utdallas.edu/~metin 2 Learning Goals u Yield management (with protection levels) and overbooking give demand flexibility where supply flexibility is not possible. u The Newsvendor model can be used: –Single decision in the face of uncertainty. –Underage and overage costs.
utdallas.edu/~metin 4 Some U.S. airline industry observations u Since deregulation in 78, 137 carriers have filed for bankruptcy until u From (the industrys best 5 years ever) airlines earned 3.5 cents on each dollar of sales: –The US average for all industries is around 6 cents. –From the industry earned 1 cent per $ of sales. u Carriers typically fill 72.4% of seats while the break-even load is 70.4%. - Utilization is about 3% higher in perhaps due to flight cancellations. u Gas prices are high and will remain so. –Downsize airlines –Merge. Domestic/international –Alternate transportation means »High speed train
utdallas.edu/~metin 5 Matching supply to demand when supply is fixed u Examples of fixed supply: –Travel industries (fixed number of seats, rooms, cars, etc). –Advertising time (limited number of time slots). –Telecommunications bandwidth. –Size of the MBA program. –Doctors availability for appointments. u Revenue management is a solution: –If adjusting supply is impossible – adjust the demand! –Segment customers into »High willingness to pay »Low willingness to pay. –Limit the number of tickets sold at a low price, i.e., control the average price by changing the mix of customers.
utdallas.edu/~metin 6 Environments suitable for revenue management u The same unit of capacity (e.g., airline seat) can be used to deliver services to different customer segments (e.g., business and leisure customers) at different prices. u High gross margins (so the variable cost of additional sales is low). u Perishable capacity (it cannot be stored) and limited capacity (all possible customers cannot always be served). u Capacity is sold in advance of demand: Costly adjustment of sold capacity. u There is an opportunity to segment customers (so that different prices can be charged) and different segments are willing to pay different prices. u It is not illegal or morally irresponsible to discriminate the customers. u Is Revenue management for incoming MBA class possible?
utdallas.edu/~metin 7 Revenue Management: Booking limits and protection levels
utdallas.edu/~metin 8 The Park Hyatt Philadelphia u 118 King/Queen rooms. u Hyatt offers a r L = $159 (low fare) discount fare for a mid-week stay, targeting leisure travelers. u Regular fare is r H = $225 (high fare) targeting business travelers. u Demand for low fare rooms is abundant. u Let D be uncertain demand for high fare rooms. –Suppose D has Poisson distribution with mean u Assume most of the high fare (business) demand occurs only within a few days of the actual stay. u Objective: Maximize expected revenues by controlling the number of low fare rooms sold.
utdallas.edu/~metin 9 Yield management decisions u The booking limit is the number of rooms to sell in a fare class or lower. u The protection level is the number of rooms you reserve for a fare class or higher. u Let Q be the protection level for the high fare class. Q is in effect while selling low fare tickets. u Since there are only two fare classes, the booking limit on the low fare class is – Q: –You will sell no more than 118-Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers Q seats protected for high fare passengers Sell no more than the low fare booking limit, Q
utdallas.edu/~metin 10 The connection to the newsvendor u A single decision is made before uncertain demand is realized. u There is an overage cost: –D: Demand for high fare class; Q: Protection level for high fare class –If D < Q then you protected too many rooms (you over protected)... –… so some rooms are empty which could have been sold to a low fare traveler. u There is an underage cost: –If D > Q then you protected too few rooms (you under protected) … –… so some rooms could have been sold at the high fare instead of the low fare. u Choose Q to balance the overage and underage costs.
utdallas.edu/~metin 11 Optimal protection level u Overage cost: –If D < Q we protected too many rooms and earn nothing on Q - D rooms. –We could have sold those empty rooms at the low fare, so C o = r L. u Underage cost: –If D > Q we protected too few rooms. –D – Q rooms could have been sold at the high fare but were sold instead at the low fare, so C u = r H – r L u Optimal high fare protection level: u Optimal low fare booking limit = 118 – Q* u Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs.
utdallas.edu/~metin 12 Hyatt example u Critical ratio: u Poisson distribution with mean 27.3 –You can also use poisson(Q,mean=27.3,1)=0.29 Excel function to solve for Q. u Answer: 24 rooms should be protected for high fare travelers. Similarly, a booking limit of = 94 rooms should be applied to low fare reservations.
utdallas.edu/~metin 13 Related performance measure calculations u How many high-fare travelers will be refused a reservation? –Expected lost sales = 4.10, From Table 13.2 u How many high-fare travelers will be accommodated? –Expected sales = Expected demand - Lost sales = = 23.2 u How many seats will remain empty? –Expected left over inventory = Q - Expected sales = = 0.8. u What is the expected revenue assuming all low fare rooms are sold –$225 x Exp. Sales(=23.2) + $159 x Booking limit(=118-24=94) = $20,166. –Without yield management worst case scenario is selling all the rooms at the low fare and making $159 x 118 = $18,762. –With revenue management revenue increases by (20,166-18,762)/18,762=7.5%
utdallas.edu/~metin 14 Example: Bulk Contracts u Most consumers of production, warehousing, and transportation assets face the problem of constructing a portfolio of long-term bulk contracts and short-term spot market contracts –Long-term contracts for low cost –Short-term contracts for flexibility u The basic decision is the size of the bulk contract u The fundamental trade-off is between wasting a portion of the low- cost bulk contract and paying more for the asset on the spot market
utdallas.edu/~metin 15 Example: Bulk Contracts For the simple case where the spot market price is known but demand is uncertain, a formula can be used c B = bulk rate c S = spot market price Q* = optimal amount of the asset to be purchased in bulk Overage cost of buying too much in bulk: c B. Underage cost of buying too little in bulk: c S - c B.
utdallas.edu/~metin 16 Numerical Example for Bulk Contracts: Buying transportation capacity to bring goods from China Bulk contract cost = c B = $10,000 per million units Spot market cost = c S = $12,500 per million units Normal monthly Demand for transportation: = 10 million units, = 4 million units Q* = Norminv(( /12.5),10,4) million units The manufacturer should sign a long-term bulk contract for Q* million units per month and purchase any transportation capacity beyond that on the spot market.
utdallas.edu/~metin 18 Ugly reality: cancellations and no-shows u Approximately 50% of reservations get cancelled at some point in time. u In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations. u Problem: –the company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. u Solution: –sell more seats (rooms, cars) than capacity. u Danger: –some customers may have to be denied a seat even though they have a confirmed reservation. –Passengers who get bumped off overbooked domestic flights to receive »Up-to $400 if arrive <= 2 hours after their original arrival time »Up-to $800 if arrive >= 2 hours after their original arrival time –According to April 16, 2008 decision of the Transportation Department
utdallas.edu/~metin 19 Hyatts Problem u The forecast for the number of customers that do not show up ( X ) is Poisson with mean 8.5. u The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will (loss of goodwill) and penalties. u How many rooms (y) should be overbooked (sold in excess of capacity)? u Newsvendor setup: –Single decision when the number of no-shows in uncertain. –Insufficient overbooking: Overbooking demand=X >y=Overbooked capacity. –Excessive overbooking: Overbooking demand=X
utdallas.edu/~metin 20 Overbooking solution u Underage cost when insufficient overbooking –if X >y then we could have sold X-y more rooms… –… to be conservative, we could have sold those rooms at the low fare, C u = r L. u Overage cost when excessive overbooking –if X
utdallas.edu/~metin 21 Optimal overbooking level u Poisson distribution with mean 8.5 u Optimal number of overbooked rooms is y=7. u Hyatt should allow up to reservations. u There is about F(6)=25.62% chance that Hyatt will find itself turning down travelers with reservations.
utdallas.edu/~metin 23 Revenue management challenges … u Demand forecasting. –Wealth of information from reservation systems but there is seasonality, special events, changing fares and truncation of demand data. u Dynamic decisions. u Variable capacity: –Different aircrafts, ability to move rental cars around. u Group reservations; Cargo overbooking. u How to construct good fences to differentiate among customers? –One-way vs round-trip tickets. –Saturday-night stay requirement. –Non-refundability. –Advanced purchase requirements. u Multi-leg passengers/multi-day reservations for cars and hotels:
utdallas.edu/~metin 24 A solution to the multi-leg customer: buckets u With segment control there are only three booking limits for the OHare-JFK leg, one for each fare class. u But an OHare-Heathrow customer may be more valuable, so you could have six booking limits, one for each fare-itinerary combination. u But that leads to many booking limits, so group similar fare-itineraries into buckets: OHare JFK Heathrow
utdallas.edu/~metin 25 Another solution to multi-legs: bid prices u Assign a bid price to each segment: u A fare is accepted if it exceeds the sum of the bid prices on the segments it uses: –For example, an OHare-JFK fare is accepted if it exceeds $290 –A OHare-Heathrow fare is accepted if it exceeds $290+$170 = $460 u The trick is to choose good bid-prices. OHare JFK Heathrow
utdallas.edu/~metin 26 Summary u Yield management (with protection levels) and overbooking give demand flexibility where supply flexibility is not possible. u The Newsvendor model can be used: –Single decision in the face of uncertainty. –Underage and overage costs. u These are powerful tools to improve revenue: –American Airlines estimated a benefit of $1.5B over 3 years. –National Car Rental faced liquidation in 1993 but improved via yield management techniques. –Delta Airlines credits yield management with $300M in additional revenue annually (about 2% of year 2000 revenue.)
utdallas.edu/~metin 27 Summary of the Course u Modules –1. Flow analysis –2. Formulations –3. Queues –4. Quality –5. Inventory –6. Revenue management u The efficient transformation of inputs into outputs to suitably satisfy customers.
utdallas.edu/~metin 28 The End My teaching is over Your learning is forever Towards better Do not give up ever