Runway Scheduling Using Generalized Dynamic Programming

Abstractly, the runway scheduling problem (RSP) can be thought of as a job shop scheduling problem [11] withprecedence and release time constraints, where the objective is to sequence a set of jobs (aircraft) in a particularordertobeprocessedbyaprocessor(runway)sothatsomecostfunctionisminimized. Fortherunwayschedulingproblem, one wants to find an efficient schedule for aircraft to use the runway. The output, then, to the runwayscheduling problem is a time for each aircraft to begin using the runway, which will be referred to as a runwayschedule.Therunwayschedulingproblemisformallydescribedasfollows: Givenanorderedsetofdepartureaircraft Q d foreachdeparturequeue d ,asetofdepartureaircraft G g foreachgate g ofcardinality1,anorderedsetofaircraft C c foreachrunwaycrossingqueue c ,asetofaircraft P i thatmustnotusetherunwaybeforeaircraft i ,anearliesttime α ( i )foraircraft i toreachtherunway,andvarioustimingconstraints(describedbelow),findthesetof non-dominating a runwayschedule(s)withrespecttobothdelayandthroughput.A diagram of a typical problem is shown below in Figure 1. This diagram shows an example airport with onedeparture runway, a ramp area, and a network of taxiways. Each aircraft on the airport surface waits to use therunwayinchainlikestructurescalledqueues. Forthisdiagram,departureaircraftlocatedwithintherampareaareattheirgatesorgatequeues,anddepartureaircraftnearthetopleftentranceofthedeparturerunwayarewaitingindeparturequeues. Finally,thereisonetaxiwaythatcrossestherunwaywithachainoftwoaircraftwaitingcross.Theseaircraftwaitingtocrosstherunwayaresaidtobewaitingintheircrossingqueue.Tobeexact,anaircraft

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