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Operations
Management
Supplement 7 –
Capacity Planning
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 7e
Operations Management, 9e
© 2008 Prentice Hall, Inc.
S7 – 1
Outline
 Capacity
 Design and Effective Capacity
 Capacity and Strategy
 Capacity Considerations
 Managing Demand
 Demand and Capacity
Management in the Service
Sector
© 2008 Prentice Hall, Inc.
S7 – 2
Outline – Continued
 Capacity Planning
 Break-Even Analysis
 Single-Product Case
 Multiproduct Case
 Applying Decision Trees to
Capacity Decisions
© 2008 Prentice Hall, Inc.
S7 – 3
Outline – Continued
 Applying Investment Analysis to
Strategy-Driven Investments
 Investment, Variable Cost, and
Cash Flow
 Net Present Value
© 2008 Prentice Hall, Inc.
S7 – 4
Learning Objectives
When you complete this supplement,
you should be able to:
1. Define capacity
2. Determine design capacity, effective
capacity, and utilization
3. Compute break-even analysis
4. Apply decision trees to capacity
decisions
5. Compute net present value
© 2008 Prentice Hall, Inc.
S7 – 5
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
© 2008 Prentice Hall, Inc.
S7 – 6
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
Figure S7.1
© 2008 Prentice Hall, Inc.
S7 – 7
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
© 2008 Prentice Hall, Inc.
S7 – 8
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
© 2008 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
© 2008 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
© 2008 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
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
© 2008 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, 3 - 8 hour shifts
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
© 2008 Prentice Hall, Inc.
S7 – 13
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%
© 2008 Prentice Hall, Inc.
S7 – 14
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%
© 2008 Prentice Hall, Inc.
S7 – 15
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
© 2008 Prentice Hall, Inc.
S7 – 16
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
© 2008 Prentice Hall, Inc.
S7 – 17
Capacity and Strategy
 Capacity decisions impact all 10
decisions of operations
management as well as other
functional areas of the organization
 Capacity decisions must be
integrated into the organization’s
mission and strategy
© 2008 Prentice Hall, Inc.
S7 – 18
Capacity Considerations
 Forecast demand accurately
 Understand the technology and
capacity increments
 Find the optimum
operating level
(volume)
 Build for change
© 2008 Prentice Hall, Inc.
S7 – 19
Average unit cost
(dollars per room per night)
Economies and
Diseconomies of Scale
25 - room
roadside motel
Economies
of scale
25
© 2008 Prentice Hall, Inc.
50 - room
roadside motel
75 - room
roadside motel
Diseconomies
of scale
50
Number of Rooms
75
Figure S7.2
S7 – 20
Build In Flexibility
Percent of North American Vehicles
Made on Flexible Assembly Lines
100% –
80% –
0–
© 2008 Prentice Hall, Inc.
Ford
Toyota
GM
Honda
20% –
Nissan
40% –
Chrysler
60% –
Figure S7.3
S7 – 21
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 complementary
demand patterns
© 2008 Prentice Hall, Inc.
S7 – 22
Complementary Demand
Patterns
Sales in units
4,000 –
3,000 –
2,000 –
1,000 –
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
© 2008 Prentice Hall, Inc.
Jet ski
engine
sales
Figure S7.3
S7 – 23
Complementary Demand
Patterns
Sales in units
4,000 –
3,000 –
Snowmobile
motor sales
2,000 –
1,000 –
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
© 2008 Prentice Hall, Inc.
Jet ski
engine
sales
Figure S7.3
S7 – 24
Complementary Demand
Patterns
Sales in units
4,000 –
Combining both
demand patterns
reduces the
variation
3,000 –
Snowmobile
motor sales
2,000 –
1,000 –
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
© 2008 Prentice Hall, Inc.
Jet ski
engine
sales
Figure S7.3
S7 – 25
Tactics for Matching
Capacity to Demand
1. Making staffing changes
2. Adjusting equipment
 Purchasing additional machinery
 Selling or leasing out existing equipment
3. Improving processes to increase throughput
4. Redesigning products to facilitate more
throughput
5. Adding process flexibility to meet changing
product preferences
6. Closing facilities
© 2008 Prentice Hall, Inc.
S7 – 26
Demand and Capacity
Management in the Service Sector
 Demand management
 Appointment, reservations, FCFS rule
 Capacity
management
 Full time,
temporary,
part-time
staff
© 2008 Prentice Hall, Inc.
S7 – 27
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 S7.5
© 2008 Prentice Hall, Inc.
S7 – 28
Approaches to Capacity
Expansion
(a) Leading demand with incremental
expansion
Demand
New
capacity
Expected
demand
1
© 2008 Prentice Hall, Inc.
2
3
Time (years)
Figure S7.5
S7 – 29
Approaches to Capacity
Expansion
(b) Leading demand with one-step
expansion
New
capacity
Demand
Expected
demand
1
© 2008 Prentice Hall, Inc.
2
3
Time (years)
Figure S7.5
S7 – 30
Approaches to Capacity
Expansion
(c) Capacity lags demand with incremental
expansion
New
capacity
Demand
Expected
demand
1
© 2008 Prentice Hall, Inc.
2
3
Time (years)
Figure S7.5
S7 – 31
Approaches to Capacity
Expansion
(d) Attempts to have an average capacity
with incremental expansion
Demand
New
capacity
Expected
demand
1
© 2008 Prentice Hall, Inc.
2
3
Time (years)
Figure S7.5
S7 – 32
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
© 2008 Prentice Hall, Inc.
S7 – 33
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
© 2008 Prentice Hall, Inc.
S7 – 34
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
© 2008 Prentice Hall, Inc.
S7 – 35
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 S7.6
© 2008 Prentice Hall, Inc.
Volume (units per period)
S7 – 36
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 cost per unit
TC = total costs = F + Vx
Break-even point
occurs when
TR = TC
or
Px = F + Vx
© 2008 Prentice Hall, Inc.
F
BEPx =
P-V
S7 – 37
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 cost per unit
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
© 2008 Prentice Hall, Inc.
S7 – 38
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)
© 2008 Prentice Hall, Inc.
S7 – 39
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
$10,000
F
BEPx =
=
= 5,714
4.00 - (1.50 + .75)
P-V
© 2008 Prentice Hall, Inc.
S7 – 40
Break-Even Example
50,000 –
Revenue
Dollars
40,000 –
Break-even
point
30,000 –
Total
costs
20,000 –
Fixed costs
10,000 –
|
–
0
© 2008 Prentice Hall, Inc.
|
|
2,000
4,000
|
6,000
Units
|
|
8,000
10,000
S7 – 41
Break-Even Example
Multiproduct Case
BEP$ =
where
© 2008 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 – 42
Multiproduct Example
Fixed costs = $3,500 per month
Item
Sandwich
Soft drink
Baked potato
Tea
Salad bar
© 2008 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 – 43
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
© 2008 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 – 44
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
© 2008 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 – 45
Decision Trees and
Capacity Decision
Market favorable (.4)
Market unfavorable (.6)
Market favorable (.4)
Medium plant
Market unfavorable (.6)
Market favorable (.4)
Market unfavorable (.6)
$100,000
-$90,000
$60,000
-$10,000
$40,000
-$5,000
$0
© 2008 Prentice Hall, Inc.
S7 – 46
Decision Trees and
Capacity Decision
Market favorable (.4)
Market unfavorable (.6)
Market favorable (.4)
Medium plant
Large Plant
Market unfavorable (.6)
EMV = (.4)($100,000)
+ (.6)(-$90,000)
Market favorable (.4)
EMV = -$14,000
Market unfavorable (.6)
$100,000
-$90,000
$60,000
-$10,000
$40,000
-$5,000
$0
© 2008 Prentice Hall, Inc.
S7 – 47
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
© 2008 Prentice Hall, Inc.
S7 – 48
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
© 2008 Prentice Hall, Inc.
S7 – 49
Net Present Value (NPV)
F
P=
(1 + i)N
where
© 2008 Prentice Hall, Inc.
F
P
i
N
= future value
= present value
= interest rate
= number of years
S7 – 50
Net Present Value (NPV)
F
P=
(1 + i)N
While
this works
where
F = future value
fine, it isP = present value
cumbersome for
larger values iof= Ninterest rate
N = number of years
© 2008 Prentice Hall, Inc.
S7 – 51
NPV Using Factors
F
P=
= FX
N
(1 + i)
where
Portion of
Table S7.1
© 2008 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 – 52
Present Value of an Annuity
An annuity is an investment which
generates uniform equal payments
S = RX
where
© 2008 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 – 53
Present Value of an Annuity
Portion of Table S7.2
Year
1
2
3
4
5
© 2008 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 – 54
Present Value of an Annuity
$7,000 in receipts per for 5 years
Interest rate = 6%
From Table S7.2
X = 4.212
S = RX
S = $7,000(4.212) = $29,484
© 2008 Prentice Hall, Inc.
S7 – 55
Present Value With Different
Future Receipts
Investment A’s
Cash Flow
Investment B’s
Cash Flow
Year
Present Value
Factor at 8%
$10,000
$9,000
1
.926
9,000
9,000
2
.857
8,000
9,000
3
.794
7,000
9,000
4
.735
© 2008 Prentice Hall, Inc.
S7 – 56
Present Value With Different
Future Receipts
Investment A’s
Present Values
Investment B’s
Present Values
1
$9,260 = (.926)($10,000)
$8,334 = (.926)($9,000)
2
7,713 = (.857)($9,000)
7,713 = (.857)($9,000)
3
6,352 = (.794)($8,000)
7,146 = (.794)($9,000)
4
5,145 = (.735)($7,000)
6,615 = (.735)($9,000)
Year
Totals
Minus initial
investment
Net present
value
© 2008 Prentice Hall, Inc.
$28,470
$29,808
-25,000
-26,000
$3,470
$3,808
S7 – 57
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