1. FRFC TRANSPORT 24-4-20081 Vehicle loading from a practical case to a Bin-Packing approach

2. FRFC TRANSPORT 24-4-20082 Plan « Marshall » Logistics TranslogisTIC Trans : freight forwarders carriers customers Logis : transportation TIC : Information and Communication Technologies Objective: create a platform to collect and share transportation information along the supply chain Tags 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

3. FRFC TRANSPORT 24-4-20083 A practical case : ARCELOR-MITTAL Liège (Who) Producing and sending coils (What) 70% road, 20% rail, 10% boat 350 trucks/day, 2 trains and 1 boat 16 depots around Liège to 800 customers Major markets : D, F, Benelux Objectives : min € and visibility for service and management (Why)

4. FRFC TRANSPORT 24-4-20084 Topics : a) Long-haul D & F and b) Eastern Europe Negotiated prices per postal code (Where) Concentration of the customers in industrial areas

5. FRFC TRANSPORT 24-4-20085 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 truck A rule : one week planning horizon Load assignment : « good practice »

6. FRFC TRANSPORT 24-4-20086 Instances : Postal zoneCoilsCustomersTrucks 674693 (1 >90%)380 503303 (2 50-50)249 5761013 (1 50, 10,…)330 332895 (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

7. FRFC TRANSPORT 24-4-20087 Coils, trucks, destinations and dates

8. FRFC TRANSPORT 24-4-20088 First approach Bin-packing : J: set of items (1,…, j,…,n) I : set of bins (1,…, i,…,n) C : capacity of the bin > 0 W j : weight of each item 0 < W j < C y i : (0,1) if bin i is used x ij : (0,1) if item j is placed in bin i subject to :

9. FRFC TRANSPORT 24-4-20089 Results : 20 – 1 = 5% or 9 – 1 = 11% ? N°Opt A-MWeightsRest (23.5-W)« First-Fit" 11222,833 1 21822,303 2 31921,093 3 4119,413 4 5618,993 5 6718,863 6 7818,743 7 81117,633 8 9917,603 9 10 17,583 10 112017,3511 12212,95310,54712 13312,90310,59713 141712,3311,1714 151612,3211,1815 16512,0911,4116 17412,0611,4417 181311,4312,0717 191511,3312,1716 201411,2912,2118 211511,2712,2318 221411,0212,4814 231310,9612,5415 24179,5613,9412 25169,314,213 2626,60316,89719* Total20 19 Greedy algorithm : First-Fit decreasing FFD

10. FRFC TRANSPORT 24-4-200810 Bounds : Martello et Toth (few items with large weights) For any « integer » 0 ≤ α ≤ C/2 Heavy, above half capacity, light L(6) = 11 + 6 + max (0, 92.763 – (6*23.5- 74.656))= 17 + (0,round up 26.419/ 23.5) = 19 (Optimal)

11. FRFC TRANSPORT 24-4-200811 CPImprovement (%) 6711,5% 5011% 5712% 3312% Preliminary results for D

12. FRFC TRANSPORT 24-4-200812 F : 2 kind of bins - 23.5 T - 27 T limited number B and more expensive C i : capacity of the bin > 0 W j : weight of each item 0 < W j < C j sorted W 1 < W 2 F i : cost of bin i subject to :

13. FRFC TRANSPORT 24-4-200813 F : 2 kind of bins « First fit » : lower results than A-M Value of B, not explicitly known?

14. FRFC TRANSPORT 24-4-200814 Second approach: Matching Problem Typically 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

15. FRFC TRANSPORT 24-4-200815 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)

16. FRFC TRANSPORT 24-4-200816 Time (Days) Wait : how long ? Too late? Early: stock or send? Criteria (reoptimization) Dynamic or on-line problem Multicoils situation Strategies: when and what ? - fixed frequency scheduling on all available orders - according to the delivery date - when a loading ratio is reached ?

17. FRFC TRANSPORT 24-4-200817 Scientific sources : Martello and Toth (Bin-packing) Coffman, Garey, Johnson (On-line) « Fully dynamic bin-packing » Ivkovic-Lloyd Bounds and Theoretical performances of algorithms.

18. FRFC TRANSPORT 24-4-200818 ? 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…

19. FRFC TRANSPORT 24-4-200819 Please don’t ask questions give answers… or provide tips, advices, guidelines…