1. 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

2. 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

3. Outline – Continued
 Capacity Planning
 Break-Even Analysis
 Single-Product Case
 Multiproduct Case
 Applying Decision Trees to
Capacity Decisions
© 2008 Prentice Hall, Inc. S7 – 3

4. Outline – Continued
 Applying Investment Analysis to
Strategy-Driven Investments
 Investment, Variable Cost, and
Cash Flow
 Net Present Value
© 2008 Prentice Hall, Inc. S7 – 4

5. 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

6. 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

7. Planning Over a Time
Horizon
Long-range Add facilities
planning Add long lead time equipment
*
Intermediate- Subcontract Add personnel
range Add equipment Build or use inventory
planning Add shifts
Schedule jobs
Short-range
planning
* Schedule personnel
Allocate machinery
Modify capacity Use capacity
* Limited options exist
Figure S7.1
© 2008 Prentice Hall, Inc. S7 – 7

8. 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

9. 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

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 – 10

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
© 2008 Prentice Hall, Inc. S7 – 11

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 – 12

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%
© 2008 Prentice Hall, Inc. S7 – 13

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 – 14

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
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

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 – 16

17. 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

18. 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

19. 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

20. Economies and
Diseconomies of Scale
(dollars per room per night)
Average unit cost
25 - room 75 - room
roadside motel 50 - room roadside motel
roadside motel
Economies Diseconomies
of scale of scale
25 50 75
Number of Rooms
Figure S7.2
© 2008 Prentice Hall, Inc. S7 – 20

21. Build In Flexibility
Percent of North American Vehicles
Made on Flexible Assembly Lines
100% –
80% –
60% –
40% –
Chrysler
20% –
Toyota
Nissan
Honda
Ford
GM
0–
Figure S7.3
© 2008 Prentice Hall, Inc. S7 – 21

22. 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

23. Complementary Demand
Patterns
4,000 –
Sales in units
3,000 –
2,000 –
1,000 –
Jet ski
engine
sales
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
Figure S7.3
© 2008 Prentice Hall, Inc. S7 – 23

24. Complementary Demand
Patterns
4,000 –
Sales in units
3,000 – Snowmobile
motor sales
2,000 –
1,000 –
Jet ski
engine
sales
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
Figure S7.3
© 2008 Prentice Hall, Inc. S7 – 24

25. Complementary Demand
Patterns
Combining both
demand patterns
reduces the
variation
4,000 –
Sales in units
3,000 – Snowmobile
motor sales
2,000 –
1,000 –
Jet ski
engine
sales
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
Figure S7.3
© 2008 Prentice Hall, Inc. S7 – 25

26. 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

27. 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

28. Approaches to Capacity
Expansion
(a) Leading demand with (b) Leading demand with
incremental expansion one-step expansion
New New
capacity capacity
Demand
Demand
Expected
Expected
demand
demand
(c) Capacity lags demand with (d) Attempts to have an average
incremental expansion capacity with incremental
New
expansion
capacity New
Demand
Expected Demand capacity Expected
demand demand
Figure S7.5
© 2008 Prentice Hall, Inc. S7 – 28

29. Approaches to Capacity
Expansion
(a) Leading demand with incremental
expansion
New
capacity
Demand
Expected
demand
1 2 3
Time (years)
Figure S7.5
© 2008 Prentice Hall, Inc. S7 – 29

30. Approaches to Capacity
Expansion
(b) Leading demand with one-step
expansion
New
capacity
Expected
Demand
demand
1 2 3
Time (years)
Figure S7.5
© 2008 Prentice Hall, Inc. S7 – 30

31. Approaches to Capacity
Expansion
(c) Capacity lags demand with incremental
expansion
New
capacity
Expected
Demand
demand
1 2 3
Time (years)
Figure S7.5
© 2008 Prentice Hall, Inc. S7 – 31

32. Approaches to Capacity
Expansion
(d) Attempts to have an average capacity
with incremental expansion
New
capacity
Expected
Demand
demand
1 2 3
Time (years)
Figure S7.5
© 2008 Prentice Hall, Inc. S7 – 32

33. 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

34. 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

35. 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

36. Break-Even Analysis
–
Total revenue line
900 –
r
800 –
Break-even point rrido Total cost line
o
700 – Total cost = Total revenue f i tc
P ro
Cost in dollars
600 –
500 –
Variable cost
400 –
300 –
s
200 – os idor
L r
r
co
100 – Fixed cost
| | | | | | | | | | | |
–
0 100 200 300 400 500 600 700 800 900 1000 1100
Figure S7.6
Volume (units per period)
© 2008 Prentice Hall, Inc. S7 – 36

37. Break-Even Analysis
BEPx = break- x= number of
even point in units units produced
BEP$ = break- TR = total
even point in dollars revenue = Px
P = price F= fixed costs
per unit (after all V =
discounts) variable cost per unit
TC = total
Break-even point costs = F + Vx
occurs when
TR = TC F
or BEPx =
P-V
Px = F + Vx
© 2008 Prentice Hall, Inc. S7 – 37

38. Break-Even Analysis
BEPx = break- x= number of
even point in units units produced
BEP$ = break- TR = total
even point in dollars revenue = Px
P = price F= fixed costs
per unit (after all V =
discounts) variable cost per unit
TC = total
BEP$ = BEPx P costs = F + Vx
F Profit = TR - TC
= P-V P
= Px - (F + Vx)
F
= (P - V)/P = Px - F - Vx
F = (P - V)x - F
= 1 - V/P
© 2008 Prentice Hall, Inc. S7 – 38

39. Break-Even Example
Fixed costs = $10,000 Material = $.75/unit
Direct labor = $1.50/unit Selling price = $4.00 per unit
F $10,000
BEP$ = =
1 - (V/P) 1 - [(1.50 + .75)/(4.00)]
© 2008 Prentice Hall, Inc. S7 – 39

40. Break-Even Example
Fixed costs = $10,000 Material = $.75/unit
Direct labor = $1.50/unit Selling price = $4.00 per unit
F $10,000
BEP$ = =
1 - (V/P) 1 - [(1.50 + .75)/(4.00)]
$10,000
= = $22,857.14
.4375
F $10,000
BEPx = = = 5,714
P-V 4.00 - (1.50 + .75)
© 2008 Prentice Hall, Inc. S7 – 40

41. Break-Even Example
50,000 –
40,000 – Revenue
Break-even
30,000 – point Total
Dollars
costs
20,000 –
10,000 –
Fixed costs
–
| | | | | |
0 2,000 4,000 6,000 8,000 10,000
Units
© 2008 Prentice Hall, Inc. S7 – 41

42. Break-Even Example
Multiproduct Case
F
BEP$ =
∑ 1-
Vi
Pi
x (Wi)
where V = variable cost per unit
P = price per unit
F = fixed costs
W = percent each product is of total dollar sales
i = each product
© 2008 Prentice Hall, Inc. S7 – 42

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 5,000
Tea .75 .25 5,000
Salad bar 2.85 1.00 3,000
© 2008 Prentice Hall, Inc. S7 – 43

44. 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
Tea Selling Variable .75 .25Forecasted 5,000 Contribution
% of
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 $2.95 $1.25 .42 .58 $20,650 .446 .259
Soft drink .80 .30 .38 .62 5,600 .121 .075
Baked 1.55 .47 .30 .70 7,750 .167 .117
potato
Tea .75 .25 .33 .67 3,750 .081 .054
Salad bar 2.85 1.00 .35 .65 8,550 .185 .120
$46,300 1.000 .625
© 2008 Prentice Hall, Inc. S7 – 44

45. Multiproduct Example BEP$ =
F
∑ 1 - V x (W )
P
i
i
i
Fixed costs = $3,500 per month
$3,500 x Forecasted
Annual 12 = $67,200
=
Item Price Cost .625 Units
Sales
Sandwich $2.95 $1.25 7,000
Soft drink .80 Daily
.30 $67,200
7,000
Baked potato 1.55 sales 312 days = $215.38
=
.47 Annual 5,000 Weighted
Tea Selling Variable .75 .25Forecasted 5,000 Contribution
% of
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)
Salad bar 2.85 1.00 x $215.38
.446 3,000
Sandwich $2.95 $1.25 .42 .58 $20,650 = 32.6 ≈ .259
.446 33
$2.95 sandwiches
Soft drink .80 .30 .38 .62 5,600 .121 .075
Baked 1.55 .47 .30 .70 7,750 .167 per day
.117
potato
Tea .75 .25 .33 .67 3,750 .081 .054
Salad bar 2.85 1.00 .35 .65 8,550 .185 .120
$46,300 1.000 .625
© 2008 Prentice Hall, Inc. S7 – 45

46. Decision Trees and
Capacity Decision
Market favorable (.4)
$100,000
Market unfavorable (.6)
t -$90,000
plan
e
Larg
Market favorable (.4)
$60,000
Medium plant
Sm Market unfavorable (.6)
all -$10,000
pla
nt
Do
Market favorable (.4)
no $40,000
th
in
g
Market unfavorable (.6)
-$5,000
$0
© 2008 Prentice Hall, Inc. S7 – 46

47. Decision Trees and
Capacity Decision
Market favorable (.4)
$100,000
Market unfavorable (.6)
t -$90,000
plan
e
Larg
Market favorable (.4)
$60,000
Medium plant
Large Plant
Sm
all
Market unfavorable (.6)
-$10,000
pla
nt
EMV = (.4)($100,000)
Do
Market favorable (.4)
no $40,000
+ (.6)(-$90,000)
th
in
g
Market unfavorable (.6)
EMV = -$14,000 -$5,000
$0
© 2008 Prentice Hall, Inc. S7 – 47

48. Decision Trees and
Capacity Decision
-$14,000
Market favorable (.4)
$100,000
Market unfavorable (.6)
t -$90,000
plan
e
Larg $18,000
Market favorable (.4)
$60,000
Medium plant
Sm Market unfavorable (.6)
all -$10,000
pla
nt $13,000
Do
Market favorable (.4)
no $40,000
th
in
g
Market unfavorable (.6)
-$5,000
$0
© 2008 Prentice Hall, Inc. S7 – 48

49. 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

50. Net Present Value (NPV)
F
P=
(1 + i)N
where F = future value
P = present value
i = interest rate
N = number of years
© 2008 Prentice Hall, Inc. S7 – 50

51. Net Present Value (NPV)
F
P=
(1 + i)N
While this works
where F = future value
fine, it is = present value
P
cumbersome for
larger values iof N
= interest rate
N = number of years
© 2008 Prentice Hall, Inc. S7 – 51

52. NPV Using Factors
F
P= = FX
(1 + i) N
where X= a factor from
Table S7.1 defined as = 1/
(1 + i)N and F = future
value
Year 5% 6% 7% … 10%
Portion of 1 .952 .943 .935 .909
Table S7.1 2 .907 .890 .873 .826
3 .864 .840 .816 .751
4 .823 .792 .763 .683
5 .784 .747 .713 .621
© 2008 Prentice Hall, Inc. S7 – 52

53. Present Value of an Annuity
An annuity is an investment which
generates uniform equal payments
S = RX
where 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
© 2008 Prentice Hall, Inc. S7 – 53

54. Present Value of an Annuity
Portion of Table S7.2
Year 5% 6% 7% … 10%
1 .952 .943 .935 .909
2 1.859 1.833 1.808 1.736
3 2.723 2.676 2.624 2.487
4 4.329 3.465 3.387 3.170
5 5.076 4.212 4.100 3.791
© 2008 Prentice Hall, Inc. S7 – 54

55. 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

56. Present Value With Different
Future Receipts
Investment A’s Investment B’s Present Value
Year
Cash Flow Cash Flow 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

57. Present Value With Different
Future Receipts
Investment A’s Investment B’s
Year Present Values 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)
Totals $28,470 $29,808
Minus initial
investment -25,000 -26,000
Net present
value $3,470 $3,808
© 2008 Prentice Hall, Inc. S7 – 57