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Optimization Models for Off-loading Flow Constrained Areas Ming Zhong, Michael O. Ball, University of Maryland, College Park Introduction Multi-Objective Integer Programming Model The Federal Aviation Administration (FAA) and the aviation community within the U.S. have recently raised new operational concepts for identifying, implementing and managing Flow Constrained Areas (FCA) based on Collaborative Routing (CR). The main purpose of the study is to determine how the FAA can meet its objectives while giving NAS users as much flexibility as possible when choosing routes. Given: P total number of involved flights. ai number of involved flights for airline company i. ∑a i =P ri = target allocated number of flights for airline company i. Objectives: (1) Efficiency: Max∑ x f ¾3-dimensional volume of airspace associated with a time interval. ¾FCAs are defined in response to 1) severe weather 2) capacity/demand imbalance due to excess demand. ∑ f | y i − ri | i Main Constraints: Reduced capacity: ∑ f ∈U FCA Flight conservation: x f ≤ ck Target allocation: Reduce by 4 Reduce by 3 Reduce by 2 0 Normal Normal 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 ∀j, ∀k Ongoing Research: Stochastic Model j ,k ∑ x f + yi = ai Goal: ¾Give flexibilities to airline companies ¾Improve system efficiency and take into account the uncertainty and dynamics of demand on FCAs. ∀i ri = a i ∑ y i / P ∀i ii Alternative Network Flow Model 1. Single sector case The underlying matrix is totally unimodular (TU) and problem can be efficiently solved as a pure network flow model. (C1,0) 28 24 20 16 12 8 4 0 Number of offloaded flights f ∈ Ai # of flights Reduced capacity during FCA for a sector Min or Min ∑ (1 − x f ) Effcient frontiers Sum of the deviations Decision variables: xf = 1, if this flight stays in this area, 0 otherwise. yi = number of offloaded flights for airline company i. (2) Equity: Weather block ¾FCA consists of 31 sectors, involving 45 airline companies/classes associated with 283 flights. ¾Data has maximum simultaneous number of flights of 7, and the reduced capacity changes from 3 to 5. i f What is a Flow Constrained Area (FCA) Computational Results (capacity, cost) (C1,0) Two-stage decision procedure: ¾Flexibility: give tokens to airline companies for some flights in the first stage. ¾Utilization: assign the rest time resource to maximize system utilization. Event time instance (1,-1) (1,-1) Reduced sector capacity Involved flight time Problem Given: ¾ Starting and ending times of FCA ¾ A set of involved flights F ¾ Entrance and exit times for each flight at each sector ¾ The reduced sector capacity in this FCA area. Goal: Partition the involved flights into two groups: 1) maintain original routes, 2) reroute outside this area Time axis Mathematical model: Decision variables: 2. Multiple sector case The underlying matrix is not totally unimodular (TU) but problem can be solved as a network flow model with side constraints. (C2,0) Xf =1 if the flight is pre-allowed to use FCA, 0 otherwise Y ф f = 1 if the flight is adjusted to pass the FCA under scenario ф while Xf =0; 0 no adjustment. Objectives: (1) Predictability:Max ∑ x (C2,0) f f (C1,0) (1,-1) (C1,0) Represents sector change (1,-1) Each layer represents one sector Side constraint: x = w Time axis φ φ (2) Utilization: Max ∑ w f x f + ∑ ∑ p y f f φ Main Constraints: Reduced capacity ∀ k,∀ j ,∀ φ ∑ x f + aφ f yφ f ≤ ck f ∈U j ,k f