FRFC TRANSPORT Vehicle loading from a practical case to a Bin-Packing approach

FRFC TRANSPORT 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

FRFC TRANSPORT 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)

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

FRFC TRANSPORT 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 »

FRFC TRANSPORT Instances : Postal zoneCoilsCustomersTrucks (1 >90%) ( ) (1 50, 10,…) (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

FRFC TRANSPORT Coils, trucks, destinations and dates

FRFC TRANSPORT 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 :

FRFC TRANSPORT Results : 20 – 1 = 5% or 9 – 1 = 11% ? N°Opt A-MWeightsRest (23.5-W)« First-Fit" 11222, , , , , , , , , , , ,95310, ,90310, ,3311, ,3211, ,0911, ,0611, ,4312, ,3312, ,2912, ,2712, ,0212, ,9612, ,5613, ,314, ,60316,89719* Total20 19 Greedy algorithm : First-Fit decreasing FFD

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

FRFC TRANSPORT CPImprovement (%) 6711,5% 5011% 5712% 3312% Preliminary results for D

FRFC TRANSPORT F : 2 kind of bins 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 :

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

FRFC TRANSPORT 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…

FRFC TRANSPORT 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)

FRFC TRANSPORT 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 ?

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

FRFC TRANSPORT ? 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…

FRFC TRANSPORT Please don’t ask questions give answers… or provide tips, advices, guidelines…