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Operations management Session 18: Revenue Management Tools

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Session 18 Operations Management2 RM: A Basic Business Need What are the basic ways to improve profits? Profits $ $ Reducing Cost Increasing Revenue Revenue Management

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Session 18 Operations Management3 Elements of Revenue Management Pricing and market segmentation Capacity control Overbooking Forecasting Optimization

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Session 18 Operations Management4 Pricing: How does it work? Objective: Maximize revenue Example (Monopoly): An airline has the following demand information: PriceDemand 0? 50150 100120 15090 20060 25030 d = (3/5)(300-p)

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Session 18 Operations Management5 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 – p 2 ) We would like to choose the price that maximizes revenue.

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Session 18 Operations Management6 Finding the price that maximizes revenue. Revenue is maximized when the price per seat is $150, meaning 90 seats are sold.

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Session 18 Operations Management7 Finding the price that maximizes revenue. r(p) = p*d(p) = (3/5)*(300p-p 2 ) r(p)=0 implies (3/5)(300-2p)=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.

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Session 18 Operations Management8 What if the airline only holds 60 people? Then, r(d) = p(d)*d = 300d-(5/3)d 2. 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. Is it possible we would want to sell less than 60 seats? To answer this question, plot revenue as a function of demand.

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Session 18 Operations Management9 What if the airline only holds 60 people? r(d) = p(d)*d = 300d-(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.

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Session 18 Operations Management10 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.

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Session 18 Operations Management11 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?

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Session 18 Operations Management12 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 Market Segmentation price demand revenue = price min {demand, capacity} capacity p1 p3 p2 additional revenue by segmentation

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Session 18 Operations Management13 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.

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Session 18 Operations Management14 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 cant be differentiated Market cant be segmented Lack of demand information Consumers dont like that different customers are getting the same products at different prices.

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Session 18 Operations Management15 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

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Session 18 Operations Management16Operations Management16 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?

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Session 18 Operations Management17Operations Management17 The Basic Question is Capacity Control Leisure Travelers Price Sensitive Book Early Schedule Insensitive f d = Discount Fare Business Travelers Price Insensitive Book Later Schedule Sensitive f f = Full fare

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Session 18 Operations Management18 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?

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Session 18 Operations Management19Operations Management19 Two-Class Capacity Control Problem A plane has 150 seats. Current s=81 seats remaining. Two fare classes (full-fare and discount) with fares f f = 300 > f d = 200 > 0. Should we save the seat for late-booking full-fare customers? We need full-fare demand information, Random variables, D f. F f (x) = Probability that D f < x.

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Session 18 Operations Management20Operations Management20 Capacity Control: Tradeoff Cannibalization - If the company sells the ticket for $200 and the business demand is larger than 80 tickets then, the company loses $100. Cost = f f – f d (=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 = f d (=200) for each spoiled seat.

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Session 18 Operations Management21Operations Management21 Marginal Analysis If we sell the discount ticket now, we get f d right away. How much do we expect to generate by holding the seat? f 0 Hold P(D~~s) fdfd Sell
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Session 18 Operations Management22Operations Management22 Decision rule Criteria: comparing f d and f f P(D>s) Accept discount bookings if f d > f f P(D>s) If 200 > 300(1–F(80)) or 0.667 > (1–F(80)). Then sell the ticket for $200. Otherwise wait and dont sell the ticket.

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Session 18 Operations Management23Operations Management23 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?

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Session 18 Operations Management24Operations Management24 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 150-84=66 seats to the discount class. 66 seats is the booking limit.

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Session 18 Operations Management25Operations Management25 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). Booking Limit Revenue

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Session 18 Operations Management26Operations Management26 Two-Class Capacity Control Problem: Another example A plane has 150 seats. Two fare classes (full-fare and discount) with fares f f = 250 > f d = 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?

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Session 18 Operations Management27 Overbooking Airlines and other industries historically allowed passengers to cancel or no-show without penalty. Some (about 13%) booked passengers dont show-up. Overbooking to compensate for no-shows was one of the first Revenue Management functionalities (1970s). bkg 90 days priordeparture time } no-shows cap } no-shows

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Session 18 Operations Management28 Overbooking: Tradeoff 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.

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Session 18 Operations Management29 Overbooking Sophisticated overbooking algorithms balance the expected costs of spoiled seats and denial boardings Typical revenue gains of 1-2% from more effective overbooking Number seats soldcapacity expected costs total costs spoilage denied boarding

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Session 18 Operations Management30 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?

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Session 18 Operations Management31 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.

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Session 18 Operations Management32 Marginal Analysis: Overbooking Criteria: Does E[revenue increase] exceed 0? Yes. (4/5)*250+(1/5)*(-450) = 110 >0. 250 250-700 =-450 P(C<5)=P(C=4) 1 person w/out seat Revenue increase Sell Hold P(C>=5) Seats for everyone. 0 Sell 155 seats?

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Session 18 Operations Management33 Marginal Analysis: Overbooking Sell 156 seats? No. It is best to sell 155 seats. 250 250-700 =-450 Sell Hold 0 Revenue increase

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Session 18 Operations Management34 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?

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Session 18 Operations Management35 Overbooking Dynamic Departure Capacity Time Bookings Number of seats sold Bookings No-show Pad AB In general, we might let the number of seats overbooked change over time …

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Session 18 Operations Management36 What have we learned? Basic Revenue Management Pricing Market Segmentation Capacity Control Overbooking Teaching notes, homework, and practice revenue management questions posted.

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