Capacity Planning
Production Planning and
Control
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
 Used to plan overtime horizon
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
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
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
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, 8 hours, 3 shifts
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
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, 8 hours, 3 shifts
Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
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, 8 hours, 3 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%
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, 8 hours, 3 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%
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, 8 hours, 3 shifts
Efficiency = 84.6%
Efficiency of new line = 75%
Expected Output = (Effective Capacity)(Efficiency)
= (175,000)(.75) = 131,250 rolls
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
Managing Demand
 Demand exceeds capacity
 Limit 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
Average unit cost
(dollars per room per night)
Economies and Diseconomies of
Scale
25 - Room
Roadside Motel
50 - Room
Roadside Motel
Economies of
scale
25
75 - Room
Roadside Motel
Diseconomies of
scale
50
Number of Rooms
75
Capacity Considerations
 Forecast demand accurately
 Understanding the technology and
capacity increments
 Find the optimal operating level
(volume)
 Build for change
Tactics for Matching Capacity to
Demand
1. Making staffing changes
2. Adjusting equipment and processes
 Purchasing additional machinery
 Selling or leasing out existing equipment
3. Improving methods to increase
throughput
4. Redesigning the product to facilitate
more throughput
Complementary Demand Patterns
Sales in units
4,000 –
3,000 –
By combining
both, the
variation is
reduced
Snowmobile
sales
2,000 –
1,000 –
JFMAMJJASONDJFMAMJJASONDJ
Time (months)
Jet ski
sales
Approaches to Capacity
Expansion
Expected
demand
New
capacity
Expected
demand
Demand
New
capacity
New
capacity
(c) Capacity lags demand with
incremental expansion
Demand
(b) Leading demand with
one-step expansion
Expected
demand
(d) Attempts to have an average
capacity with incremental
expansion
Demand
Demand
(a) Leading demand with
incremental expansion
New
capacity
Expected
demand
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
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
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
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
|
Volume (units per period)
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
BEPx =
F
P-V
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
Break-Even Example
Fixed costs = $10,000 Material = $.75/unit
Direct labor = $1.50/unit Selling price = $4.00 per unit
$10,000
F
BEP$ =
=
1 - (V/P) 1 - [(1.50 + .75)/(4.00)]
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 - (V/P) 1 - [(1.50 + .75)/(4.00)]
$10,000
=
= $22,857.14
.4375
$10,000
F
BEPx =
=
= 5,714
4.00 - (1.50 + .75)
P-V
Break-Even Example
50,000 –
Revenue
Dollars
40,000 –
Break-even
point
30,000 –
Total
costs
20,000 –
Fixed costs
10,000 –
|–
|
|
|
|
|
0
2,000
4,000
6,000
8,000
10,000
Units
Break-Even Example
Multiproduct Case
BEP$ =
where
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
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
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
$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
Multiproduct Example
BEP =
$
Fixed costs = $3,500 per month
∑
F
1 - Vi x (Wi)
Pi
$3,500
x Forecasted
12
Annual
=
= $67,200
Cost
Sales Units
.625
Item
Price
Sandwich
$2.95
$1.25
7,000
$67,200
Soft drink
.80
.30
7,000
Daily
=
= $215.38
Weighted
Baked potato
1.55
.47 Annual
5,000
sales
312
days
% 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
Sandwich
Soft drink
Baked
potato
Tea
Salad bar
$2.95
.80
1.55
$1.25
.30
.47
.42
.38
.30
.58
.62
.70
$20,650
$2.95
5,600
7,750
.75
2.85
.25
1.00
.33
.35
.67
.65
3,750
8,550
$46,300
= 32.6 .259
33
.446
sandwiches
.121
.075
.167per day
.117
.081
.185
1.000
.054
.120
.625
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
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
Net Present Value (NPV)
P=
where
F
P
i
N
F
(1 + i)N
= future value
= present value
= interest rate
= number of years
NPV Using Factors
P=
where
Portion of
Table S7.1
F
= FX
N
(1 + i)
X = a factor from Table S7.1
defined as = 1/(1 + i)N and
F = future value
Year
1
2
3
4
5
5%
.952
.907
.864
.823
.784
6%
.943
.890
.840
.792
.747
7%
.935
.873
.816
.763
.713
…
10%
.909
.826
.751
.683
.621
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
Present Value of an Annuity
Portion of Table S7.2
Year
1
2
3
4
5
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
Questions?