Agenda
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Agenda ƒ Introduction ƒ The process from timetable to crew plan ƒ The problem: Shortening the process ƒ Details on TURNI, a crew planning optimization tool ƒ Objective function ƒ A solution: Design of Experiments ƒ Chosen parameters ƒ The experiments ƒ The analysis ƒ The closed form ƒ Validity of the closed form ƒ Future work
description
Agenda. Introduction The process from timetable to crew plan The problem: Shortening the process Details on TURNI, a crew planning optimization tool Objective function A solution: Design of Experiments Chosen parameters The experiments The analysis The closed form - PowerPoint PPT Presentation
Transcript of Agenda
Agenda
ƒ Introductionƒ The process from timetable to crew planƒ The problem: Shortening the processƒ Details on TURNI, a crew planning optimization toolƒ Objective functionƒ A solution: Design of Experiments
ƒ Chosen parametersƒ The experimentsƒ The analysis
ƒ The closed formƒ Validity of the closed formƒ Future work
Goals of this paper
Goalƒ Reduce the time to agree on a cost efficient crew plan accepted by the union and wanted by the drivers
Toolƒ Parameter analysis and preparation
Dimensions at S-togs
2*170 km tracks80 stations~ 1100 departures on a daily basis80 trains running530 drivers hereof 150 in reserve300.000 passengers a day A target regularity of >95 % A target reliability of >97 %
ƒ 3 crew depots (KH, KJ, HI)ƒ 2 break facilities (KH, HL)
The S-train network
Line A
KH
HI
UND
24
22
41
11
40
22
North 92South 68Round 160 min
Frequency 20 minRolling stock 8
Lines
Round Rolling stock Line
120 6 C, A+
140 7 B, B+
160 8 A
180 9 E
200 10 H, H+
Efficiency of driver duties
100101102103
104105106107
2002 2003 2004 2005 2006
Index (year 2002 = 100)
Efficiency of driver duties
Timetable
Rolling stock
Crew
Management
The planning process
The decision cycle
Crew
Management
Before (many repetitions)
After (full picture)
Crew
Management
…
TURNI
Crew optimization system www.turni.itƒ Used by bus companies in Italyƒ Used by railway company NSR in Holland
ƒ 2001: Kroon and Fischetti, Crew Scheduling for Netherlands Railways "Destination: Customer”
ƒ 2000: Kroon and Fischetti. Scheduling train drivers and guards: the dutch noord-oost case.
Minimum transfer
time
Pre- and post times
Meal break rule
Maximum duty lengthDuty examples
Rostering Rules
Maximum percentage late duties
Maximum percentage long duties (>8 hrs)
Maximum average duty
length
The different objective functions
S-tog Penalty TURNIEfficiency / Working time Yes Small YesNo of duties implicitly Large Yes Break size implicitly Small YesDuty length Implicitly Small YesPassenger trips (taxis) implicitly Small YesShort duties implicitly Small Yes
Convergence of a TURNI run, OBJ2Total working time
86000
86500
87000
87500
88000
88500
89000
89500
90000
0 100 200 300 400 500 600
Seed 1
Seed 2
Seed 3
Seed 4
Seed 5
Parameters of the rules
Description Factor 0 1 At most 3:20 of driving on line H without a break A 20 30 Max average working time B 07:20 07:30 Rule of variation of specific type C 2 0 Max no of duties longer than 8:00 hours D 10% 20% Amount of extra minutes in connection with breaks E 4 2 Max working time after 17:00 F 07:15 07:45
Parameter analysis, methods
Method 1: One parameter at a timeƒ Only one parameter is changed each timeƒ Each parameter can be tried at many levels
Method 2: Lagrange multipliersƒ TURNI use them.ƒ One multiplier for each restriction in the math modelƒ Measure the improvement of OBJ2 when changing the parameter one unit
Method 3: Design of experimentsƒ Used here
Design of experimentsA B C0 (-) 0 (-) 0 (-)0 (-) 1 (+) 0 (-)1 (+) 0 (-) 1 (+)1 (+) 1 (+) 1 (+)0 (-) 0 (-) 1 (+)0 (-) 1 (+) 1 (+)1 (+) 0 (-) 0 (-)1 (+) 1 (+) 0 (-)
Full factorial design, 23=8 runsFractional factorial design 23-1=4See for instance Design and Analysis of Experiments by Douglas C. Montgomery (2004)
Parameter analysis
Method Speed Levels 2. Order effects
3. Order effects
Different objective functions
Change one parameter
Fast Many No No Ok
Lagrange multipliers
Very fast One No No No
Design of experiments
Slower Two Yes Possible Ok
The general linear model
OBJ = const+A+B+C….+D+E+F+AB+AC+AD+AE+AF+BC+BD+BE+BF+CD+CE+CF+DE+DF+EF+error.
No 3. order effects.
Model validity 98,5%
Results and analysis
Effects Value Value/Const (%) P-valueConst 86776A 44 0.1% 0.035B 1144 1.3% 0.000C -591 -0.7% 0.000D -172 -0.2% 0.000E -493 -0.6% 0.000F -36 0.0% 0.477AB -204 -0.2% 0.045AC -174 -0.2% 0.080AD -3 0.0% 0.978AE 129 0.1% 0.179AF -54 -0.1% 0.563BC -292 -0.3% 0.009BD -281 -0.3% 0.010BE -164 -0.2% 0.097BF -121 -0.1% 0.206CD -113 -0.1% 0.236CE 237 0.3% 0.024CF 65 0.1% 0.482DE 30 0.0% 0.742DF 225 0.3% 0.030EF -108 -0.1% 0.254
Interesting features
Synergetic effects:When changing both C and D, the effect is larger than the sum of the effect of C and D alone: -591-172-113=-876
Counterintuitive signs:Difference between OBJ1 and OBJ2
Significance level 5%From 1st order effects: leave F out. F is not significantFrom 2nd order effects: keep F, since DF is significant
Rule of variation was redefined after this analysis.
The closed form
Let fA denote the level of parameter A.
With only two factors you would haveOBJ = const + fAA+fBB+fAfBAB + error
fA = {0,1}
The closed form
0 1
1
0
B
A
A+B+AB
fB
fA
0
? fAA+fBB+fAfBAB
The closed form
Let fA denote the level of parameter A.
With only two factors you would haveOBJ = const + fAA+fBB+fAfBAB + error
fA = {0,1}
fA arbitrary
Justifying the closed form
A B C D E F OBJ Model value
%-diff
0 0 0 0 0 0 86742 86776 0.04%
0 0 0 0 1 0 86319 86284 -0.04%
0 0 0 1 0 1 86776 86793 0.02%
0 0 0 1 1 1 86239 86222 -0.02%
0 0 1 1 1 0 85646 85674 0.03%
The last parameter setting is ”best” possible
Future work
ƒ Introduce center points. Requires a non-linear modelƒ Larger experiments,
ƒ Screening (remove insignificant)ƒ Priorities
ƒ Use DoE in rolling stock rostering or other planning problems from the railway industry
Questions?
