21 5 2 0 0 810 JOURNAL OF MANAGEM ENT SC IENCES Vol. 21 No. 5 October, 2 0 0 8,,,116023 :,,, ;,, VRPTW MD2 VRPTW MDVRPTW ;,,;,, : ; ; ; ; ; : C93 : A : 1672-0334 (2008) 05-0111 - 10 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 116023, 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 : 2008-05 - 21 : 2008-08 - 30 : (70671014, 70571009) ; (70725004) : (1962 - ),,,,,, : E2mail: wxp@ dlut. edu. cn
112 (Journal ofmanagement Sciences) 200810 1,,,,,,,, 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 3. 1, 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
5 : 113 0 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
114 (Journal ofmanagement Sciences) 200810 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 4 4. 1 0, 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 : 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 5 5. 1 = 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
116 (Journal ofmanagement Sciences) 200810, (20) t i [19 ],,, S ort2v a lue, 0,,, S ort2v a lue,,,,,, ;,,, 5. 2. 2 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, 5. 2 5. 2. 1, [ 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), 5. 2. 3 (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) 5. 2. 4 (9) k d k,, d k
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, 6. 1 7, 5 10 3 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 = 500 10 VRPTW, 1: 0-8 - 2-11 - 1-4 - 0, 2: 0-10 - 5-13 - 0, 3: 0-9 - 7-6 - 0, 4: 0-3 - 14-12 - 15-0, 585. 19, [ 22 ] 585. 77 1 Table 1 Da ta of D epot and Custom ers x ( km) y ( km) q ( kg) ( h) ( h) 0 50 50 0 0 + 1 19 0 1. 00 10 3 74 144 2 33 3 1. 80 10 3 58 128 3 35 21 1. 10 10 3 15 85 4 53 19 0. 60 10 3 96 166 5 70 94 1. 90 10 3 47 117 6 27 44 1. 40 10 3 85 155 7 10 69 1. 20 10 3 21 91 8 56 4 0. 20 10 3 9 79 9 16 81 1. 70 10 3 37 107 10 68 76 0. 80 10 3 21 121 11 41 10 0. 90 10 3 74 174 12 83 43 0. 80 10 3 58 158 13 25 91 1. 90 10 3 15 125 14 73 29 1. 60 10 3 56 156 15 70 18 0. 90 10 3 87 187
118 (Journal ofmanagement Sciences) 200810 6. 2, 3,, 32. 65, 4 8 11 14,, 2 2 Table 2 Changes of T im e W indows and D elivery W e ight of Custom ers 4 8 11 14 [ 96, 166 ] [ 9, 79 ] [ 74, 174 ] [ 56, 156 ] 0. 60 0. 20 0. 90 1. 80 [ 10, 54 ] [ 20, 70 ] 1. 60 1. 40 1. 90 6. 3,,, 0-3 - 14-12 - 15-0 3,0-10 - 5-13 - 0 10,, 1 2 3 4,, 4 8 11, 4 14,, 3,, 1-8 - 2-0 - 1, 0-11 - 1-0, 0-4 - 0, 2-5 - 13-0 - 2, 3-9 - 7-6 - 0-3, 0-14 - 0, 4-12 - 15-0 - 4 6. 4,,, MDVRPTW,, 1-4 - 8-15 - 0-1, 2-0 - 2, 3-13 - 9-7 - 0-3, 4-5 - 0-4, 0-1 - 2-11 - 0, 0-6 - 0, 0-14 - 12-0, 169 6. 5, N = 80, P x = 0. 80, P m = 0. 07, Gen = 500 = 5, k c k 2010, 1-4 - 8-0 - 1, 2-5 - 13-0 - 2, 3-9 - 7-6 - 0-3, 4-12 - 15-11 - 0-4, 0-14 - 2-1 - 0, 189 3 6. 6 (1) 3,, ;,, (2) VRPTW,,,,,,,, 5. 2. 4 ;, 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 805. 04 20 149. 83 7 605. 70 31 276. 38 7 611. 22 14 136. 06 5 ( % ) 24 30 9 29 ( % ) - 1 55 51 29
5 : 119, P x 0. 80, P m 0. 07,,, 7,,,,,,,,,, VRPTW MDVRPTW MDVRPTW,,,, ;,,,,,,,,, : [ 1 ] D ror M, Powell W B. Stochastic and Dynam ic Models in Transportation [ J ]. Operations Research, 1993, 41 (1) : 11-14. [ 2 ] Huisman D, Freling R, W agelmans A. A Robust So2 lution App roach to the Dynam ic Vehicle Scheduling Problem [ J ]. Transportation Science, 2004, 38 ( 4 ) : 447-458. [ 3 ] L i J ing2quan, Denis Borenstein, Pitu B M irchandani. A Decision Support System for the Single 2depot Ve2 hicle Rescheduling Problem [ J ]. Computers & Oper2 ations Research, 2007, 34 (4) : 1008-1032. [ 4 ]. [ D ]. :, 2005. Zhang Y H. Study of Commerical Vehicle Emergent D ispatch [ D ]. Being: Being University of Technol2 ogy, 2005. ( in Chinese) [ 5 ],,. [ J ]., 2007, 21 (4) : 114-118. Zhong S Q, Du G, He G G. Study on U rgency Vehi2 cle Scheduling Problem with the Changes of Time W indows and Delivery W eight of Customers [ J ]. Journal of Industrial Engineering and Engineering Management, 2007, 21 (4) : 114-118. ( in Chinese) [ 6 ] Yu G, A rguello M, Song M, McMowan S, W hite A. A New Era for Crew Recovery at Continental A irline [ J ]. Interfaces, 2003, 33 (1) : 5-22. [ 7 ] W u Cheng2Lung. Inherent Delays and Operational Reliability of A irline Schedules [ J ]. Journal of A ir Transport Management, 2005, 11 ( 4) : 273-282. [ 8 ] C W alker, J Snowdon, D Ryan. Simultaneous D isrup2 tion Recovery of a Train Timetable and Crew Roster in Real Time [ J ]. Computers and Operations Re2 search, 2005, 32 (8) : 2077-2094. [ 9 ] Portougal V ictora, Trietsch Dan. Setting Due Dates in a Stochastic Single Machine Environment [ J ]. Com2 puters & Operations Research, 2006, 33 ( 6 ) : 1681-1694. [ 10 ],,. [ J ]., 2005, 25 ( 7) : 9-16. Yu H, Chen J, Yu G. How to Coordinate Supp ly Chain under D isrup tions [ J ]. System s Engineering Theory & Practice, 2005, 25 (7) : 9-16. ( in Chinese) [ 11 ] Stn Van de Vonder, Erik Demeulemeester, W illy Herroelen, Roel Leus. The U se of Buffers in Project M anagement: The Trade 2off between Stability and M akespan [ J ]. International Journal of Production E2 conom ics, 2005, 97 (2) : 227-240. [ 12 ]. [ D ]. :, 2007. Zhang Y. D isrup tion Management Model of Delaying Problem in Logistics D istribution [ D ]. Dalian: Dalian University of Technology, 2007. ( in Chinese) [ 13 ],,. VRPTW TABU SEARCH [ J ]., 2006, 26 (2) : 231-236. W ang M C, Gao C X, Zeng Y T. Recovery of the VRPTW D isrup tion and the Tabu Search A lgorithm [ J ]. Journal of Mathematics, 2006, 26 ( 2 ) : 231-236. ( in Chinese) [ 14 ] Yu Gang, Xiangtong Q i. D isrup tion Management: Frame2 work, Models and App lications[m ]. Singapore: World Scientific Publishing Co. Pte. L td., 2004. [ 15 ] Tan K, Lee T, Ou K, Lee L H. A Messy Genetic A l2 gorithm for the Vehicle Routing Problem with Time W indow Constraints [ C ] Proceedings of IEEE Con2
120 (Journal ofmanagement Sciences) 200810 gress on Evolutionary Computation. South Korea, 2001: 679-686. [ 16 ],,. [ J ]., 2001, 36 (2) : 211-213. Xie B L, L i J, L iu J X. A Heuristic Genetic A lgo2 rithm for the Travelling Salesman Problem with Time Restraints [ J ]. Journal of Southwest J iaotong Univer2 sity, 2001, 36 (2) : 211-213. ( in Chinese) [ 17 ] Hwang H S. An Imp roved Model for Vehicle Routing Problem with Time Constraint Based on Genetic A l2 gorithm [ J ]. Computers & Industrial Engineering, 2002, 42 (224) : 361-369. [ 18 ] Baker B, Ayechew M. A Genetic A lgorithm for the Vehicle Routing Problem [ J ]. Computers and Opera2 tions Research, 2003, 30 (5) : 787-800. [ 19 ],,,. [ J ]., 2004, 40 (21) : 82-83. Zou T, L i N, Sun D B, L i J. Genetic A lgorithm for M ultip le 2depot Vehicle Routing Problem [ J ]. Com2 puter Engineering and App lications, 2004, 40 ( 21) : 82-83. ( in Chinese) [ 20 ],,. [ J ]., 2003, 34 ( 7) : 64-69. You J J, J i C M, Fu X. New Method for Solving M ulti2objective Problem Based on Genetic A lgorithm [ J ]. Journal of Hydraulic Engineering, 2003, 34 (7) : 64-69. ( in Chinese) [ 21 ]. MATLAB [ M ]. :, 2005. Lei Y J. MATLAB Genetic A lgorithm Toolbox and Ap2 p lication [M ]. Xi an: Xidian University Press, 2005. ( in Chinese) [ 22 ]. [ D ]. :, 2004. Zhong S Q. Study on Intelligent A lgorithm for Vehicle Scheduling in Logistics D istribution [ D ]. Tianjin University, 2004. ( in Chinese) Tianjin: B iography:wang Xu2p ing is an associate p rofessor in Insti2 tute of System Engineering at Dalian University of Technolo2 gy. H is research areas include electronic commerce and logis2 tics management, information system s integration, etc.,, 2009 ;;; ;,, ( IE),,,,,IE,,,, 1996, 120, A4,,12/,72, 10 /, 60, 4-585,,, : 1954 806 : 200030 : / : 0086-21 - 62933226 E - ma il: qdx2@ yahoo. com. cn http: / / jiem. net,, : 2009,,,,