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Algorithms 2018,11, 55
With theobjective tominimize thesumofalldelays forall trainsreachingtheirļ¬naldestination
withadelay larger thanthreeminutes, theobjective functioncanbeformulatedas follows,where the
parameternj foreachtrain jā Jholds theļ¬naleventof train j :
min
z f :=ā
jāJ znj (A1)
Wealsohave the following threeblocksof constraints. Theļ¬rst block concerns the timingof
the events belonging to each train j and its sequence of events, deļ¬nedby the event listOj āO.
Theseconstraintsdeļ¬netherelationbetweenthe initial scheduleandrevisedschedule,asaneffect
of thedisturbance. Equation(A7) isusedtocompute thedelayofeacheventexceedingĪ¼ timeunits,
whereĪ¼ is set to threeminutes in thiscontext.
xendj,i = x begin
j,i+1, iāOj, jā J : i =nj, jā J (A2)
xbeginj,i = b static
j,i , iāO : bstaticj,i >0, jā J (A3)
xendj,i = e static
j,i , iāO : estaticj,i >0, jā J (A4)
xendj,i ā„ xbeginj,i +dj,i, iāO, jā J (A5)
xbeginj,i ā„ binitialj,i , iāO : psj,i=1, jā J (A6)
xendj,i āeinitialj,i āuā¤ zj,i, iāO, jā J (A7)
In the following part, N is a large constant. The second block of constraints concerns the
permitted interactionbetweentrains,giventhecapacity limitationsof the infrastructure (including
safetyrestrictions):
ā
uāMm qj,i,u=1, iāOm,māM, jā J (A8)
qj,i,u+qjā²,iā²,uā1ā¤Ī»j,i,jā²,iā²+Ī³j,i,jā²,iā², i, iā² āOm,uāMm,māM : i< iā², j = jā² ā J (A9)
xbeginjā²,iā² āxendj,i ā„Ī Meeting
m Ī³j,i,jā²,iā² āN (
1āĪ³j,i,jā²,iā² )
, i, iā² āOm,māM : i< iā²,miā² =mi, j = jā² ā J (A10)
xbeginjā²,iā² āxendj,i ā„Ī Following
m Ī³j,i,jā²,iā² āN (
1āĪ³j,i,jā²,iā² )
, i, iā² āOm,māM : i< iā²,miā² =mi j = jā² ā J (A11)
xbeginj,i āxendjā²,iā² ā„Ī Meeting
m Ī»j,i,jā²,iā² āN (
1āĪ»j,i,jā²,iā² )
, i, iā² āOm,māM : i< iā²,miā² =mi j = jā² ā J (A12)
xbeginj,i āxendjā²,iā² ā„Ī Following
m Ī»j,i,jā²,iā²āN (
1āĪ»j,i,jā²,iā² )
, i, iā² āOm,māM : i< iā²,miā² =mi, j = jā² ā J (A13)
Ī»j,i,jā²,iā²+Ī³i,iā² ā¤1, i, iā² āOm,māM : i< iā², j = jā² ā J (A14)
xbeginj,i ,x end
j,i ,zj,iā„0, iāO, jā J (A15)
Ī³j,i,jā²,iā²,Ī»j,i,jā²,iā² ā {0,1}, iā² āOm, iāM : i< iā², j = jā² ā J (A16)
qj,i,uā{0,1}, iāOm,uāMm,māM, jā J (A17)
References
1. BostonConsultancyGroup.The2017EuropeanRailwayPerformance Index;BostonConsultancyGroup:Boston,
MA,USA,18April2017.
2. EuropeanCommissionDirectorateGeneral forMobilityandTransport.Studyon thePrices andQualityofRail
PassengerServices;ReportReference:MOVE/B2/2015-126;EuropeanCommissionDirectorateGeneral for
MobilityandTransport: Brussel,Belgium,April2016.
112
zurĆ¼ck zum
Buch Algorithms for Scheduling Problems"
Algorithms for Scheduling Problems
- Titel
- Algorithms for Scheduling Problems
- Autoren
- Frank Werner
- Larysa Burtseva
- Yuri Sotskov
- Herausgeber
- MDPI
- Ort
- Basel
- Datum
- 2018
- Sprache
- englisch
- Lizenz
- CC BY 4.0
- ISBN
- 978-3-03897-120-7
- Abmessungen
- 17.0 x 24.4 cm
- Seiten
- 212
- Schlagwƶrter
- Scheduling Problems in Logistics, Transport, Timetabling, Sports, Healthcare, Engineering, Energy Management
- Kategorien
- Informatik
- Technik