Constrained Forecast Evaluation (CFE)

Ronald P. Menich

AGIFORS Res & YM 2-5 June 2003

HNL

Outline Define what constrained forecasts are Illustrate concepts with a sequence of examples Discuss constrained forecast evaluation (CFE) simulation

processRelate CFE to revenue opportunity measures

Definition

• A constrained forecast is a forecast of bookings, as we expect them to be when constrained by inventory controls (usually, by recommended inventory controls from an RMS).

• A constrained forecast is not a forecast constructed solely from historical constrained demand observations.

Value of Constrained Forecasts

Constrained forecasts can be used to estimate realistic projected load factors, revenues, and seating mixes.

• If capacity is 100 and the unconstrained show up forecast is 135, then the constrained onboard forecast will be no greater than 100. The 135 is the potential that could fly on a stretchable aircraft, but the 135 cannot fly on the 100 seat aircraft.

Constrained forecasts also help validate RMS recommended control values.

Typical RMS Process Flow

Unconstrain

Forecast

Optimize / Recommend Controls

Evaluate Constrained Forecasts

Example Constrained Forecast

• Assume– Deterministic demand.– No cancellations. Ignore no shows and day of departure activity.– Single cabin, single class/bucket within that cabin– Zero current bookings– Unconstrained final demand 135, recommended cabin authorization

110• Example constrained final demand forecast

= min( 135, 110 )= 110

135

final

Today is

days left 15

Unconstrained and Constrained Trajectories

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Unconstrained

Future

Authorization = 110

Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization

110

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Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization Constrained

Simulation

To produce a constrained forecast, an RMS performs a simulation that takes as input the unconstrained forecasts, the recommended controls, and the seats available logic of the target inventory control system.

The RMS simulates the acceptance and rejection of bookings requests, and the cancellations of bookings on hand.

The RMS simulates forward in time from the current days left through to departure.

More Complex Example

• Assume– Deterministic demand– Bookings at rate 30/day, days left 14-8, no cancellations.– Bookings at rate 0/day, days left 7-1, cancellation rate 6%/day– Single cabin, single class/bucket within that cabin– Zero current bookings– Unconstrained final demand 135, constant recommended cabin

authorization 110 (no profiling)

Unconstrained and Constrained Trajectories

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Unconstrained

135

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All bookings,

no cancellations

All cancellations,

no bookings

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Future

Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization

Authorization = 110

71

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Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization Constrained

… And More Complex

• Same unconstrained demand of 135 and recommended authorization of 110 in both examples.

• When no cancellations were possible, the constrained final demand forecast was 110

• With the cancellation model, the constrained final demand forecast was only 71.

Can we increase authorization sufficiently so as to hit the final target of 110 ?

Unconstrained and Constrained Trajectories

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Unconstrained

135

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Future

Authorization = 171

Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization

110

final

Open, open, closed, closed, open, …, open, depart

Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization Constrained

… And More Complex

The constant authorization just evaluated results in positive seats available, followed by zero seats available, followed by positive seats available close to departure.

What if instead we evaluated a recommended authorization that profiles down as we get close to departure?

Unconstrained and Constrained Trajectories

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Unconstrained

135

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Authorization = max 171, min 110

Unconstrained and Constrained Trajectories

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Unconstrained Profiled Authorization

110

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Open, open, closed, closed, …, closed, depart

Unconstrained and Constrained Trajectories

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Unconstrained Profiled Authorization Constrained

… And Even More Complex

Constrained forecast evaluation must not only consider cabin/compartment-level controls, but also class/bucket-level seat mix controls as well:

• Booking limits• Protection levels• Parallel or serial nesting• Class/bucket-level profiling• Complicated seats available logic

SimulationCalculate Seats Available

Accept/Reject Incremental Booking Requests

Advance Time Clock

Re-Profile Recommended Controls

Compute Current Bookings

Assess Cancellations

The Ideal

• Ideally, an RMS would perform a detailed stochastic (involves probability) discrete event simulation to evaluate constrained forecasts.

• [Or, if the inventory control system were simple enough, the RMS might be able to evaluate a closed-form constrained forecast formula.]

• Such a simulation would be executed hundreds of thousands of times in order to estimate expected behavior and distributions.

Today’s Reality

• An RMS must execute its forecasting, recommendation, and evaluation steps very quickly in order to handle the massive data processing volumes.

• This processing time requirement makes discrete event simulation non-desirable at present, because it is computationally intensive.

Engineering Choices for Today

• Use deterministic simulation• Simulate fractional booking requests and cancellations each

period• Use multi-day time intervals far from departure• Assume cheap-to-high ordering of demands within one period

… but Moore’s Law makes the ideal ever more viable.

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Months from Today

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Revenue Opportunity Measures

• At any particular point in time, there are controls operative in the inventory control system.

• The RMS produces recommended controls.• Evaluate constrained forecasts subject to recommended

controls.• Evaluate constrained forecasts subject to current controls.• The difference in constrained forecasts between recommended

and current controls is the basis for a revenue opportunity estimate.

71

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Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization Constrained

Current Authorization = 110

Constrained Forecast = 71

110

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Unconstrained and Constrained Trajectories

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Unconstrained Constant Authorization Constrained

Recommended Authorization = 171

Constrained Forecast = 110

Revenue Opportunity Measures

• Constrained forecast difference = 110 (recommended) - 71 (current)= 39 seats

• If the average fare were $200, then the revenue opportunity would be39 * $200 = $7800.

If the recommended controls were rejected in favor of keeping the current controls, then $7800 would be lost.

Summary

• Constrained forecast evaluation (CFE) simulates the acceptance/rejection of unconstrained demand by the inventory control system.

• Constrained forecasts can be used to produce revenue opportunity metrics and realistic revenue forecasts and projected load factors.

• CFE is computationally intensive.