Chapter 9
Capacity and
Aggregate
Planning
BA 320 Operations Management
Capacity Planning
 Establishes overall level of
productive resources
 Affects lead time
responsiveness, cost &
competitiveness
 Determines when and how
much to increase capacity
BA 320 Operations Management
Capacity Expansion
 Volume & certainty of anticipated
demand
 Strategic objectives for growth
 Costs of expansion & operation
 Incremental or one-step
expansion
BA 320 Operations Management
Capacity Expansion Strategies
BA 320 Operations Management
Capacity Expansion Strategies
(a) Capacity lead strategy
(b) Capacity lag strategy
Capacity
Demand
Units
Units
Demand
Capacity
Time
Time
(c) Average capacity strategy
(d) Incremental vs. one-step expansion
One-step expansion
Capacity
Units
Units
Demand
Incremental
expansion
Demand
Figure 9.1
Time
Time
BA 320 Operations Management
Average cost per room
Best Operating Levels
Figure 9.2
# Rooms
BA 320 Operations Management
Average cost per room
Best Operating Levels
Best operating
level
Economies
of scale
250
Figure 9.2
Diseconomies
of scale
500
1000
# Rooms
BA 320 Operations Management
Aggregate Production
Planning (APP)
 Matches market demand to company
resources
 Plans production 6 months to 12 months
in advance
 Expresses demand, resources, and
capacity in general terms
 Develops a strategy for economically
meeting demand
 Establishes a company-wide game plan
for allocating resources
BA 320 Operations Management
Inputs and Outputs to APP
BA 320 Operations Management
Inputs and Outputs to APP
Capacity
Constraints
Demand
Forecasts
Size of
Workforce
Strategic
Objectives
Company
Policies
Aggregate
Production
Planning
Production
per month
(in units or $)
Inventory
Levels
Financial
Constraints
Units or dollars
subcontracted,
backordered, or lost
Figure 9.3
BA 320 Operations Management
Adjusting Capacity to
Meet Demand
1. Producing at a constant rate and using inventory
to absorb fluctuations in demand (level
production)
2. Hiring and firing workers to match demand (chase
demand)
3. Maintaining resources for high demand levels
4. Increase or decrease working hours (overtime
and undertime)
5. Subcontracting work to other firms
6. Using part-time workers
7. Providing the service or product at a later time
period (backordering)
BA 320 Operations Management
Strategy Details
 Level production - produce at constant
rate & use inventory as needed to meet
demand
 Chase demand - change workforce levels
so that production matches demand
 Maintaining resources for high demand
levels - ensures high levels of customer
service
BA 320 Operations Management
Strategy Details
 Overtime & undertime - common when
demand fluctuations are not extreme
 Subcontracting - useful if supplier meets
quality & time requirements
 Part-time workers - feasible for unskilled
jobs or if labor pool exists
 Backordering - only works if customer is
willing to wait for product/services
BA 320 Operations Management
Level Production
BA 320 Operations Management
Level Production
Demand
Units
Production
Time
Figure 9.4 (a)
BA 320 Operations Management
Chase Demand
Demand
Units
Production
Time
Figure 9.4 (b)
BA 320 Operations Management
APP Using Pure Strategies
QUARTER
Spring
Summer
Fall
Winter
Hiring cost
Firing cost
Inventory carrying cost
Production per employee
Beginning work force
SALES FORECAST (LB)
80,000
50,000
120,000
150,000
= $100 per worker
= $500 per worker
= $0.50 pound per quarter
= 1,000 pounds per quarter
= 100 workers
Example 9.1
BA 320 Operations Management
APP Using Pure Strategies
QUARTER
Spring
Summer
Fall
Winter
SALES FORECAST (LB)
80,000
50,000
120,000
150,000
Level production
Hiring cost = $100 per worker
Firing cost = $500 per worker
(50,000carrying
+ 120,000
+ 150,000
80,000)
Inventory
cost
= $0.50+pound
per quarter
4
Production per employee = 1,000 pounds per quarter
Beginning work
forcepounds
= 100 workers
= 100,000
Example 9.1
BA 320 Operations Management
Level Production Strategy
QUARTER
Spring
Summer
Fall
Winter
SALES
FORECAST
80,000
50,000
120,000
150,000
PRODUCTION
PLAN
INVENTORY
100,000
100,000
100,000
100,000
400,000
20,000
70,000
50,000
0
140,000
Cost = 140,000 pounds x 0.50 per pound = $70,000
Example 9.1
BA 320 Operations Management
Chase Demand Strategy
QUARTER
SALES PRODUCTION
FORECAST
PLAN
Spring
Summer
Fall
Winter
80,000
50,000
120,000
150,000
80,000
50,000
120,000
150,000
WORKERS
NEEDED
80
50
120
150
WORKERS WORKERS
HIRED
FIRED
0
0
70
30
20
30
0
0
100
50
Cost = (100 workers hired x $100) + (50 workers fired x $500)
= $10,000 + 25,000 = $35,000
Example 9.1
BA 320 Operations Management
APP Using Mixed Strategies
MONTH
January
February
March
April
May
June
DEMAND (CASES)
1000
400
400
400
400
400
MONTH
DEMAND (CASES)
July
August
September
October
November
December
500
500
1000
1500
2500
3000
Production per employee = 100 cases per month
Wage rate = $10 per case for regular production
= $15 per case for overtime
= $25 for subcontracting
Hiring cost = $1000 per worker
Firing cost = $500 per worker
Inventory carrying cost = $1.00 case per month
Beginning work force = 10 workers
Example 9.2
BA 320 Operations Management
APP by Linear Programming
Minimize Z = $100 (H1 + H2 + H3 + H4)
+ $500 (F1 + F2 + F3 + F4)
+ $0.50 (I1 + I2 + I3 + I4)
Subject to
Demand
constraints
where
Ht = # hired for period t
Ft = # fired for period t
It = inventory at end
of period t
Pt = units produced
in period t
Wt = workforce size
for period t
Example 9.3
Production
constraints
Work force
constraints
P1 - I1
I1 + P2 - I2
I2 + P3 - I3
I3 + P4 - I4
1000 W1
1000 W2
1000 W3
1000 W4
100 + H1 - F1
W1 + H2 - F2
W2 + H3 - F3
W3 + H4 - F4
= 80,000
= 50,000
= 120,000
= 150,000
= P1
= P2
= P3
= P4
= W1
= W2
= W3
= W4
BA 320 Operations Management
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
APP by the Transportation
Method
QUARTER
EXPECTED
DEMAND
REGULAR
CAPACITY
OVERTIME
CAPACITY
SUBCONTRACT
CAPACITY
1
2
3
4
900
1500
1600
3000
1000
1200
1300
1300
100
150
200
200
500
500
500
500
Regular production cost per unit
Overtime production cost per unit
Subcontracting cost per unit
Inventory holding cost per unit per period
Beginning inventory
$20
$25
$28
$3
300 units
Example 9.4
BA 320 Operations Management
The Transportation Tableau
Table 9.2
PERIOD OF USE
PERIOD OF PRODUCTION
1
Beginning
1
2
2
0
Inventory
300
Regular
600
3
—
20
300
6
—
23
100
29
1000
100
34
100
37
500
Subcontract
28
31
34
Subcontract
Regular
23
—
26
1200
25
28
150
31
150
28
31
—
1300
Overtime
200
Regular
250
—
23
25
—
28
500
1300
Overtime
200
Subcontract
500
Demand
900
1500
1600
34
20
28
Subcontract
4
—
31
20
300
26
28
1200
Capacity
9
—
25
Regular
Unused
Capacity
4
Overtime
Overtime
3
3
3000
250
500
1300
200
31
500
20
1300
25
200
28
500
250
BA 320 Operations Management
Burruss’
Production Plan
REGULAR
SUBENDING
PERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY
1
2
3
4
Total
900
1500
1600
3000
7000
1000
1200
1300
1300
4800
100
150
200
200
650
0
250
500
500
1250
Table 9.3
BA 320 Operations Management
500
600
1000
0
2100
Other Quantitative
Techniques
 Linear decision rule (LDR)
 Search decision rule (SDR)
 Management coefficients model
BA 320 Operations Management
Demand Management
 Shift demand into other periods
 Incentives, sales promotions,
advertising campaigns
 Offer product or services with
countercyclical demand patterns
 Partnering with suppliers to reduce
information distortion along the
supply chain
BA 320 Operations Management
Demand Distortion along
the Supply Chain
BA 320 Operations Management
Hierarchical Planning Process
BA 320 Operations Management
Hierarchical Planning Process
Production
Planning
Capacity
Planning
Resource
Level
Product lines
or families
Aggregate
production
plan
Resource
requirements
plan
Plants
Individual
products
Master
production
schedule
Rough-cut
capacity
plan
Critical
work
centers
Components
Material
requirements
plan
Capacity
requirements
plan
All
work
centers
Manufacturing
operations
Shop
floor
schedule
Input/
output
control
Individual
machines
Items
Figure 9.5
BA 320 Operations Management
Available-to-Promise
ON-HAND = 50
Forecast
Customer orders
Master production schedule
Available to promise
ON-HAND = 50
Forecast
Customer orders
Master production schedule
Available to promise
1
2
100
100
200
PERIOD
3
4
100
100
200
1
2
100
90
200
40
100
120
6
100
100
200
PERIOD
3
4
100
130
200
0
5
100
70
ATP in period 1 = (50 + 200) - (90 + 120) = 40
ATP in period 3 = 200 - (130 + 70) = 0
ATP in period 5 = 200 - (20 + 10) = 170
Example 9.5
BA 320 Operations Management
5
6
100
20
200
170
100
10
Available-to-Promise
BA 320 Operations Management
Available-to-Promise
Product
Request
Yes
Is the product
available at
this location?
No
Availableto-promise
Yes
No
Allocate
inventory
Yes
Figure 9.6
Is an alternative
product available
at this location?
Is this product
available at a
different
location?
No
Is an alternative
product available
at an alternate
location?
Yes
No
Allocate
inventory
Capable-topromise date
Is the customer
willing to wait for
the product?
Availableto-promise
Yes
No
Lose sale
BA 320 Operations Management
Revise master
schedule
Trigger production
Aggregate Planning
for Services
Most services can’t be inventoried
Demand for services is difficult to predict
Capacity is also difficult to predict
Service capacity must be provided at the
appropriate place and time
5. Labor is usually the most constraining
resource for services
1.
2.
3.
4.
BA 320 Operations Management
Yield Management
Cu
P(n < x) 
Cu + Co
where
n = number of no-shows
x = number of rooms or seats overbooked
Cu = cost of underbooking; i.e., lost sale
Co = cost of overbooking; i.e., replacement cost
P = probability
BA 320 Operations Management
Yield Management
NO-SHOWS
PROBABILITY
0
1
2
3
.15
.25
.30
.30
Example 9.4
BA 320 Operations Management
Yield Management
NO-SHOWS
PROBABILITY
P(N < X)
0
1
2
3
.15
.25
.30
.30
.00
.15
.40
.70
Expected number of no shows
0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75
Optimal probability of no-shows
Cu
75
P(n < x)  C + C =
= .517
75
+
70
u
o
Example 9.4
BA 320 Operations Management
.517
Yield Management
NO-SHOWS
PROBABILITY
P(N < X)
Cost of overbooking
0
.15
.00
[2(.15) + 1(.25)]$70
= $38.50 .25
Cost of bumping customers
1
.15
Lost revenue from .40
no-shows.517
2(.30)$75 = $22.50 .30
3
.70
$61.00 .30
Total cost of overbooking
by
2 rooms
Expected number of no shows
Expected savings = ($131.225 - $61) = $70.25 a night
0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75
Optimal probability of no-shows
Cu
75
P(n < x)  C + C =
= .517
75
+
70
u
o
Example 9.4
BA 320 Operations Management