# Operations management

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Operations management
Session 18: Revenue Management Tools

What are the basic ways to improve profits? Profits \$ Increasing Revenue Reducing Cost Revenue Management Session 18 Operations Management

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

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

Pricing: How does it work?
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. 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) * (300p – p2) We would like to choose the price that maximizes revenue. Session 18 Operations Management

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

Finding the price that maximizes revenue.
r(p) = p*d(p) = (3/5)*(300p-p2) r’(p)=0 implies (3/5)(300-2p)=0 or p=150 Pricing each seat at \$150 maximizes revenue. d(150)=(3/5)*( )=90 This means we will sell 90 seats. Session 18 Operations Management

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 = 300d-(5/3)d2. Session 18 Operations Management

What if the airline only holds 60 people?
r(d) = p(d)*d = 300d-(5/3)d2. 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

Pricing to Maximize Revenue: The General Strategy
Write revenue as a function of price. Find the price that maximizes the revenue function. Find the demand associated with that price. 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.) Is this strategy specific to airlines? No. Session 18 Operations Management

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

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 p3 p2 additional revenue by segmentation revenue = price • min {demand, capacity} p1 capacity demand Session 18 Operations Management

Pricing and Market Segmentation
It is the airline interest to: Reduce the consumer surplus Sell all seats How can this be achieved? 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. Session 18 Operations Management

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

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

Revenue Management Dilemma for Airlines
High-fare business passengers usually book later than low-fare leisure passengers Should I give a seat to the \$300 passenger which wants to book now or should I wait for a potential \$400 passenger? The world of Revenue Management could be so easy if the full-fare passengers would book before the discount passengers (and if we wouldn’t have any no-shows or cancellations). Unfortunately, it is closer to the opposite. Most full-fare passengers are late booking business passengers and most discount passengers are early booking leisure passengers. Here the game of Revenue Management starts. Should I give a seat to the passenger who stands in front of me and is willing to pay 300 dollars or should I gamble and wait for a potential 400 dollar passenger which might show-up later? A similar risk-balancing game is played in overbooking. Should I increase the overbooking level by one, lowering the risk of empty, spoiled seats but simultaneously increasing the risk of over sales and denied boardings? Session 18 Operations Management Operations Management 16 16

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

The Basic Question is Capacity Control
Consider one plane, with one class of seats. 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. The problem is that the leisure customers book early, and the business customers book late. How do we decide how many seats to reserve for the business class customers? Session 18 Operations Management

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

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 full-fare customer turned away. 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 Operations Management 20 20

Marginal Analysis If we sell the discount ticket now, we get fd right away. 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 Operations Management 21 21

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

Example Two fairs: \$200, \$300 The demand for the \$300 tickets is equally likely to be anywhere between 51 and 150 With 81 seats left, should the airline sell a ticket for \$200? P(D>=81)=1-F(80) = 0.7 200 < 0.7*300 = 210 Clearly the airline should close the \$200 class. What if there were 101 seats left? Session 18 Operations Management Operations Management 23 23

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

Booking Limit: Intuition
If booking limit is too low, we risk spoilage (having unsold seats). 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 Operations Management 25 25

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

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

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

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

Operations Management
Example 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. Fair price is \$250; denied boarding cost is estimated to be \$700. How many tickets should the airline sell? Session 18 Operations Management

Operations Management
Example 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. Fair price is \$250; denied boarding cost is estimated to be \$700. How many tickets should the airline sell? Clearly the airline should sell 154 seats because the number of cancellations is known to be at least 4. Session 18 Operations Management

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

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

Operations Management
Overbooking Example 2 The airline has a flight with 150 seats. The airline knows the number of cancellations will be 0,1,2, or 3. Furthermore, P(C=0) = 0.01, P(C=1) = 0.1, P(C=2) = 0.8, P(C=3) = 0.09 Fair price is \$250; denied boarding cost is estimated to be \$700. How many tickets should the airline sell? Session 18 Operations Management

Operations Management
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 Time Session 18 Operations Management A B Departure

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

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