Operations management Session 18 Revenue Management Tools Session

Operations management Session 18: Revenue Management Tools Session 18 Operations Management

RM: A Basic Business Need Session 18 Increasing Revenue Reducing Cost w What are the basic ways to improve profits? Revenue Management $ Profits Operations Management 2

Elements of Revenue Management w Pricing and market segmentation w Capacity control w Overbooking w Forecasting w Optimization Session 18 Operations Management 3

Pricing: How does it work? w Objective: Maximize revenue n Example (Monopoly): An airline has the following demand information: Price 0 50 100 150 200 250 Session 18 d = (3/5)(300 -p) Demand ? 150 120 90 60 30 Operations Management 4

Pricing: How does it work? w What is the price that the airline should charge to maximize revenue? Note that this is equivalent to determining how many seats the airline should sell. n The revenue depends on price, and is: Revenue = price * (demand at that price) r(p) = p * d(p) = p * (3/5) * (300 – p) = (3/5) * (300 p – p 2) n Session 18 We would like to choose the price that maximizes revenue. Operations Management 5

Finding the price that maximizes revenue. Revenue is maximized when the price per seat is $150, meaning 90 seats are sold. Session 18 Operations Management 6

Finding the price that maximizes revenue. r(p) = p*d(p) = (3/5)*(300 p-p 2) r’(p)=0 implies (3/5)(300 -2 p)=0 or p=150 Pricing each seat at $150 maximizes revenue. d(150)=(3/5)*(300 -150)=90 This means we will sell 90 seats. Session 18 Operations Management 7

What if the airline only holds 60 people? Is it possible we would want to sell less than 60 seats? To answer this question, plot revenue as a function of demand. First note that actually, revenue = price * min(demand, capacity). Second note that it is equivalent to think in terms of price or demand; i. e. , d(p) = (3/5)*(300 -p) implies p(d) = 300 -(5/3)d. Then, r(d) = p(d)*d = 300 d-(5/3)d 2. Session 18 Operations Management 8

What if the airline only holds 60 people? r(d) = p(d)*d = 300 d-(5/3)d 2. It is obvious from the graph that revenue is maximized when 90 seats are sold (demand is 90), as we found originally. It is also clear that we want to sell as many seats as possible up to 90, because revenue is increasing from 0 to 90. Conclusion: sell 60 seats at price p(60)=300 -(5/3)*60=200. Session 18 Operations Management 9

Pricing to Maximize Revenue: The General Strategy w Write revenue as a function of price. w Find the price that maximizes the revenue function. w Find the demand associated with that price. w Ensure that there is enough capacity to satisfy that demand. Otherwise, sell less at a lower price. (This assumes that the revenue function increases up until the best price, and then decreases. ) w Is this strategy specific to airlines? No. Session 18 Operations Management 10

Pricing and Market Segmentation w Should it be a single price? w Most airlines do not have a single price. w Suppose the airline had 110 seats, so that the revenue-maximizing price of $150 (equivalently selling 90 seats) meant having 20 seats go unsold. w Is there a way to divide the market into customers that will pay more and those that will pay less? Session 18 Operations Management 11

Market Segmentation Passengers are very heterogeneous in terms of their needs and willingness to pay (business vs leisure for example). A single product and price does not maximize revenue price p 3 additional revenue by segmentation revenue = price • min {demand, capacity} p 1 p 2 capacity Session 18 Operations Management demand 12

Pricing and Market Segmentation w It is the airline interest to: n Reduce the consumer surplus n Sell all seats n How can this be achieved? l l Session 18 Sell to each group at their reservation price (segmentation of the market) In the previous example, price tickets oriented for business customers higher than $150 and those oriented for leisure customers lower than $150. Operations Management 13

Pricing and Market Segmentation w The idea of market segmentation does not just apply to airlines. Where else do we see this? w Why are companies using a single price? n Easy to use and understand n Product can’t be differentiated n Market can’t be segmented n Lack of demand information n Consumers don’t like that different customers are getting the “same products” at different prices. Session 18 Operations Management 14

Pricing and Market Segmentation w What are the difficulties in introducing multi-prices? n Information l n May be hard to obtain demand information for different segments. How to avoid leakages from one segment to another? l Fences w Early purchasing, non refundable tickets, weekend stay over. n Competition Session 18 Operations Management 15

Revenue Management Dilemma for Airlines w High-fare business passengers usually book later than low-fare leisure passengers w Should I give a seat to the $300 passenger which wants to book now or should I wait for a potential $400 passenger? Session 18 Operations Management 16

The Basic Question is Capacity Control Business Travelers Leisure Travelers • Price Insensitive • Book Later • Schedule Sensitive • Price Sensitive • Book Early • Schedule Insensitive fd = Discount Fare Session 18 ff = Full fare Operations Management 17

The Basic Question is Capacity Control w Consider one plane, with one class of seats. w We would like to sell as many higher-priced tickets to business customers as we can first, and then sell any leftover seats to leisure customers at a discount. w The problem is that the leisure customers book early, and the business customers book late. w How do we decide how many seats to reserve for the business class customers? Session 18 Operations Management 18

Two-Class Capacity Control Problem w A plane has 150 seats. Current s=81 seats remaining. w Two fare classes (full-fare and discount) with fares ff = 300 > fd = 200 > 0. w Should we save the seat for late-booking full-fare customers? w We need full-fare demand information, w Random variables, Df. w Ff (x) = Probability that Df < x. Session 18 Operations Management 19

Capacity Control: Tradeoff w Cannibalization - If the company sells the ticket for $200 and the business demand is larger than 80 tickets then, the company loses $100. Cost = ff – fd (=100) for each fullfare customer turned away. w Spoilage - If the company does not sell the ticket for $200 and the business demand is smaller than 81 tickets then, the company loses $200. Cost = fd (=200) for each “spoiled” seat. Session 18 Operations Management 20

Marginal Analysis w If we sell the discount ticket now, we get fd right away. w How much do we expect to generate by holding the seat? fd Sell P(D>s) ff Hold P(D<s) Session 18 Operations Management 0 21

Decision rule w Criteria: comparing fd and ff. P(D>s) w Accept discount bookings if fd > ff. P(D>s) w If 200 > 300(1–F(80)) or 0. 667 > (1–F(80)). Then sell the ticket for $200. Otherwise wait and don’t sell the ticket. Session 18 Operations Management 22

Example w Two fairs: $200, $300 w The demand for the $300 tickets is equally likely to be anywhere between 51 and 150 w With 81 seats left, should the airline sell a ticket for $200? n P(D>=81)=1 -F(80) = 0. 7 n 200 < 0. 7*300 = 210 n Clearly the airline should close the $200 class. w What if there were 101 seats left? Session 18 Operations Management 23

Booking Limit w What is the booking limit (the maximum number of seats available to be sold) of the $200 class in this case? n 200 = (1–F(x))*300 n 1/3 = F(x) n F(83) < 1/3 < F(84) n n Accept discount bookings until 84 seats remain. Then accept only full-fare bookings. In other words, we will sell 150 -84=66 seats to the discount class. 66 seats is the booking limit. Session 18 Operations Management 24

Booking Limit: Intuition w If booking limit is too low, we risk spoilage (having unsold seats). w If booking limit is too high, we risk cannibalization (selling a seat at a discount price that could have been sold at full-fare). Revenue Booking Limit Session 18 Operations Management 25

Two-Class Capacity Control Problem: Another example w A plane has 150 seats. w Two fare classes (full-fare and discount) with fares ff = 250 > fd = 200 > 0. w The demand for full-fare tickets is equally likely to be anywhere between 1 and 100. w What is the booking limit that maximizes revenue? w Intuitively, should this be higher or lower than in the previous example? Session 18 Operations Management 26

Overbooking w Airlines and other industries historically allowed passengers to cancel or no-show without penalty. w Some (about 13%) booked passengers don’t show-up. w Overbooking to compensate for no-shows was one of the first Revenue Management functionalities (1970’s). bkg } no-shows cap 90 days prior Session 18 departure Operations Management time 27

Overbooking: Tradeoff w Airlines book more passengers than their capacity to hedge against this uncovered call, Airlines need to balance two risks when overbooking: Spoilage: Seats leave empty when a booking request was received. Lose a potential fare. Denied Boarding Risk: Accepting an additional booking leads to an additional denied-boarding. Session 18 Operations Management 28

Overbooking w Sophisticated overbooking algorithms balance the expected costs of spoiled seats and denial boardings w Typical revenue gains of 1 -2% from more effective overbooking expected costs spoilage Session 18 capacity total costs Operations Management denied boarding Number seats sold 29

Example w The airline has a flight with 150 seats. The airline knows the number of cancellation would be between 4 to 8, all numbers are equally likely. w Fair price is $250; denied boarding cost is estimated to be $700. w How many tickets should the airline sell? Session 18 Operations Management 30

Example w The airline has a flight with 150 seats. The airline knows the number of cancellation would be between 4 to 8, all numbers are equally likely. w Fair price is $250; denied boarding cost is estimated to be $700. w How many tickets should the airline sell? n Clearly the airline should sell 154 seats because the number of cancellations is known to be at least 4. Session 18 Operations Management 31

Marginal Analysis: Overbooking Sell 155 seats? Revenue increase P(C>=5) Seats for everyone. Sell P(C<5)=P(C=4) 1 person w/out seat Hold 250 -700 =-450 0 w Criteria: Does E[revenue increase] exceed 0? Yes. (4/5)*250+(1/5)*(-450) = 110 >0. Session 18 Operations Management 32

Marginal Analysis: Overbooking Revenue increase Sell 156 seats? 250 Sell 250 -700 =-450 Hold 0 No. It is best to sell 155 seats. Session 18 Operations Management 33

Overbooking Example 2 w The airline has a flight with 150 seats. The airline knows the number of cancellations will be 0, 1, 2, or 3. Furthermore, n P(C=0) = 0. 01, P(C=1) = 0. 1, P(C=2) = 0. 8, P(C=3) = 0. 09 w Fair price is $250; denied boarding cost is estimated to be $700. w How many tickets should the airline sell? Session 18 Operations Management 34

Overbooking Dynamic In general, we might let the number of seats overbooked change over time … Bookings Number of seats sold No-show “Pad” Capacity Bookings Session 18 A B Operations Management Departure Time 35

What have we learned? w Basic Revenue Management n Pricing n Market Segmentation n Capacity Control n Overbooking w Teaching notes, homework, and practice revenue management questions posted. Session 18 Operations Management 36