-31
B<A
C<A
C<B
C<B<A
Time Value of Money - Net Present
Value
 Future cash receipt of amount F is worth less than F
today.
F = Future value N years in the future.
P = Present value today.
i = Interest rate.
F  P(1  i )
N
F
P
(1  i ) N
7-32
Annuities
 An annuity is a annual series of equal payments.
R = Amount received every year for N years.
S = Present value today.
S = RX
where X is from Table S7.2.
Example: What is present value of $1,000,000 paid in 20
equal annual installments?
For i = 6%/year, S = 50000  11.47 = $573,500
For i = 14%/year, S = 50000  6.623 = $331,150
7-33
Limitations of Net Present Value
 Investments with the same NPV will differ:

Different lengths.

Different salvage values.

Different cash flows.
 Assumes we know future interest rates!
 Assumes payments are always made at the
end of the period.
7-34