Operations
Management
Capacity Planning
© 2006
Prentice
Hall, Inc. Hall, Inc.
©
2006
Prentice
S7 – 1
Capacity
 The throughput, or the number of
units a facility can hold, receive,
store, or produce in a period of time
 Determines fixed costs
 Determines if demand will be
satisfied
 Three time horizons
© 2006 Prentice Hall, Inc.
S7 – 2
Planning Over a Time
Horizon
Long-range
planning
Add facilities
Add long lead time equipment
Intermediaterange
planning
Subcontract
Add equipment
Add shifts
Short-range
planning
Add personnel
Build or use inventory
*
Modify capacity
*
Schedule jobs
Schedule personnel
Allocate machinery
Use capacity
* Limited options exist
© 2006 Prentice Hall, Inc.
S7 – 3
Design and Effective
Capacity
 Design capacity is the maximum
theoretical output of a system
 Normally expressed as a rate
 Effective capacity is the capacity a
firm expects to achieve given current
operating constraints
 Often lower than design capacity
© 2006 Prentice Hall, Inc.
S7 – 4
Utilization and Efficiency
Utilization is the percent of design capacity
achieved
Utilization = Actual Output/Design Capacity
Efficiency is the percent of effective capacity
achieved
Efficiency = Actual Output/Effective Capacity
© 2006 Prentice Hall, Inc.
S7 – 5
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
© 2006 Prentice Hall, Inc.
S7 – 6
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
© 2006 Prentice Hall, Inc.
S7 – 7
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
© 2006 Prentice Hall, Inc.
S7 – 8
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
© 2006 Prentice Hall, Inc.
S7 – 9
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
Efficiency = 148,000/175,000 = 84.6%
© 2006 Prentice Hall, Inc.
S7 – 10
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
Efficiency = 148,000/175,000 = 84.6%
© 2006 Prentice Hall, Inc.
S7 – 11
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, 3 – ‘8 hour shifts’
Efficiency = 84.6%
Efficiency of new line = 75%
Expected Output = (Effective Capacity)(Efficiency)
= (175,000)(.75) = 131,250 rolls
© 2006 Prentice Hall, Inc.
S7 – 12
Bakery Example
Actual production last week = 148,000 rolls
Effective capacity = 175,000 rolls
Design capacity = 1,200 rolls per hour
Bakery operates 7 days/week, three- ‘8 hour shifts’
Efficiency = 84.6%
Efficiency of new line = 75%
Expected Output = (Effective Capacity)(Efficiency)
= (175,000)(.75) = 131,250 rolls
© 2006 Prentice Hall, Inc.
S7 – 13
Managing Demand
 Demand exceeds capacity
 Curtail demand by raising prices,
scheduling longer lead time
 Long term solution is to increase capacity
 Capacity exceeds demand
 Stimulate market
 Product changes
 Adjusting to seasonal demands
 Produce products with complimentary
demand patterns
© 2006 Prentice Hall, Inc.
S7 – 14
Average unit cost
(dollars per room per night)
Economies and
Diseconomies of Scale
25 - Room
Roadside Motel
Economies
of scale
25
© 2006 Prentice Hall, Inc.
50 - Room
Roadside Motel
75 - Room
Roadside Motel
Diseconomies
of scale
50
Number of Rooms
75
Figure S7.2
S7 – 15
Capacity Considerations
 Forecast demand accurately
 Understanding the technology
and capacity increments
 Find the optimal operating level
(volume)
 Build for change
© 2006 Prentice Hall, Inc.
S7 – 16
Approaches to Capacity
Expansion
Expected
demand
Demand
(c) Capacity lags demand with
incremental expansion
New
capacity
Expected
demand
Demand
New
capacity
(b) Leading demand with
one-step expansion
New
capacity
Expected
demand
(d) Attempts to have an average
capacity with incremental
expansion
Demand
Demand
(a) Leading demand with
incremental expansion
New
capacity
Expected
demand
Figure S7.4
© 2006 Prentice Hall, Inc.
S7 – 17
Break-Even Analysis
 Technique for evaluating process
and equipment alternatives
 Objective is to find the point in
dollars and units at which cost
equals revenue
 Requires estimation of fixed costs,
variable costs, and revenue
© 2006 Prentice Hall, Inc.
S7 – 18
Break-Even Analysis
 Fixed costs are costs that continue
even if no units are produced
 Depreciation, taxes, debt, mortgage
payments
 Variable costs are costs that vary
with the volume of units produced
 Labor, materials, portion of utilities
 Contribution is the difference between
selling price and variable cost
© 2006 Prentice Hall, Inc.
S7 – 19
Break-Even Analysis
Assumptions
 Costs and revenue are linear
functions
 Generally not the case in the real
world
 We actually know these costs
 Very difficult to accomplish
 There is no time value of money
© 2006 Prentice Hall, Inc.
S7 – 20
Break-Even Analysis
–
Total revenue line
900 –
800 –
Cost in dollars
700 –
Break-even point
Total cost = Total revenue
Total cost line
600 –
500 –
Variable cost
400 –
300 –
200 –
100 –
Fixed cost
|
|
|
|
|
|
|
|
|
|
|
–
0 100 200 300 400 500 600 700 800 900 1000 1100
|
Figure S7.5
© 2006 Prentice Hall, Inc.
Volume (units per period)
S7 – 21
Break-Even Analysis
BEPx = Break-even point in
units
BEP$ = Break-even point in
dollars
P = Price per unit (after
all discounts)
x = Number of units
produced
TR = Total revenue = Px
F = Fixed costs
V = Variable costs
TC = Total costs = F + Vx
Break-even point
occurs when
TR = TC
or
Px = F + Vx
© 2006 Prentice Hall, Inc.
F
BEPx =
P-V
S7 – 22
Break-Even Analysis
BEPx = Break-even point in
units
BEP$ = Break-even point in
dollars
P = Price per unit (after
all discounts)
x = Number of units
produced
TR = Total revenue = Px
F = Fixed costs
V = Variable costs
TC = Total costs = F + Vx
BEP$ = BEPx P
F
=
P
P-V
F
=
(P - V)/P
F
=
1 - V/P
Profit = TR - TC
= Px - (F + Vx)
= Px - F - Vx
= (P - V)x - F
© 2006 Prentice Hall, Inc.
S7 – 23
Break-Even Example
Fixed costs = $10,000
Direct labor = $1.50/unit
Material = $.75/unit
Selling price = $4.00 per unit
$10,000
F
BEP$ =
=
1 - [(1.50 + .75)/(4.00)]
1 - (V/P)
© 2006 Prentice Hall, Inc.
S7 – 24
Break-Even Example
Fixed costs = $10,000
Direct labor = $1.50/unit
Material = $.75/unit
Selling price = $4.00 per unit
$10,000
F
BEP$ =
=
1 - [(1.50 + .75)/(4.00)]
1 - (V/P)
$10,000
=
= $22,857.14
.4375
$10,000
F
BEPx =
=
= 5,714
4.00 - (1.50 + .75)
P-V
© 2006 Prentice Hall, Inc.
S7 – 25
Break-Even Example
Multiproduct Case
BEP$ =
where
© 2006 Prentice Hall, Inc.
V
P
F
W
i
F
∑
Vi
1x (Wi)
Pi
= variable cost per unit
= price per unit
= fixed costs
= percent each product is of total dollar sales
= each product
S7 – 26
Multiproduct Example
Fixed costs = $3,500 per month
Item
Sandwich
Soft drink
Baked potato
Tea
Salad bar
© 2006 Prentice Hall, Inc.
Price
$2.95
.80
1.55
.75
2.85
Cost
$1.25
.30
.47
.25
1.00
Annual Forecasted
Sales Units
7,000
7,000
5,000
5,000
3,000
S7 – 27
Multiproduct Example
Fixed costs = $3,500 per month
Annual Forecasted
Item
Price
Cost
Sales Units
Sandwich
$2.95
$1.25
7,000
Soft drink
.80
.30
7,000
Baked potato
1.55
.47 Annual 5,000 Weighted
% of Contribution
Tea Selling Variable .75
.25Forecasted 5,000
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $
Sales (col 5 x col 7)
Salad bar
2.85
1.00
3,000
Sandwich
Soft drink
Baked
potato
Tea
Salad bar
© 2006 Prentice Hall, Inc.
$2.95
.80
1.55
$1.25
.30
.47
.42
.38
.30
.58
.62
.70
$20,650
5,600
7,750
.446
.121
.167
.259
.075
.117
.75
2.85
.25
1.00
.33
.35
.67
.65
3,750
8,550
$46,300
.081
.185
1.000
.054
.120
.625
S7 – 28
BEP Example
=
Multiproduct
V
∑ 1 - P x (W )
F
$
i
i
i
Fixed costs = $3,500 per month
$3,500
x Forecasted
12
Annual
=
= $67,200
.625
Item
Price
Cost
Sales Units
Sandwich
$2.95
$1.25
7,000
$67,200
Daily
Soft drink
.80
.30
7,000
=
= $215.38
sales
312 days
Baked potato
1.55
.47 Annual
5,000 Weighted
% of Contribution
Tea Selling Variable .75
.25Forecasted 5,000
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $
Sales (col 5 x col 7)
Salad bar
2.85
1.00
3,000
.446 x $215.38
= 32.6  .259
33
Sandwich
$2.95
$1.25
.42
.58
$20,650
.446
$2.95
sandwiches
Soft drink
Baked
potato
Tea
Salad bar
© 2006 Prentice Hall, Inc.
.80
1.55
.30
.47
.38
.30
.62
.70
5,600
7,750
.75
2.85
.25
1.00
.33
.35
.67
.65
3,750
8,550
$46,300
.121
.075
per
day
.167
.117
.081
.185
1.000
.054
.120
.625
S7 – 29
Decision Trees and
Capacity Decision
-$14,000
Market favorable (.4)
Market unfavorable (.6)
$100,000
-$90,000
$18,000
Market favorable (.4)
Medium plant
Market unfavorable (.6)
$60,000
-$10,000
$13,000
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
$0
© 2006 Prentice Hall, Inc.
S7 – 30
Strategy-Driven Investment
 Operations may be responsible
for return-on-investment (ROI)
 Analyzing capacity alternatives
should include capital
investment, variable cost, cash
flows, and net present value
© 2006 Prentice Hall, Inc.
S7 – 31
Net Present Value (NPV)
F
P=
(1 + i)N
where
© 2006 Prentice Hall, Inc.
F
P
i
N
= future value
= present value
= interest rate
= number of years
S7 – 32
NPV Using Factors
F
P=
= FX
N
(1 + i)
where
Portion of
Table S7.1
© 2006 Prentice Hall, Inc.
Year
1
2
3
4
5
X = a factor from Table S7.1
defined as = 1/(1 + i)N and
F = future value
5%
.952
.907
.864
.823
.784
6%
.943
.890
.840
.792
.747
7%
.935
.873
.816
.763
.713
…
10%
.909
.826
.751
.683
.621
S7 – 33
Present Value of an Annuity
An annuity is an investment which
generates uniform equal payments
S = RX
where
© 2006 Prentice Hall, Inc.
X = factor from Table S7.2
S = present value of a series of
uniform annual receipts
R = receipts that are received every
year of the life of the investment
S7 – 34
Present Value of an Annuity
Portion of Table S7.2
Year
1
2
3
4
5
© 2006 Prentice Hall, Inc.
5%
.952
1.859
2.723
4.329
5.076
6%
.943
1.833
2.676
3.465
4.212
7%
.935
1.808
2.624
3.387
4.100
…
10%
.909
1.736
2.487
3.170
3.791
S7 – 35
Process, Volume, and Variety
Volume
Figure 7.1
Low
Volume
High Variety
one or few
units per run,
high variety
(allows
customization)
Changes in
Modules
modest runs,
standardized
modules
Changes in
Attributes
(such as grade,
quality, size,
thickness, etc.)
long runs only
© 2006 Prentice Hall, Inc.
Repetitive
Process
Process Focus
projects, job shops
(machine, print,
carpentry)
Standard Register
High
Volume
Mass Customization
(difficult to achieve,
but huge rewards)
Dell Computer Co.
Repetitive
(autos, motorcycles)
Harley Davidson
Poor Strategy
(Both fixed and
variable costs
are high)
Product Focus
(commercial
baked goods,
steel, glass)
Nucor Steel
S7 – 36