frfc transport 24-4-20081 vehicle loading from a practical case to a bin-packing approach

FRFC TRANSPORT 24-4-2008 1

Vehicle loading

from a practical case

to

a Bin-Packing approach


Plan « Marshall » Logistics TranslogisTIC

Trans : freight forwarders carriers customersLogis : transportationTIC : Information and Communication Technologies

Objective: create a platform to collect and share transportation information along the supply chainTags or marks on freight or boat, car, train, truck GPS (location) and order number, expected arrival time, tracking and tracing, alerts, weather forecast…

23 partners : HEC-Ulg, UCL, N-Side partners for optimization, Sodiplan (Geomatic), and FPMs for telecommunication


A practical case : ARCELOR-MITTAL Liège (Who)Producing and sending coils (What)70% road, 20% rail, 10% boat350 trucks/day, 2 trains and 1 boat16 depots around Liège to 800 customersMajor markets : D, F, Benelux

Objectives : min € and visibility for service and management (Why)


Topics : a) Long-haul D & F and b) Eastern EuropeNegotiated prices per postal code (Where)

Concentration of the customers in industrial areas


How ?Technical constraints:- Delivery date- Capacity (44T Benelux, 40 T D & F others) - Available capacity : 27.5 T ; 23.5 T (or F 27 T) Economic constraints: - price depends on destination - extra cost if loading at 2 depots in Liège

Current optimization: « manual planning »

Current habit (not a rule) : 1 customer per truckA rule : one week planning horizonLoad assignment : « good practice »


Instances :

Postal zone Coils Customers Trucks67 469 3 (1 >90%) 38050 330 3 (2 50-50) 24957 610 13 (1 50, 10,…) 33033 289 5 (44, 28, 13, 13%) 126

Reduction : Set sequenced in weeks (Static)Notes :- the average number of coils per truck vary from a destination to another typically 1, 2 sometimes 3 exceptionnally 4 and once 8…- the number of customers vary from a postal code to another


Coils, trucks, destinations and dates


First approach Bin-packing :J: set of items (1,…, j,…,n)I : set of bins (1,…, i,…,n)C : capacity of the bin > 0Wj : weight of each item 0 < Wj < C yi : (0,1) if bin i is usedxij : (0,1) if item j is placed in bin i

subject to :

n

iiyZMin

1

Jjx

IiyCxW

n

iij

n

jiijj

1

1

,1

,


Results : 20 – 1 = 5% or 9 – 1 = 11% ?

N° Opt A-M Weights Rest (23.5-W) « First-Fit"1 12 22,833 12 18 22,303 23 19 21,093 34 1 19,413 45 6 18,993 56 7 18,863 67 8 18,743 78 11 17,633 89 9 17,603 9

10 10 17,583 1011 20 17,35 1112 2 12,953 10,547 1213 3 12,903 10,597 1314 17 12,33 11,17 1415 16 12,32 11,18 1516 5 12,09 11,41 1617 4 12,06 11,44 1718 13 11,43 12,07 1719 15 11,33 12,17 1620 14 11,29 12,21 1821 15 11,27 12,23 1822 14 11,02 12,48 1423 13 10,96 12,54 1524 17 9,56 13,94 1225 16 9,3 14,2 1326 2 6,603 16,897 19*

Total 20 19

Greedy algorithm : First-Fit decreasing FFD


Bounds :Martello et Toth (few items with large weights)For any « integer » 0 ≤ α ≤ C/2

j

j

j

WCNjJ

CWCNjJ

cWNjJ

2/:

2/:

:

3

2

1

Heavy, above half capacity, light

C

WCJW

JJLJj Jj

jj

3 2

2

21 ,0max

L(6) = 11 + 6 + max (0, 92.763 – (6*23.5- 74.656))=17 + (0,round up 26.419/ 23.5) = 19 (Optimal)


CP Improvement (%)

67 11,5%

50 11%

57 12%

33 12%

Preliminary results for D


F : 2 kind of bins- 23.5 T- 27 T limited number B and more expensiveCi : capacity of the bin > 0Wj : weight of each item 0 < Wj < Cj sorted W1< W2

Fi : cost of bin i

subject to :

n

iii yFZMin

1

Jjx

IiyCxW

n

iij

n

jiiijj

1

1

,1

,


Jjx

nBiyxW

BiyxW

yFyFZMin

n

iij

n

jiijj

n

jiijj

n

Bii

B

ii

1

1

1

15.23

127

,1

),...,1(,5.23

),...,1(,27

F : 2 kind of bins

« First fit » : lower results than A-MValue of B, not explicitly known?


Second approach: Matching ProblemTypically 1 or 2 coils per truck (Limit > 23,5 / 3 T) Algorithm (P), but independant sets.Sometimes 3, 4 coils…

20

5

8

15

3

20

5

8

15

3


Dynamic Problem (Rem: on-line)

For 1 coil (not order)

1) Delivery date : commercial2) Ready for transportation (no visibility)

3) Freight reservation date: Logistics 4) Expected departure (typically the following week)

Time (Days)


Time (Days)

Wait : how long ? Too late?

Early: stock or send? Criteria (reoptimization)

Dynamic or on-line problemMulticoils situation

Strategies: when and what ?- fixed frequency scheduling on all available orders- according to the delivery date- when a loading ratio is reached ?


Scientific sources :

Martello and Toth (Bin-packing)

Coffman, Garey, Johnson (On-line)

« Fully dynamic bin-packing » Ivkovic-Lloyd

Bounds and Theoretical performances of algorithms.


?

b) Eastern countries: long haul with intermediate delivery

AUT, CHE, CZE, HUN, POL, ROM, SVK, SVN

Where to stop? Driving time, available connections

Routing model: time-windows, path…


Please don’t ask questions give answers…

or provide tips, advices, guidelines…

frfc transport 24-4-20081 vehicle loading from a practical case to a bin-packing approach

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