SchedulAir. Airline planning & airline scheduling with Unified Optimization. decisal. Copyright 2014 Decisal Ltd. All rights reserved.
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1 Copyright 2014 Decisal Ltd. All rights reserved. Airline planning & airline scheduling with Unified Optimization SchedulAir
2 Overview Unified Optimization Benders decomposition
3 Airline planning & scheduling Long-Term Medium- & Short-Term Fleet Planning Network Planning Fleet Assignment Aircraft Rotations Crew Scheduling Which aircraft types and how many aircraft? Which flights? Which fleet for each flight? Which schedule for each aircraft? Which schedule for each crew? Unified Optimization Benders decomposition
4 SchedulAir unified management & optimization Long-Term Medium- & Short-Term Fleet Planning Network Planning Fleet Assignment Aircraft Rotations Crew Scheduling PlanUnified SchedUnified SchedulAir Unified Optimization Benders decomposition
5 PlanUnified: comparison with other products PlanUnified u n i f i e d o p t i m i z a t i o n Fleet Planning Other Products sequential optimization Fleet Planning Network Planning Network Planning Fleet Assignment Fleet Assignment Unified Optimization Benders decomposition
6 SchedUnified: comparison with other products SchedUnified u n i f i e d o p t i m i z a t i o n Fleet Assignment Other Products sequential optimization Fleet Assignment Aircraft Rotations Aircraft Rotations Crew Pairing Crew Pairing Unified Optimization Benders decomposition
7 Optimization results Users report savings of USD 300 / flight within a month of using our system Unified Optimization Benders decomposition
8 Benders decomposition min c T x + c(y ) A x + y = b x 0, y Y Unified Optimization Benders decomposition
9 Benders problems min c T x + c(y ) A x + y = b x 0, y Y Master Problem min c(y) +???? y Y Subproblem min c T x A x = b - ỹ x 0 Unified Optimization Benders decomposition
10 Benders subproblem given a MP solution Master Problem min c(y) +???? y Y min c T x + c(y ) A x + y = b x 0, y Y ỹ Subproblem min c T x A x = b - ỹ x 0 Unified Optimization Benders decomposition
11 Dual Benders subproblem min c T x + c(y ) A x + y = b x 0, y Y Master Problem min c(y) +???? y Y Subproblem min c T x A x = b - ỹ x 0 Dual of Subproblem max (b - ỹ) T π A T π c Unified Optimization Benders decomposition
12 Duality theorem min c T x + c(y ) A x + y = b x 0, y Y Master Problem Subproblem min c(y) +? Duality Theorem z = min c T x??? (b - ỹ) T π z A x = b - ỹ y Y x 0 Dual of Subproblem max (b - ỹ) T π A T π c Unified Optimization Benders decomposition
13 Duality theorem min c T x + c(y ) A x + y = b x 0, y Y Master Problem min c(y) +???? y Y (b - ỹ) T π z z = Subproblem min c T x A x = b - ỹ x 0 Dual of Subproblem max (b - ỹ) T π A T π c Unified Optimization Benders decomposition
14 Benders algorithm min c T x + c(y ) A x + y = b x 0, y Y Master Problem min c(y) + z (b - y) T π i z y Y ỹ i π i Subproblem min c T x A x = b - ỹ i x 0 Dual of Subproblem max (b - ỹ i ) T π i A T π i c Unified Optimization Benders decomposition
15 Unified Optimization Benders decomposition
16 Decisal Research & Development Born from cutting edge research at Imperial College London Based in London, UK IBM partner Unified Optimization Benders decomposition
17 Decisal & IBM Unified Optimization Benders decomposition
18 Conclusions Long-Term Medium- & Short-Term Fleet Planning Network Planning Fleet Assignment Aircraft Rotations Crew Scheduling PlanUnified SchedUnified SchedulAir
the only system with Unified Management & Optimization of: crew SchedulAir decisal
the only system with Unified Management & Optimization of: flights aircraft crew SchedulAir u n i f i e d m an ag e m e n t & o p t i m i z at i o n decisal m a k i n g d e c i s i o n s o p t i m a l
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