Managing Capacity and Demand
Learning Objectives
 Describe
the strategies for matching
capacity and demand for services.
 Recommend an overbooking strategy.
 Use Linear Programming to prepare a
weekly workshift schedule.
 Prepare a work schedule for part-time
employees.
 Use yield management.
Strategies for Matching Supply
and Demand for Services
DEMAND
STRATEGIES
Developing
complementary
services
Developing
reservation
systems
SUPPLY
STRATEGIES
Partitioning
demand
Sharing
capacity
Establishing
price
incentives
Crosstraining
employees
Promoting
off-peak
demand
Using
part-time
employees
Yield
management
Increasing
customer
participation
Scheduling
work shifts
Creating
adjustable
capacity
Segmenting Demand at a Health Clinic
Percentage of average daily
physician visits
140
130
120
Smoothing Demand by Appointment
Scheduling
110
Day
Appointments
100
Monday
Tuesday
Wednesday
Thursday
Friday
90
80
70
60
1
2
3
Day of week
4
5
84
89
124
129
114
Discriminatory Pricing for Camping
Experience
type
1
2
3
4
Days and weeks of camping season
Saturdays and Sundays of weeks 10 to 15, plus
Dominion Day and civic holidays
Saturdays and Sundays of weeks 3 to 9 and 15 to 19,
plus Victoria Day
Fridays of weeks 3 to 15, plus all other days of weeks
9 to 15 that are not in experience type 1 or 2
Rest of camping season
No. of
days
14
Daily
fee
$6.00
23
2.50
43
0.50
78
free
EXISTING REVENUE VS PROJECTED REVENUE FROM DISCRIMINATORY PRICING
Experience
type
1
2
3
4
Total
Existing flat fee of $2.50
Campsites
occupied
Revenue
5.891
$14,727
8,978
22,445
6,129
15,322
4,979
12,447
25,977
$ 64,941
Discriminatory fee
Campsites
occupied (est.)
Revenue
5,000
$30,000
8,500
21,250
15,500
7.750
….
….
29,000
$59,000
Hotel Overbooking Loss Table
Number of Reservations Overbooked
NoProbshows
ability
0
.07
1
.19
2
.22
3
.16
4
.12
5
.10
6
.07
7
.04
8
.02
9
.01
Expected loss, $
0
0
40
80
120
160
200
240
280
320
360
121.60
1
2
3
4
5
100
200
300
400
500
0
100
200
300
400
40
0
100
200
300
80
40
0
100
200
120
80
40
0
100
160
120
80
40
0
200
160
120
80
40
240
200
160
120
80
280
240
200
160
120
320
280
240
200
160
91.40 87.80 115.00 164.60 231.00
6
7
8
9
600
700
800
900
500
600
700
800
400
500
600
700
300
400
500
600
200
300
400
500
100
200
300
400
0
100
200
300
40
0
100
200
80
40
0
100
120
80
40
0
311.40 401.60 497.40 560.00
Daily Scheduling of
Telephone Operator Workshifts
2500
30
Number of operators
Topline profile
Calls
2000
1500
1000
500
0
12
2
4
6
8
10
12
Time
2
4
6
8
10
12
25
20
Scheduler program assigns
tours so that the number of
operators present each half
hour adds up to the number
15
10
required
5
012
Tour
2
4
6
8
10
12
Time
2
4
6
8
10
12
LP Model for Weekly Workshift
Schedule with Two Days-off Constraint
Objective function:
Minimize
x1 + x2 + x3 + x4 + x5 + x6 + x7
Constraints:
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Operator
1
2
3
4
5
6
7
8
Total
Required
Excess
Su
x
…
…
…
…
…
…
x
6
3
3
x2 + x3 + x4 + x5 + x6
x3 + x4 + x5 + x6 + x7
x1
+ x4 + x5 + x6 + x7
x1 + x2
+ x5 + x6 + x7
x1 + x2 + x3
+ x6 + x7
x1 + x2 + x3 + x4
+ x7
x1 + x2 + x3 + x4 + x5
xi  0 and integer
3
6
5
6
5
5
5
Schedule matrix, x = day off
M
Tu
W
Th
x
…
…
…
x
x
…
…
...
x
x
…
...
x
x
…
…
…
…
x
…
…
…
x
…
…
…
x
…
…
…
…
6
5
6
5
6
5
6
5
0
0
0
0
F
…
…
…
…
x
x
x
…
5
5
0
Sa
...
…
…
…
…
…
…
x
7
5
2
Tellers required
5 6
2 3 4
7
Scheduling Part-time Bank Tellers
Tellers required
0 1 2 3 4 5
Decreasing part-time teller demand histogram
0
1
Two Full-time Tellers
Mon.
Tues.
Object ive
Minimize
Wed.
Thurs.
5
4
3
2
1
4
3
2
1
1
5
2
Fri.
Mon.
Wed.
Thurs
Fri.
funct io n:
x1 +
Co nst raint s:
Sunday
Mo nday
x2 +x3 +x4 +x5 +x6 +x7
x2 +x3 +x4 +x5 +x6
x3 +x4 +x5 +x6 +x7


b1
b2
DAILY PART-TIME WORK SCHEDULE, X=workday
Teller
1
2
3,4
5
Mon.
x
x
x
….
Tues.
….
….
….
….
Wed.
x
….
….
x
Thurs.
….
x
….
….
Fri.
x
x
x
x
Tues.
Ideal Characteristics for Yield Management
 Relatively
Fixed Capacity
 Ability to Segment Markets
 Perishable Inventory
 Product Sold in Advance
 Fluctuating Demand
 Low Marginal Sales Cost and High
Capacity Change Cost
Percentage of capacity allocated
to different service classes
Seasonal Allocation of Rooms by
Service Class for Resort Hotel
First class
30%
20%
50%
Standard
20%
30%
20%
50%
60%
Budget
10%
Peak
(30%)
Summer
30%
Shoulder
(20%)
Fall
50%
30%
Off-peak
(40%)
Winter
Shoulder
(10%)
Spring
Percentage of capacity allocated to different seasons
Demand Control Chart for a Hotel
300
Expected Reservation Accumulation
2 standard deviation control limits
200
150
100
50
Days before arrival
86
81
76
71
66
61
56
51
46
41
36
31
26
21
16
11
6
0
1
Reservations
250
Yield Management Using the
Critical Fractile Model
Cu
( F  D)
P(d  x ) 

Cu  Co
p F
Where x = seats reserved for full-fare passengers
d = demand for full-fare tickets
p = proportion of economizing (discount) passengers
Cu = lost revenue associated with reserving one too few seats
at full fare (underestimating demand). The lost opportunity is the
difference between the fares (F-D) assuming a passenger, willing
to pay full-fare (F), purchased a seat at the discount (D) price.
Co = cost of reserving one to many seats for sale at full-fare
(overestimating demand). Assume the empty full-fare seat would
have been sold at the discount price. However, Co takes on two
values, depending on the buying behavior of the passenger who
would have purchased the seat if not reserved for full-fare.
if an economizing passenger
D
Co  
 ( F  D)
if a full fare passenger (marginal gain)
Expected value of Co = pD-(1-p)(F-D) = pF - (F-D)
Topics for Discussion
 What
organizational problems can arise from the
use of part-time employees?
 How can computer-based reservation systems
increase service capacity utilization?
 What possible dangers are associated with
developing complementary services?
 Will the widespread use of yield management
eventually erode the concept of fixed prices?
 What possible negative effects can yield
management have on customer relations?
Interactive Exercise
Watch the PowerPoint presentation
concerning the overbooking experience at
the Doubletree Hotel in Houston, Texas.
How could this situation been handled
differently?