OPSM 405 Service Management Koç University OPSM 405 Service Management Class 12: Yield management: discount allocation and pricing Zeynep Aksin zaksin@ku.edu.tr

Announcements Next group case assignment due next Monday (groups of 2-3) Instructions on last slide Data on student CD of the textbook and handouts section of course webpage There is no one right answer, though there are better answers.. … groups will compete in class

Yield Management System Reservation System current demand cancellations Forecasting cancellation rate estimates future demand estimates Overbooking Levels overbooking levels Discount Allocation fare class allocations

The displacement cost method A general framework for allocation Attempt to evaluate the opportunity cost (displacement cost/bid prices) of using resources required to meet current demand Accept current request if ... Revenue > Displacement Cost Advantages intuitive conceptually simple sophisticated applications O-D control (airlines) multi-night stays (hotels) group evaluations near-optimal (provided “correct” displacement costs are used!)

Generic procedure STEP 1: Forecast demand-to-come for each ... - product (e.g. fare-class/booking class) - resource (e.g. flight leg, day-of-week) STEP 2: Using forecast, determine best allocation of remaining capacity to products. STEP 3: Using the results of STEP 2, calculate the displacement cost of the capacity required by a new request to the revenue it brings in to evaluate accept/deny decisions.

A rough-cut approach: Simple deterministic displacement Assumptions Forecast is perfect Future demand for each resource (flight-leg, hotel room-day) is independent Procedure - Determine revenue (net contribution) of each demand class - Rank demand from highest revenue to lowest - Greedy allocation/displacement - allocation: highest revenue classes first - displacement: lowest revenue classes first

Example: A reservation agent has a group that wants to book Remaining Capacity 100 70 A B C 100 85 70 Forecast of Leg Demand 60 15 KEY A reservation agent has a group that wants to book 20 seats from A to C at a rate of $80 per person. Should we accept the group? Discount $60 Full Fare $100

Analysis: Net Revenue = New Revenue - Total Displacement Cost 100 B 70 C 100 20 85 70 Forecast of Demand to Come 20 60 15 Forecasted revenue displacement: 15 x $0 + 5 x $60 = $300 Forecasted revenue displacement: 10 x $60 + 10x $100 = $1600 KEY Discount $60 Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $300 - $1600 = - $300 ==> DO NOT accept the group. Full Fare $100

Result depends on remaining capacity.... 100 B 80 C 100 20 85 80 20 Forecast of Demand to Come 60 15 Forecasted revenue displacement: 15 x $0 + 5 x $60 = $300 Forecasted revenue displacement: 20 x $60 + 0x $100 = $1200 KEY Discount $60 Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $300 - $1200 = $ 100 ==> DO accept the group. Full Fare $100

and the forecast .... A 100 B 80 C 100 95 20 80 20 Forecast of Demand to Come 60 15 Forecasted revenue displacement: 20 x $60 + 0x $100 = $1200 Forecasted revenue displacement: 5 x $0 + 15 x $60 = $900 KEY Discount $60 Net Revenue = New Revenue - Total Displacement Cost = 20x$80 - $900 - $1200 = - $500 ==> DO NOT accept the group. Full Fare $100

Hedging against forecast error Assumptions: fare classes full-fare discount revenue r1 r2 demand X1 X2 Sequence of Events: discount demand arrives accept/reject discount res. S1 protection level A2 = C-S1 discount allocation full-fare demand arrives

Analysis Approach 1: Deterministic Allocation If we knew demand for high fare with certainty, Approximation:

Analysis Approach 2: Optimal Allocation Accept if $r1 $0 $r2 no S seats remaining: accept low fare? $0 yes $r2 Accept if Optimal protection level is smallest value of S satisfying this condition.

Example Demand for high fare uniformly distributed between 10 and 50. C=100 seats r1=$250 r2=$100 Demand for low fare uniformly distributed between 50 and 90.

Example Reserve 34 seats for full fare demand. Allocate $250 $100 10 34 50 Reserve 34 seats for full fare demand. Allocate 100-34=66 seats to discount fare demand.

EMSR-b Heuristic “Nested allocations” #seats remaining aircraft cabin

Set protection levels to satisfy …. Average fare of classes i and higher Aggregate demand of classes i and higher F(z) standard normal dist. This is the heuristic used in many commercial systems.

Weighted average fares and aggregate mean & variance .. Example: Class Fare Mean Variance 1 $100 30 50 2 $80 30 80 3 $40 50 120 Weighted average fares and aggregate mean & variance .. 1 $100 30 50 2 $90 60 130 3 $67.3 110 250 Set protection level 1:

Set protection level 2 (for classes 1 & 2 combined): There is not protection level for the lowest class (class 3) #seats remaining Accept all three classes Accept class 1 only Accept class 1 and 2 only

Allocation Procedure Alternative: demand control chart based on history Do not accept discount fare demands Days before arrival demands Accept discount fare demands

Some complications in pricing Multiple products are more complex Diversion/demand shifting Other products Competitor’s products Same product on different day Ex: Peak load pricing Cross-elasticity: demand for one product is affected by price of other available products Joint capacity constraints often mean incremental sales of one product require reduction in sales of other products “shadow price” of joint capacity constraint is important to understand

Competition often forces price matching (e.g. discount airline fares) As a result of all these factors, pricing is often done at an aggregate level considering long-term supply/demand balances and competitor’s actions. Capacity allocation is then used to manage short-run fluctuations.

Example: Pricing interacts with capacity allocation Premium customer information Price 100 110 90 Demand 100 80 120 Scenario 1: unlimited capacity, only premium customers 10000 8800 10800

Example cont. Premium customer information Price 100 110 90 Demand 100 80 120 Scenario 2: capacity=100, discount unlimited demand at $50 Premium 10000 8800 9000 Discount 0 1000 0

Example cont. Premium customer information Price 100 110 90 Demand 100 80 120 Scenario 3: capacity=100, discount unlimited demand at $75 Premium 10000 8800 9000 Discount 0 1500 0

Discount allocation example During the recent economic slump, Blackjack Airline discovered that airplanes on its Los Angeles-to-Las Vegas route have been flying with more empty seats than usual. To stimulate demand, it has decided to offer a special, nonrefundable, 14-day advance-purchase “gamblers fare” for only $49 one-way based on a round-trip ticket. The regular full-fare coach ticket costs $69 one-way. The Boeing 737 used by Blackjack, has a capacity 95 in coach, and management wants to limit the number of seats that are sold at the discount fare in order to sell full-fare tickets to passengers who have not made advance travel plans. Considering recent experience, the demand for full-fare tickets appears to have a normal distribution, with a mean of 60 and a standard deviation of 15. Calculate the number of full-fare seats to reserve.

Solution Accept full-fare if ;

Overbooking example A commuter airline overbooks all its flights by one passenger (i.e., the ticket agent will take seven reservations for an airplane that only has six seats). The no-show experience for the past 20 days is shown below: No-shows 0 1 2 3 4 Frequency 6 5 4 3 2 Using the critical fractile P(d<x) ≤ Co/(Co+Cs), find the maximum implied overbooking opportunity loss Cs if the revenue Co from a passenger is $20.

Solution No Shows Frequency Probability P(d<x) 6 0.30 0.00 1 5 0.25 2 4 0.20 0.55 3 0.15 0.75 0.10 0.90 If overbook by 1, then P(d<x) must be at least .30 and less than .55. P(d<x) ≤

Summary: RM is a new twist on some old demand management ideas segmentation peak-load pricing With some new twists ... tactical application of these concepts Small differences matter! systematic/disciplined approach data intensive/ IS intensive

For Monday Prepare MotherLand Air at the end of chapter (9 in old edition) Analyze the information provided and develop a dynamic policy on Price (select from list provided in the case) Overbooking level Seat allocation (nested reservation limits) Inform me of your group’s policy at least 2 hours before class (for each of the “weeks away from takeoff” on Table 9.8) If you want to start out with a static policy, I just need one set of price, overbooking, discount allocation numbers. Bring printout of data to class for use during the game Write up a report describing your analysis and justifying your choice for the above tactics. Clearly state all of your assumptions and explain all of your work. Also articulate how you plan to react to demand announcements in class; i.e. what is your plan. In class we will play a game: I will announce demand realizations, you as a group can update/change your strategy

Illustration of policy to be determined before class 24 20 16 12 8 7 6 5 4 3 2 1 Price Full 1000    Disc 400  D. Disc 100  Seat 120  Allocation 50  0