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Lecture 12: Advanced Booking and Capacity Constraints AEM 4160: Strategic Pricing Prof. Jura Liaukonyte 2

Lecture Plan  HW3, HW 4  Advanced Booking

Advanced Booking and Capacity Constraints 4

Dynamic Pricing  Dynamic pricing is a blanket term for any shopping experience where the price of an item fluctuates frequently based on complicated algorithms.  A retailer might frequently change the price of an item based on consumer demand, price fluctuations at a competing retailer, or even the time of day and weather conditions.  Dynamic pricing can be found in a wide variety of industries.

Dynamic Pricing  One segment on the rise with dynamic pricing is professional sports with Real Time Pricing.  E.g., the St. Louis Cardinals set their ticket price algorithms based on factors like team performance, pitching match ups, weather, and ticket demand.

Dynamic Pricing  In certain grocery stores, the price consumers pay for the exact same product can differ based on personal data collected through loyalty card programs.  At a Safeway in Denver, a 24-pack of Refreshe bottled water costs $2.71 for Customer A. For Customer B, the price is $3.69.  The difference? The vast shopping data Safeway maintains on both customers through its loyalty card program.  Customer A has a history of buying Refreshe brand products, but not its bottled water, while customer B, a Smartwater partisan, is unlikely to try Refreshe.  A Safeway Web site shows Customer A the lower price, which is applied when she swipes her loyalty card at checkout

Some U.S. airline industry observations  From (the industry’s 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.  Carriers typically fill 72.4% of seats while the break-even load is 70.4%.

American: DFW-LAX All Tickets Sold in 2004Q4

The “Prime Booking Window”  Don’t buy your ticket too early!  Best time to buy your ticket is 54 days in advance

Advanced Selling  Requires an inverse relationship between consumer price sensitivity and customer arrival time.  Less price sensitive customers are unwilling to purchase in the advance period so that advance purchases are made to only low-valuation customers  Similar to traditional models of second-degree price discrimination.

Advanced Booking  Consumers making reservations differ in their probability of showing up to collect the good or the service at the pre-agreed time of delivery.  Firms can save on unused capacity costs, generated by consumers’ cancellations and no-shows, by varying the degree of partial refunds  Airline companies in selling discounted tickets where cheaper tickets allow for a very small refund (if any) on cancellations,  Whereas full-fare tickets are either fully-refundable or subject to low penalty rates.

Advanced Booking and Partial Refunds  Partial refunds are used to control for the selection of potential customers who make reservations but differ with respect to their cancellation probabilities.

Capacity Constraints  Examples of fixed supply – capacity constraints:  Travel industries (fixed number of seats, rooms, cars, etc).  Advertising time (limited number of time slots).  Telecommunications bandwidth.  Size of the Dyson business program.  Doctor’s availability for appointments.

The Park Hyatt Philadelphia  118 King/Queen rooms.  Hyatt offers a r L = $159 (low fare) discount fare targeting leisure travelers.  Regular fare is r H = $225 (high fare) targeting business travelers.  Demand for low fare rooms is abundant.  Let D be uncertain demand for high fare rooms.  Assume most of the high fare (business) demand occurs only within a few days of the actual stay.  Objective: Maximize expected revenues by controlling the number of low fare rooms sold.

Yield management decisions  The booking limit is the number of rooms to sell in a fare class or lower.  The protection level is the number of rooms you reserve for a fare class or higher.  Let Q be the protection level for the high fare class. Q is in effect while selling low fare tickets.  Since there are only two fare classes, the booking limit on the low fare class is 118 – 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

The connection to the newsvendor  A single decision is made before uncertain demand is realized.  D: Demand for high fare class;  Q: Protection level for high fare class  There is an overage cost:  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.  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.  Choose Q to balance the overage and underage costs.

“Too much” and “too little” costs  As Q increases => Overage costs increase  As Q increases => Underage costs decrease  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.  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

Balancing the risk and benefit of ordering a unit  As Q increases by one more unit, the chance of overage increases  Expected loss on the Q th unit = C o x F(Q), where F(Q) = Prob{Demand <= Q)  Essentially: overage costs multiplied by probability of overage costs happening  The benefit of ordering one more unit is the reduction in the chance of underage:  Expected benefit on the Q th unit = C u x (1-F(Q))  Essentially: underage costs multiplied by probability of underage costs happening As more units are ordered,  the expected benefit from ordering one unit decreases  while the expected loss of ordering one more unit increases.

Graphical Analysis

Expected profit maximizing order quantity  To minimize the expected total cost of underage and overage, order Q units so that the expected marginal cost with the Q th unit equals the expected marginal benefit with the Q th unit:  Rearrange terms in the above equation ->  The ratio C u / (C o + C u ) is called the critical ratio.  Hence, to minimize the expected total cost of underage and overage, choose Q such that we don’t have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratio

Optimal protection level  Optimal high fare protection level:  Optimal low fare booking limit = 118 – Q*  Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs.  Recall: C o = r L ; C u = r H – r L

Hyatt example  Critical ratio:  Demand for high fare is uncertain, but has a normal distribution with a mean of 30 and Standard deviation of 10.  See the Excel File Posted on the course website for calculations.  You can use normdist(Q,mean,st.dev, 1)=0.29 Excel function to solve for Q (see column E).  Answer: 25 rooms should be protected for high fare travelers. Similarly, a booking limit of = 93 rooms should be applied to low fare reservations.

Revenue Management: Overbooking

Hold the reservation!  e=related e=related

Ugly reality: cancellations and noshows  Approximately 50% of reservations get cancelled at some point in time.  In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations.  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.  Solution:  sell more seats (rooms, cars) than capacity.  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  If the airline is not able to get you to your final destination within one hour of your original arrival time, the airline must pay you an amount equal to 200% of your one-way fare, with a maximum of $650.  According to usa.gov

Hyatt’s Problem  The forecast for the number of customers that do not show up ( X ) is Normal distribution with mean 9 and Standard Deviation 3.  The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will (loss of goodwill) and penalties.  How many rooms (y) should be overbooked (sold in excess of capacity)?  setup:  Single decision when the number of no-shows in uncertain.  Insufficient overbooking: Overbooking demand=X>y=Overbooked capacity.  Excessive overbooking: Overbooking demand=X <y=Overbooked capacity.

Overbooking solution  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.  Overage cost when excessive overbooking  if X <y then we bumped y-X customers …  … and incur an overage cost C o = $350 on each bumped customer.  Optimal overbooking level:  Critical ratio:

Optimal overbooking level  Normal Distribution  Mean=9  Standard Dev. 3  Optimal number of overbooked rooms is y=7.  Hyatt should allow up to reservations.  There is about F(7)=25.24% chance that Hyatt will find itself turning down travelers with reservations.

Advance Selling  Buyers make purchase commitments before the tie of service delivery.  Most common benefit:  Price discount and guarantee of future capacity  Recent development in technology make it appropriate for nearly al services  Electronic tickets  Smart cards  Biometrics

Technology and Advanced Sales  A service provider can improve profits by selling the service in advance when the customer has uncertainty.  prevent the resale of advance tickets (arbitrage).  lower the actual transaction costs associated with advance sales for both service providers and buyers.  allow far more complex price schedules involving either bundles of services or purchases with complex restrictions on customer usage.  provide more information about buyers and demand over time.

Arbitrage: old problem  less profitable or perhaps makes it completely unprofitable.  very profitable buyers, who would have been willing to pay a high spot price, now purchase from the arbitrageur at a lower price. Profits go to the arbitrageur of the ticket rather than the service provider.

Advanced Selling and The New Technology  There are two ways that new technology (such as electronic tickets) benefits advance selling by discouraging or preventing the resale of  To hide the true value of a ticket.  by recording buyer identities on the tickets.

New Technology  New technologies allow far more complex transactions.  These transactions can involve service packages with non-linear pricing, bundling, and variable consumption periods.  For example, a hotel package can sell:  A three-night stay at a lower price than a two-night stay,  or it can bundle a 3-night stay with a dinner, a breakfast, and, perhaps, tickets to local events.  Highly complex packages are possible for many services from car washes to landscaping services.

Demand Learning  Moreover, prices as well as all package components can continuously change over time as the service provider learns demand and available capacity changes (e.g., due to cancellations).  The service provider can now instantaneously adjust to changing conditions.  Overbooking becomes more calculated and more common

Estimate your demand  With these new technologies, sellers can run advance- selling experiments  By limiting quantities sold, learn more about buyer reactions and current demand conditions.