A SCENARIO AGGREGATION–BASED APPROACH FORDETERMINING A ROBUST AIRLINE FLEET COMPOSITIONFOR DYNAMİC CAPACİTY ALLOCATİONOvidiu Listes, Rommert Dekker

AGENDA Introduction Literature Review Fleet Composition Problem Model

Deterministic Model Stochastic Model Scenario Aggregation Algorithm Scenario Generation

Case Study Conclusion

1.INTRODUCTİON

Random demand fluctuations lead to -low average load factors -a significant number of not accepted

passengers

Dynamic allocation of airline fleet capacity:

Using most recent estimates of customers demands for accordingly updating the assignments of aircrafts to the flight schedule

Fleet Assignment

Fleet Composition

This paper focuses on creating an approach to the airline fleet composition problem that accounts explicitly for stochastic demand fluctuations

2. LITERATURE REVIEW

Berge&Hopperstad(1993)

Hane et al.(1995)

Talluri(1996)

Gu et al.(1994)

3. THE FLEET-COMPOSİTİON PROBLEM

Complex, upper-management decides on it.

Paper adresses problem from OR perspective. Model it in relation to the basic fleet assignment.

Demand is assumed to follow independent normal distribution, variability specified as the K-factor(sd/mean).

Each aircraft has-Fixed cost-Operational cost-Capacity for each fair class-Range capability-Family indicator

o Assumptions:-Identical flying&turn around time-No recapture-Minimum number of aircrafts required is taken

into account

4.MODELFleet composition problem can be considered as a multicommodity flow problem based on the construction of a space-time network

4.1. DETERMİNİSTİC MODEL

NP-hard for more than three aircraft types

4.2. STOCHASTİC MODELS representative scenarios and

solution for individual demand

scenarios

is same for every scenario hence, for every scenario s.

Because of huge number of integer second-stage variables a branch-and-bound type of procedure is not practical.

For small examples: LP relaxation of SP denoted by LSP includes

many integer-valued decision variables.

LP relaxation gap turns out to be less than 0.5% in these cases.

4.3.1 THE SCENARİO AGGREGATİON–BASED APPROACH

Scenario aggregation is a decomposition-type of method.

Main Idea: Iteratively solving individual scenario problems, perturbed in a certain sense, and to aggregate, at each iteration, these individual solutions into an overall implementable solution

4.3.2. THE SCENARİO AGGREGATİON ALGORİTHM

Admissible solution: Feasible for each scenario s.

z variables indexed over scenario s then additional constraint:

: solution from previous iteration

This constraint is relaxed in the Lagrangian sense using multipliers ws .

THE SCENARİO AGGREGATİON ALGORİTHM

is an implementable solution not necessarily admissible

w is interpreted as information prices

Stopping Criteria: Variance error wrt z variables is used

Stop when:

Criteria Selection:-Low ρ values encourage progress in primal sequence -ε is set to 3% of minimum total number of planes

ROUNDİNG PROCEDURE

fractional first stage solution with

For any given fractional solution u [u] denotes integer part of u and {u} denotes fractional part of u

A constant c is selected between 0 and 0.5

Rounding Procedure:

4.4 SCENARİO GENERATİONDemand assumed to follow a normal distribution:

Descriptive Sampling: A purposive selection of the sample values—aiming to achieve a close fit with the represented distribution—and the random permutations of these values

4.5 FLEET PERFORMANCE EVALUATİON

New simulated demands from demand distribution is used, size 3 to 4 times greater than number of scenarios used.

Generic Fleet Flexibility

Fleet Interchangibility

5. CASE STUDY

Small case validates method, Large case shows extend Nine aircraft types 40% business, 60% economy seats Small case: Large Case:

-342 flight legs-18 airports -15 planes-50 scenarios-Mean Demand :14-65 for economy class26-48 for business class

-1978 flight legs-50 airports -68 planes-25 scenarios-Mean Demand :18-57 for economy class21-43 for business class

GENERİC FLEXİBİLİTY-SMALL CASE

FLEET INTERCHANGİBİLİTY-SMALL CASE

GENERİC FLEXİBİLİTY-LARGE CASE

FLEET INTERCHANGİBİLİTY-LARGE CASE

6.CONCLUSİON

Increase in load factor up to 2.6% Decrease in spill up to 3.3%. Profit increase up to 14.5%.

Finally, The scenario-aggregation based

approach handles effects of fluctuating passenger demand on fleet-planning process and generates flexible fleet configurations that support dynamic assignments.

Thanks for listening