Study on D isruption M anagem en t of Veh icle Routing Problem w ith the Changes of T im e W indows and D elivery W e ight of Custom ers

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1 JOURNAL OF MANAGEM ENT SC IENCES Vol. 21 No. 5 October, ,,, :,,, ;,, VRPTW MD2 VRPTW MDVRPTW ;,,;,, : ; ; ; ; ; : C93 : A : (2008) Study on D isruption M anagem en t of Veh icle Routing Problem w ith the Changes of T im e W indows and D elivery W e ight of Custom ers WANG Xu2p ing, XU Chuan2lei, HU Xiang2pei Institute of System s Engineering, Dalian University of Technology, Dalian , China Abstract: To tackle the disrup tion that is caused by the demands of customers in the logistics, the paper p roposes disrup tion recovery strategies and solutions based on the theory of disrup tion management. The trans2 formation method for the disrup tion recovery of the vehicle routing p roblem is put foward on the basis of the mul2 tip le depots, and the disrup tion recovery strategies and the methods of deviation measurement are given, which is the foundation of the disrup tion management modeling for the vehicle routing p roblem. After the disrup tion is illustrated and distinguished by analyzing and identifying the changes of time windows and delivery weight of customers, the disrup tion management model is constructed, and the normalization method for the model is giv2 en, making the model compatible with VRPTW, MDVRPTW and disrup tion management for MDVRPTW. On the basis of the characteristic of the model, the chromosome code based on customer is ameliorated, which can indicate the disrup tion recovery strategies; according to the disrup tion management, the genetic algorithm is de2 signed to solve the model. The rep resentative result and analysis are p rovided in this paper, and the experiment indicates the validity of the model and algorithm. Keywords: disrup tion management; disrup tion recovery; vehicle routing p roblem; time window; capacity constraint; genetic algorithm : : : ( , ) ; ( ) : ( ),,,,,, : E2mail: wxp@ dlut. edu. cn

2 112 (Journal ofmanagement Sciences) ,,,,,,,, 2, ( vehi2 cle routing p roblem with time window, VRPTW ) NP 2 Hard, TW / D VRPTW, [ 1 ] ;, [ 2 ],, scheduling re 2scheduling,, L i J ing2quan,, SDVRP, [ 3 ] ;, VRP,, 0,, [ 4 ] ;,, [ 5 ] schedulingre 2sched2 uling,,,,,,, [ 6, 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ],, [ 12 ] ; VRPTW,,,, [ 13 ],,,,, ;,, ;,,, VRPTW MDVRPTW MDVRPTW ;, ;, ; , 3, ; ;, kr m 1,,, 1, k 1 k 1 d, k 1 dk 1 L T dk 1, D t, k 1 ( co x, co y ), D k 1 ( co x, co y ), D t, L T dk, 0, 1 0, k 1 D D t, d D k 1 k 1 k 1 0 2, k 2 k 2 d k 2, dk 2 L T dk 2, D t, k 2 i, i S ervicet i, k 2 i S T i, i ( co x i, co y i ), D k 2 ( co x i, co y i ), D t + S ervicet i - S T i, L T dk 2, 0, g i, k 2 D D t + S ervicet k 2 i - S T i, d D k 2 k 2

3 5 : V, D, D = {D 1, D 2,, D k } ( k V ), (k ) d, d = { d 1, d 2,, d k } ( k V ), m,, D t,, 0, 0, k r m 3. 2 VRPTW, 3 (1) (2),,, ( ), ( ) (3),,,, ; ;,, 3, 3, 3 k, m ) E ( P) E ( P), tm k = - 1; ( i, j, k, m ) E ( P) E ( P), t m k = 0 (1),, (2),,,, P,,,, i s i, P i ( s m ) ik ik i, (k) d = { d 1, d 2,, d k },,,, P plan,, P; { 0} 0 ; T ; R, R = T D; R 1 ( ), R 1 = R d; V, V = {V 1, V 2,, V m } (m { 0} D ) ; P = { ( i, j, k, m ) ( i, j, k, m ) plan, Π i, jt d, k V, m = D k D }, ( i, j, k, m ) m k ij; f D k D k ; b D k D k, k f D k b D k, k f D k, b D k, D, kd k, D k b D k dspa th = { (D k, b D k, k, m ) Π b D k T d, D k D, k V, m = D k D }; k d k D k dd pa th = ( d k, D k, k, m ) ( d k, D k, k, m ) P, Π d k d, D k D, k V, m = D k D },, ; D k b D k (D k, b D k, k, m ) ( f D k, b D k, k, m ),, P, P = P dspa th dd pa th E ( P) P, E ( P) P, t m k, t m k, kv m m { 0} D ir 1 ( i, j, k, m ) E ( P) E ( P), tm k = 1; ( i, j, 0, ( s m ) ik - s i = 0, Π i d m, k V m, m D (3),, k c k, i c i, x m k = 1m kij 0

4 114 (Journal ofmanagement Sciences) m { 0} D ir 1 kv m c x m k x m k k V V kk m { 0} jr m m { 0} D ir 1 kv m , jc k t m k (1 - x m k ) c i,, ;,,,, ET i i, L T i i, i[ ET i, L T i ];, ET i i, L T i i, i [ ET i, L T i ], 3 (1), L T i > L T i,l T i < s i, i, (2), ET i < ET i,et i > s i, i ET i,,, kt l k k, L T i s i, k T l k, ET i - s i > T l k, (3), k C l k k, i C l k,, g i - g i > C l k, g i i L T i < s i ET i - s i > T l k g i - g i > C l k 4. 2 [14 ],,,,,,,,,,,,,, ;,,,, ( s m ) ik m k i, Π i R, Π k V m, Πm { 0} D, ( lexicographic goal p rogramm ing structure, Lex), m inl ex P 1 : { x m k kv m m { 0} D ir [ ( s m ) ik - s i + w i ] + (1 - x m k ) } (1) P : t m k 2 0, j + P 3 : s. t. k V V kv m { 0} jr m m { 0} D ir 1 kv m (1 - x m k t m k k V m { 0} jr kv V m kv m m { 0} D x m k jr kv m x m k = x m k [ x m k t m k + ) t m k ] (2) 0, jc k + ir 1 [ c x m k t m k + c i (1 - x m k ) ] (3) Φ kr m i = m { 0} D (4) j, d k = 1i = m D, k V m (5) x m k = jt x m k jt kv m x m k m { 0} D ih - x m k ir 1 m { 0} D kv m j, i Φ 1i = m { 0}, k V m (6) Φ 1Π i R (7) x m k m { 0} D kv m hj = 0 Π h R (8) x m k d k, j = 1j = m D, k V m (9) i x m k g ir x m k ji = x m k t j j{ 0} D Φ Q k m { 0} D, k V m (10) j{ 0} D = x m k ir 1 kv m { 0} D m = 0i = m { 0} D, k V m [ ( s m ik ) + t + st i ]j R (11) (12) w i = max(0, ET i - t i ) i R (13) ( s m ) = ET i ET i Ε t i ik i R (14) t i ET i < t i

5 5 : 115 ET i Φ ( s m ) Φ L T ik i i R 1, k V m, Πm { 0} D (15) ( s m ) - s ik i = 0Π i d m, k V m, m D (16) t m k = x m k 1( i, j, m, k) E ( P) E ( P) 0( i, j, m, k) E ( P) E ( P) - 1( i, j, m, k) E ( P) E ( P) { 0, 1} Π i, j R 1, k V m, m { 0} D (17) (18), V Α V ;; w i ; h i j ; ; ; Q k k ; t ij; st i i;, 4. 3, = 1; (1),, (2),, ;, ; (3),, (4) ( ) ; (5), ; (6),, ; (7) (8) ; (9) k d k ; (10) ; (11) ; (12) ; (13) ; (14) (15) ; (16) (k ) d = { d 1, d 2,, d k } 0, ; (17), 4. 3,, VRPTW, VRPTW MDVRPTW MDVRPTW,3 VRPTW, (1) P ; R, R = { 1, 2,, n}; V (V ), q; Q k = q, Π k V ; D = < (2) = 0,= 0,= 0, (3) ( s m ) ik - s i 0 (4),, c i,, VRPTW,c i = 0 MDVRPTW, {0} NM MDVRPTW, (1) P, R, R = { 1, 2,, n}; V (V ) = { K 1, K 2,, K m } (m NM ) ; Q k = q k, q k k, Π k { K 1, K 2,, K m }; D = < (2) = 0,= 0,= 0, (3) ( s m ) - s ik i 0 (4),, c i,, MDVRPTW,c i = 0 ( ), k d { t 1, t 2,, t n }, { t 1, t 2,, t n } ( ) t i, ; g ti t i, ( x ti, y ti ) t i, D t, L T ti t i, ( x k, y k ) k (D k ), LD k k D k, speed, { t 1, t 2,, t n } t i ( x k - x ti ) 2 + ( y k - y ti ) 2 speed Q k + LD k Φ L T ti - D t k { 0} D (19) Ε g ti k { 0} D (20) (19) t i

6 116 (Journal ofmanagement Sciences) , (20) t i [19 ],,, S ort2v a lue, 0,,, S ort2v a lue,,,,,, ;,,, D etim e = max[ ( s m ) ik - L T i, 0 ] ir 1m { 0} D kv m D ecap = max( m { 0} D kv m g i ir x m k - Q k, 0) Tota ld e = D etim e + D ecap (19) (20) t i () C i, C i, Cd i, Cv i t i C i, , [ 1517 ], [ 18, 19 ] VRPTW,,, [ 19 ],,, Tota ld e,, 4, Tota ld e P 1 P 2 P 3,, Tota ld e, P 1, ;,,, N, ind i i, R ( ind i ), [20 ] (1),, F ( ind i ) = [N - R ( ind ) i ]2 N 2 R ( ind i ) R ( ind i ) > 1 = 1 (21) (2),, (1, 2), (1) (G 1, G 2,, G N ), G i, D epot2n um V eh icle2n um S ort2v a lue 3, i D epot2 N um V eh icle2n um, S ort2v a lue, ( ),,, [21 ] (2),,,,,,, (3),,,,, D epot2n um V eh icle2n um S ort2v a lue, (9) (9) k d k,, d k

7 5 : 117 D epot2n um D k V eh icle2n um k S ort2v a lue,,,,, t i, C i C m, t i D epot2n um Cd m,, V eh icle2n um Cv m S ort2v a lue ; C i, S ort2v a lue0 t i S ort2v a lue0, D epot2n um m ({ 0} D ), V eh icle2n um k (V m ) D epot2n um V eh icle2n ums ort2v a lue 6, Matlab, , kg,, ; 1, 1,, VRPTW, [ 19 ]V eh icle2 N um S ort2v a lue, V eh icle2n um S ort2v a lue,, ; V eh icle2n um S ort2v a lue,n = 80, P x = 0. 80, P m = 0. 20, Gen = VRPTW, 1: , 2: , 3: , 4: , , [ 22 ] Table 1 Da ta of D epot and Custom ers x ( km) y ( km) q ( kg) ( h) ( h)

8 118 (Journal ofmanagement Sciences) , 3,, , ,, 2 2 Table 2 Changes of T im e W indows and D elivery W e ight of Custom ers [ 96, 166 ] [ 9, 79 ] [ 74, 174 ] [ 56, 156 ] [ 10, 54 ] [ 20, 70 ] ,,, , ,, ,, , 4 14,, 3,, , , , , , , ,,, MDVRPTW,, , , , , , , , , N = 80, P x = 0. 80, P m = 0. 07, Gen = 500 = 5, k c k 2010, , , , , , (1) 3,, ;,, (2) VRPTW,,,,,,,, ;, VRPTW, P x 0. 80, P m 0. 20, 3 Table 3 Com para tive Results of D isruption M anagem en t, Scheduling Accord ing to the O r ig ina l One and Rescheduling ( % ) ( % )

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