DOOR TO DOOR FREIGHT TRANSPORTATION F O R M U L A T I O N S

Transcription

1 DOOR TO DOOR FREIGHT TRANSPORTATION F O R M U L A T I O N S

2 PROJET RESPET Aims o develop quaniaive approaches o door o door freigh ransporaion Members: LAAS-CNRS INRIA LIA DHL JASSP

3 MAIN GOALS Model door o door nework operaion. Take ino accoun conflicing objecives relaed o he subjec (economical, environmenal, QoS, ec). Develop a mehodology based on exac/hybrid algorihms. Firs year main focus: ILP modeling.

4 SCENARIO Schedule ransporaion over a nework using consolidaion erminals

5 MODEL 1 Assume conainers are already assembled and ready o be ranspored. G = nework; N, A - graph represening N se of erminals i, j,, k ; A se of roues i, j,, j, k ; P se of conainers; T = *1,, T+ se of periods.

6 MODEL 1 - PARAMETERS Terminals: S i - Sorage capaciy of erminal i. C i - Sorage cos of erminal i. δ + i = j i, j A+ Se of erminals which i has a direc roue o. δ i = j j, i A+ Se of erminals ha have a direc roue o i. Roues: Δ ij - ransporaion ime beween erminals i and j. Q ij - Capaciy of roue (i, j). C ij - Transporaion cos of roue i, j.

7 MODEL 1 - PARAMETERS Conainers: φ p - Release period of conainer p. ω p - Deadline period of conainer p. o p - Origin of conainer p. d p - Desinaion of conainer p. φ p ω p

8 MODEL 1 - OBJECTIVE Decision variables: x ijp = 1, if conainer p is sen from i o j a 0, oerwise s ip = 1, if conainer p is sored a i a period 0, oerwise Objecive: minimize: ( C i s ip + C ij x ijp ) T p P i N i,j A

9 MODEL 1 - CONSTRAINTS Capaciy consrains p P s ip S i, i N, T p P x ijp Q ij, i, j A, T

10 MODEL 1 - CONSTRAINTS Deparure and arrival consrains ω p =φ p ω =φ p j δ + (i) j δ (i) x ijp x jip = 1, p P, i = o p = 1, p P, i = d p

11 MODEL 1 - CONSTRAINTS Flow conservaion consrain s ip + Δ ji x jip j δ (i) = s ip + x ijp j δ + (i) p P, T, i o p d p,

12 MODEL 2 Assign orders o conainers. L se of orders; Period of assignmen is no aken ino accoun. P se of conainers; Assume here are as many conainers as orders ( P = L );

13 MODEL 2 - PARAMETERS Conainers: V p - Sorage capaciy of conainer p. Orders: v l - weigh of order l; φ l - Release period of order l; ω l - Deadline period of order l; o l - Origin of order l; d l - Desinaion of order l.

14 MODEL 2 - OBJECTIVE Decision variables: x ijp s ip = = 1, if conainer p is sen from i o j a 0, oerwise 1, if conainer p is sored a i a period 0, oerwise y lp = 1, if order l is assigned o conainer p. 0, oerwise Objecive: minimize: ( C i s ip + C ij x ijp ) T p P i N i,j A

15 MODEL 2 - CONSTRAINTS Capaciy consrains p P s ip S i, i N, T p P x ijp Q ij, i, j A, T l L v l y lp V p, p P

16 MODEL 2 - CONSTRAINTS Assignmen consrains p P y lp = 1, l L y lp + y mp 1, p P, l, m L, d l d m

17 MODEL 2 - CONSTRAINTS Origin and desinaion of each conainer is unknown apriori. Deparure and arrival consrains ω l =φ j δ + l (i) ω l =φ j δ l (i) x ijp x jip y lp, l L, p P, i = o l y lp, i L, p P, i = d l

18 MODEL 2 - CONSTRAINTS Origin and desinaion of each conainer is unknown apriori. Flow conservaion consrains s ip + Δ x ji jip j δ (i) s ip + x ijp j δ + i + y lp, p P, i N, T l L d l =i s ip + Δ x ji jip j δ (i) + y lp l L o l =i s ip + x ijp j δ + i, p P, i N, T 1 x ijp j δ + i Δ x ji jip j δ i 1, p P, i N, T

19 MODEL 3 Take ino accoun sorage of orders Pick-up and delivery ime windows for each order; Time windows for conainers ransporaion. Addiional cos if order is shipped or arrives ouside is ime window

20 MODEL 3 - PARAMETERS φ l - Time window for picking up order l or shipping conainer p; ω l - Time window for delivery of order l or arrival of conainer p; C l - Sorage cos of order l. φ l φ l + ω l ω l + φ p φ p + ω p ω p +

21 MODEL 3 - OBJECTIVE Decision variables: x ijp s ip 1, if conainer p is sen from i o j a = 0, oerwise 1, if conainer p is sored a i a period 0, oerwise if order l is assigned o conainer p. 0, oerwise if order l is sored a period. 0, oerwise = y lp = 1, z l = 1,

22 MODEL 3 - OBJECTIVE Objecive: minimize: ( C i s ip + C ij x ijp ) + C l z l T p P i N i,j A l L T

23 MODEL 3 - CONSTRAINTS Deparure and arrival consrains φ p + =max (φ j δ + l,φ p ) (i) x ijp y lp, i N, p P min(ω l +,ωp + ) =ω p j δ (i) Δ ij x jip y lp, i N, p P φ l φ l + ω l ω l + φ p φ p + ω p ω p +

24 MODEL 3 - CONSTRAINTS Order sorage consrains z l y lp j δ + i =φ l + x ijp, l L, p P, φ l +, φ p +, i = o l z l y lp + ω l x jip 1, l L, p P, ω p, ω l, i = d l j δ i = φ l φ l + ω l ω l + φ p φ p + ω p ω p +

25 MODEL 4 Take ino accoun differen ransporaion modes and vehicles V1 = A B C B C V2 = A B D A D V3 = B - C. C Differen mode erminals and mode ransfer arcs A B D

26 MODEL 4 TIME SPACE NETWORK R se of all vehicles: Each vehicle v is represened by a differen nework. G r = (V r, A r ) - ime space nework of vehicle r. Transpor nework is he union of all vehicles G = (V, A). V = r R V r - All vehicle erminals; A = A A s A m ; A = r R A r - All vehicle roues;

27 PERSPECTIVES Take ino accoun conflicing objecives relaed o he subjec (economical, environmenal, QoS, ec). Develop a mehodology based on exac/hybrid algorihms.

28 Thank you!