Managing Capacity and
Demand
Shin‐Ming Guo
NKFUST
• Managing dynamic demand
• Service capacity is perishable
• Yield Management
Case: Increase Revenue with Fixed Capacity
• The Park Hyatt Philadelphia, 118 King/Queen rooms.
• Regular fare is rH= $225 (high fare) targeting business travelers.
• Hyatt offers a rL= $159 (low fare) discount fare for a mid‐week stay targeting leisure travelers. • Demand for low fare rooms is abundant.
• Most of the high fare demand occurs only within a few days of the actual stay.
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Booking Limits and Yield Management
• Choice 1: Do not accept low fare reservation. Hope that high fare customers will eventually show up.
• Choice 2: Accept low fare reservations without any limit. • Choice 3: Accept low fare reservations but reserve rooms for high fare customers
• Objective: Maximize expected revenues by controlling the sale of low fare rooms. 3
Service Capacity
Capacity: amount of output over a period of time

Participation: Need to be near customers

Simultaneity: Inability to transport services

Perishability: Inability to store services

Heterogeneity: Volatility of demand
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Focus: Matching Capacity with Demand
• Demand can vary and is unpredictable.
• Capacity is inflexible and maybe costly.
• Demand < Capacity  Impossible to stock service
• Demand > Capacity  Customers may not wait for service
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Economic Consequences of Mismatch
Air travel
Emergency Room Retailing
Supply
Seats on specific flight
Medical service
Demand
Travel for specific Urgent need for time & destination medical service Supply
Empty seat
Exceeds
Demand Demand
Exceeds Supply
Overbooking; Profit loss
Doctors, nurses, and infrastructure are under‐utilized Consumer
electronics Kids buying video games
High inventory costs
Crowding and delays Foregone profit; in the ER, Deaths
Consumer dissatisfaction 6
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7
Matching Supply and Demand for Services
DEMAND
Strategies
1 Managing Variability
3 Establishing
price incentives
5 Developing
complementary
services
Capacity
Strategies
2 Partitioning
demand
Sharing
capacity
4 Promoting off‐peak
demand
9 Cross‐
training
employees
6 Developing
reservation
systems 10 Using
part‐time
employees
7 Increasing
customer
participation
8 Scheduling
work shifts
Creating
adjustable
capacity
11 Yield
Management
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1. Managing Customer-induced Variability
Type of Variability
Accommodation
Reduction
Arrival
Provide generous staffing
Require reservations
Capability
Adapt to customer skill levels
Target customers based on capability
Request
Cross‐train employees
Limit service breadth
Effort
Do work for customers
Reward increased effort
Subjective
Preference
Diagnose expectations and adapt
Persuade customers to adjust expectations
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2. Segmenting Demand
Too many walk‐in patients on Mondays at a health clinic.
140
Smoothing Demand by Appointment
Scheduling
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Appointments
84
89
124
129
114
120
100
Before
Smoothing
After
Smoothing
80
60
40
20
0
Mon. Tue. Wed. Thur. Fri.
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3. Offering Price Incentives
• Differential Pricing
– Weekend rates for phone calls.
– Summer pricing by utility companies.
• Promoting Off‐Peak Demand
– Different sources of demand
– Hotel: conventions for business or professional groups during the off‐season.
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4. Discriminatory Pricing for Camping
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6
5. Developing Complementary Services
• A new service is the complementor if customers value your service more when they already have purchased the existing service.
• Movie theaters offer popcorns and soft drinks.
• A new service is the complementor if it results in a more uniform demand.
• Restaurants offer the “afternoon tea” service.
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6. Reservation and Overbooking
• Taking reservations is like preselling the service.
• Reservations may benefit consumers by reducing waiting and guarantee service availability.
• Approximately 50% of reservations get cancelled.
• Multiple reservations, late arrivals, no‐shows.
The company may fail to receive any revenue if a customer cancels the reservation or does not show up.
• Non‐refundable pre‐payment, overbooking
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7
Overbooking to Protect Revenue
Overbooking—accept more reservations than supply
Example: On average there would be 10 cancellations or no‐
shows. So the hotel can accept 10 more reservations.
Too much overbooking: some customers may have to be denied a seat even though they have a confirmed reservation.
Too little overbooking: waste of capacity, loss of revenue
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Example: Surfside Hotel
expected number of no‐shows = 0(0.07)+1(0.19)+…+9(0.01)=3.04
Expected opportunity loss = 3.04 × $40 = $121.60
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Cost of too many overbooking: Co=$100 for accommodation at some other hotel and additional compensation.
Cost of not enough overbooking: Cu=$40 per room.
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Overbooking Solution
C
 0.286
• Critical ratio C uC  40 40
 100
u
o
• Find x such that x is the largest number that satisfies P(number of no‐shows < x) ≤ 0.286
• Optimal number of overbooking = 2
• There is about a 26% chance that the hotel will have more customers than rooms.
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Strategies for Managing Capacity
7. Increasing customer participation
8. Creating adjustable capacity
Different aircrafts, ability to move rental cars around.
9. Cross‐training employees
10. Using part‐time employees
11. Revenue Management
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7. Customer Participation
Customer participates actively in the service process.
Objectives:
• Cost reduction (less personnel is needed)
• Capacity becomes more “variable”, according to demand
Disadvantages:
• Customer expects quicker service
• Customer expects low prices (compensation for his help)
• Quality of customers “work” cannot be controlled by company (e.g., customer can leave his waste on the table)
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8. Workshift Scheduling
• The peak to valley variation is 125 to 1.
• Carefully schedule the workforce so that the required service level can be maintained with the minimal cost.
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Convert Demand and Schedule Shifts
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11
Scheduling Consecutive Days Off
forecast
A
B
C
D
Mon
4
4
3
2
1
Tue
3
3
2
1
0
Wed
4
4
3
2
1
Thu
2
2
1
0
0
Fri
3
3
2
2
1
Sat
1
1
1
1
1
Sun
2
2
2
1
1
Scheduling Hourly Work Times: First Hour Principle Requirement Assigned On Duty 10 11 12 4 6 8 4 2 2
8
4 6 1 2 3 4 5 8 6 4 4 6 0 0 0 0 0
8 8 8 8 8
6 7 8 9 8 10 10 6 4
4
2 0 8 10 10 10 23
9. Cross-training & Part-time Employees
Training employees to be able to do different tasks
• Demand peaks: Each employee performs his specialized work (e.g., cashier in a supermarket)
• Low demand: Employee performs additional tasks: Job is enlarged (e.g., filling the shelves in a supermarket)
Using part‐time employees
• When demand peaks can be foreseen: Additional staff can be employed for these times (e.g., lunchtime in restaurants)
• Skills needed low: Students can be taken (e.g., bakery)
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11. Revenue Management
• Return = Revenue – Operations Cost
= Throughput  Price – Fixed Costs –Throughput  Variable Costs
– Reduce fixed costs
– Reduce variable costs
– Increase price
– Increase throughput
• If capacity is fixed and perishable, fixed costs are high and variable costs are low, increasing price and/or throughput to improve profitability.
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Some U.S. Airline Industry Observations
• Carriers typically fill 72.4% of seats and have a break‐even load of 70.4%.
• From 1995‐1999 (the industry’s best 5 years ever) airlines earned 3.5 cents on each dollar of sales
• Very high fixed costs and perishable capacity.
• More ticket sales means more revenue and more profit.
• American Airlines estimated a profit of $1.5B over 3 years contributed by revenue management.
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Yield Management: Airline Pricing
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Example: Blackjack Airline
95 seats
d = demand for full fare ($69) ~ N(60, 152)
Expected revenue=6960=$4140
Demand for “gamblers fare” ($49) is abundant
Expected revenue=4995=$4655
Decision:
x = seats reserved for full fare passengers
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Optimal Booking Solution
Cost of too many seats reserved: Co=$49
Cost of not enough seats reserved: Cu=$20
P(d  x) 
Cu
 20  0.29
Cu  Co 20  49
d 
•z  
 d  60 ~ N (0,1)
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• (z)=P(d < x)=0.29  z= -0.55
z  x  60  0.55
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 x  60  (0.55)15  51
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Optimal Revenue for Blackjack Airline
• Z= ‐0.55  Normal Loss Function L(z)
=NORMDIST(z,0,1,0)‐z*(1‐NORMSDIST(z)) =0.7328
• For full fare customer expected loss (due to not enough seats reserved) =L(z)∙=0.7328=10.99
expected sales + expected loss = expected full fare demand
 expected sales=expected demand‐expected loss =60‐10.99=49.01
• Expected total revenue=49.01*69+(95‐51)*49 =$5537
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Yield Management for a Resort Hotel
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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
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