Comparison Analysis of Two Heterogeneous Multi-temperature Fleet Vehicle Routing Problems

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1 Comparison Analysis of Two Heterogeneous Multi-temperature Fleet Vehicle Routing Problems M

5 (60) (18~25) (-2~7) (-18) Vehicle Routing Problem, VRP (Heterogeneous Multi-temperature Fleet Vehicle Routing Problem, HMFVRP) Solomon VRPTW Taillard VRP 168 HMFVRP 72% 50% N3 N4( ) HMFVRP1 N3-1 HMFVRP2 N3-5 ( ) ( ) HMFVRP2 HMFVRP1 HMFVRP2 i

6 Comparison Analysis of Two Heterogeneous Multi-temperature Fleet Vehicle Routing Problems Student: Ya-Wen Hsu Advisor: Dr. Yuh-Jen Cho Abstract Recently, the demand of the cold logistics/chain and the multi-temperature distribution has rapidly grown. Carriers must deliver goods with different temperate, such as hot food (over 60 ), normal temperature good (18~25 ), refrigeration food (-2~7 ) and frozen food (under -18 ), to customers. How to distribute multi-temperate goods at the same time and with lower cost becomes an interesting research issue. This thesis considers two special operational situations: first, carriers utilize the engine-driven frozen truck divided into three parts to hold different temperate goods, and second, carriers utilize the multi-temperature storage box to hold different temperate goods in a general truck. We transfer the previous situations into two Heterogeneous Multi-temperature Fleet Vehicle Routing Problems, HMFVRP1 and HMFVRP2. Then, we also develop a simple heuristic algorithm to solve these HMFVRPs. This heuristic algorithm firstly applies a modified Farthest-start Nearest Neighbor (FNN) method to construct an initial solution, and then improves the initial solution by sequentially executing 2_opt, Or_opt, 1_0, and 1_1 neighborhood searches. A bank of 168 instances created by modifying the Solomon s VRPTW benchmark instances, Taillard s VRP benchmark instances and Homberger s VRP benchmark instances is used to compare the performance of HMFVRP1 and HMFVRP2. Furthermore, real costs and capacities of different size of trucks are set for these test instances. Experimental results present that, in average, HMFVRP2 performs well than HMFVRP1 in both of fleet size and traveling distance. Such a finding maybe offers an alternative to improve the performance of practical multi-temperate distribution. Keywords: Cold Logistics; Heterogeneous Multi-temperature Fleet Vehicle Routing Problem (HMFVRP); Heuristic method. ii

7 95 7 iii

8 ...i Abstract...ii...iii... iv... vi...vii...vii HMFVRP HMFVRP HMFVRP HMFVRP iv

9 HMFVRP HMFVRP v

10 HMFVRP (2-OPT) (Or-OPT) (1-0) (1-1) HMFVRP1 HMFVRP HMFVRP1 HMFVRP HMFVRP HMFVRP vi

11 () VRP VRP () () HMFVRP HMFVRP (24 ) HMFVRP HMFVRP1 () HMFVRP HMFVRP2 () HMFVRP1 HMFVRP HMFVRP1 HMFVRP HMFVRP1 HMFVRP HMFVRP1 HMFVRP vii

12 1.1 (Cold Chain)3T (Time) (Temperature) (Tolerance)3T

13 10 ( ) 1,400 ~ 1, ,938 40,849 35, , ,969 29,415 39, , ,830 35,851 40, , ,821 38,540 41, , ,366 42,012 47, , ,176 18,427 20,893 23,249 11,259 35, , ,356 19,881 24,907 26,949 12,373 37, , ,350 21,671 29,682 32,459 12,875 42, , ,563 22,716 35,393 38,801 13,262 60, , ,828 22,885 38,009 45,571 13,823 82, ,345 ITIS 1415 (60) ( ) ( 18) (0~+7) (-2~+2) (-18 ) (-30 ) 1.3 2

14 ~+7-2~ ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1415 WTO 14 ( ) ( ) (0~5) (-18~-25) 3

15 ( ) ( 35 ~40 ) (0~5) (-18~-25) ( ) () ()

16 1.4 () ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1415 Starbucks IS ~

17 1.2 (Vehicle Routing ProblemVRP) (Heterogeneous Multi-temperature Fleet Vehicle Routing Problem, HMFVRP) (Vehicle Routing Problem) 1.3 HMFVRP C# 6

18 HMFVRP ( ) Solomon25 VRPTW HMFVRP C# 7

19 1.2 8

20 (Heterogeneous Multi-temperature Fleet Vehicle Routing Problem, HMFVRP) (Vehicle Routing Related Problems, VRRP) (Vehicle Routing Problem, VRP) ( )

21 VRP( ) 18 Minimze N N M i= 0 j= 0 k= 1 N M C x k ij ij (2.1) k subject to x = 1 ( j = 1, K, N ) (2.2) i= 0 k= 1 N M j = 0 k = 1 N i = 0 x x ij ( i = 1, K N ) k ij = 1, N k k ih xhj = 0, j = 0 ( h = 0, K, N; k = 1, K M ) (2.3) (2.4) N d i x ij Q, j 0 N i = 0 = N j= 1 N i= 1 x x y y ( k = 1, K M ) ( k = 1, M ) k 0 j 1 K, ( k = 1, M ) k i 0 1 K, M k i j + N xij N 1, k = 1 ( i j = 1, KK N ) (2.5) (2.6) (2.7) (2.8) x k ij = 0 or 1 for all i, j, k (2.9) k k xij k ( i, j) xij = 1 k k i j xij = 0c ij ( i, j) d i i N 0 Q M ( ) (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) (2.7) (2.8) (2.9) Bodin et al.20 VRP (Cluster First-Route Second) (Route First-Cluster Second) 10

22 (SavingsInsertion) (Exchange for Improvement) ( ), 2-opt3-optOr-opt (Mathematical-Programming Based) (Interactive Optimization) (Branch and Bound) (Branch and Cut) (Column Generation)

23 2.1 ( ) Nearest Neighbor Farthest Neighbor K 2 3 K-opt K 3-Opt p=3 p=2 Or-opt p=1 Christofides & Eilon

24 2.1.2 (VRP with Time Windows, VRPTW) ( ) ( ) (Multi-Depot VRP, MDVRP) VRP VRP (Traveling Salesman Problem, TSP) (Vehicle Routing Problem, VRP) / (Heterogeneous Fleet VRP, HVRP) (Periodic VRP, PVRP) (VRP with Time Windows, VRPTW) / / 13

25 2.2 VRP () (VRP with Backhauls, VRPB) (Multi-Depot VRP, MDVRP) (Dynamic DVRP) VRP, ( ) / / / 7 Golden 24 X X k =1 k i,j X k =0 k ij ij r i i N = 1,2,..., N, N 0 N { } T { 1,2,..., T, } T = T T C ij i,j k C k q j j k Q k k 1,..., T 1 2 C < C <... < C 1 2 = Q < Q <... < T ij T Q 14

26 24 Minimze T N k= 1 j= 1 T N C k X k oj + T N N k = 1 i= 0 j= 0 C. X (2.10) k subject to X = 1 j N k = 0 i= 0 ij N N k X ih i= 0 j= 0 X k hj = 0 ij k ij j N, k T (2.11) (2.12) r = 0 0 (2.13) r r j j r X k ij i T k= 1 i= 0 K ( q j + Qk ) X ijk Qk i 0 + N, j N N Q k X k ij k = 1 j N {,1} i, j N k T (2.14) (2.15) 0, (2.16) (2.10) (2.11) (2.12) (2.13) (2.14) (Sub-tour Breaking) (2.15) (2.16) Tarantitlis & Kiranoudis 31 HFFVRP(Heterogeneous fixed fleet vehicle routing problem) 32 OMDVRP (Open Mulit-Depot Vehicle Routing Problem) (Threshold Accepting AlgorithmTA) BATA(Backtracking Adaptive Threshold Accepting Algorithm) LBTA(The List Based Threshold Accepting method) 3334 Filip Ghetsens & Bruce Golden23 FSCVRP(The fleet size and composition vehicle routing problem) (lower bound procedure) (two-stage heuristic) ( ) 1 Salhi & Rand29 VFMVRCVehicle Fleet Mix Vehicle Routing Composition Problem (Perturbation 15

27 Procedures) VRP VRP SRP Reduction ReallocationCombiningSharingSwappingRelax/CombineRelax/Share Reduction Reallocation Combining Sharing Swapping Relax/Combine Relax/Share Relax/Redu* Relax/Real* Relax/Swap* 29 Luiz S Ochi27 Scatter Search( ) Gendreau22 Tabu Search GENIUS GENIUS (Adaptive Memory Procedure) (Aspiration Criterion) Tabu Search Golden Wassan, N.A.& Osman, I.H.35 Tabu Search (The mix fleet vehicle routing problem) MFVRP Tabu Search MFVRP (reactive tabu search concepts) (variable neighborhood) (special data memory structures) (hashing function) 16

28 (Tabu List) (Aspiration Level) (Candidate List) (Stopping Criterion) (variable neighbourhoods searchvns) intensification diversification Golden et al Taillard Liu, F-H, Shen, S-Y26 (The fleet size and mix vehicle routing problem) FSMVRP Clarke and Wright (Saving Method) (cheapest insertion method) (insertion-based savings heuristics) (VRPTW) (time and capacity feasibility conditions) 168 Dullaert, W.21 The fleet size and mix vehicle routing problem FSMVRP Solomon 1987 Golden et al 1984 Clarke and Wright 17

29 Saving Method CSCombined Savings OOSOptimistic Opportunity SavingsROSRealistic Opportunity Savings ACSAdapt Combined SavingsAOOSAdapt Optimistic Opportunity SavingsAROSAdapt Realistic Opportunity Savings F-H LiuS-Y Shen 1999 Solomon Koo, Pyung Hoi25 Tabu Search VRP Renaud, J. & Boctor, Fayez F.28 VRP (The fleet size and mix vehicle routing problem) FSMVRP petal method 5 Order( )1-petal( )2-petal( )Petals Selection( ) Improvement( ) Tabu Search FSMVRP Fleet Size and Mixed Vehicle Routing Problem Bruce Gloden (MGT+OrOPT) Salhi & Rand MGORSR MGSROR MGT( ) OrOPT Salhi & Rand

30 17 FSMVRP Fleet Size and Mixed Vehicle Routing Problem 7 Generic Intensification and Diversification Search, GIDS HVRP MIC Weighted Initialization, WI Neighborhood Search, NS GSI G1 G2 Generic Search PSD Cost Perturbation, CP Filip Ghetsens & Bruce Golden23 Salhi & Rand 29 FSCVRP VFMVRC FSMVRP 1998 Luiz S Ochi 27 (MGT+OrOPT)(Bruce Gloden) (Salhi & Rand) HFVRP FSMVRP Tabu Search 1999 Gendreau22 HFVRP Liu, F-H & Shen, S-Y26 FSMVRP Tarantitlis & Kiranoudis 31 HFFVRP GENIUS Tabu Search Insertion-based savings heuristics BATA HVRP GIDS Wassan,N.A. & Osman, I.H. 35 Tarantitlis & Kiranoudis 32 MFVRP OMDVRP Tabu Search VNS LBTA 19

31 2.4 () 2002 Dullaert, W. 21 FSMVRP 2002 Renaud, J. & Boctor, Fayez F.28 FSMVRP Sweep-based algorithm Petal method 2003 Tarantitlis & Kiranoudis 33 HFFVRP LBTA 2004 Tarantitlis & Kiranoudis 34 HFFVRP BATA 2004 Koo, Pyung Hoi25 FSVRP Tabu Search (Multi-temperature Storage Box) Multi-temperature Storage Box Vehicle Routing Problem(MSBVRP) 2-OPT MSBVRP 6 M M = {1, 2,, m} m N N = {0, 1, 2,, n} 0 1~n V V = {1, 2,, v} v c ij i j hi d i h f g 20

32 p q x ijk = 1 k i j y hk k h z i 6 Minimize f n n v j= 1 k= 1 m v h= 1 k= 1 n n v x0 jk + g yhk + cij xijk (2.17) i= 0 j= 0 k= 1 Subject to x0 jk 1 k V (2.18) j= 1 n n x ijk x jik j= 0 j= 0 n v x ijk j= 0 k= 1 = 1 = 0 i Nk, V i N \{0} (2.19) (2.20) n d n x hi ijk i= 1 j= 0 m h=1 y hk p q y hk 0 h M, k V k V (2.21) (2.22) z z + n x n 1 i& j N \{0}, k V (2.23) i j ijk x ijk + = 0 or1, y I, z 0 h M, i & j N, k V (2.24) hk i (2.17) (2.18)(2.19) (2.20) (2.21) (2.22) (2.23) (2.24) Tarantitlis & Kiranoudis ( ) Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP) Back-tracking adaptive threshold accepting (BATA) BATA 21

33 Open Mulit-Depot Vehicle Routing Problem (OMDVRP) The List Base Threshold Accepting (LBTA) LBTA VRPTW 4 9 (Stochastic Vehicle Routing Problem with Time Windows, SVRPTW) (VRPTW)

34 DVRP VRPTW VRPTW Tarantitlis & Kiranoudis31 HFFVRP Tarantitlis & Kiranoudis32 OMDVRP BATA LBTA SVRPTW MSBVRP (MFVRP) (VRPTW) 6 (MFVRP) MSBVRP (MFVRP) 23

35 HMFVRP1 HMFVRP2 3.1 (Heterogeneous Multi-temperature Fleet Vehicle Routing Problem, HMFVRP) VRP VRP HMFVRP N HMFVRP1 HMFVRP2 24

36 3.1.1 HMFVRP1 3.1 Frozen foods Chilled products General goods

37 3.1.2 HMFVRP2 3.2 G C F General goods Chilled products Frozen foods

38 VRP VRP HMFVRP HMFVRP HMFVRP1 HMFVRP

39 (Intra-route arc exchange) (Inter-route node exchange) 4.1 VRP NP-Hard (Farthest Neighbor) HMFVRP OPT Or-OPT OPT Or-OPT 4.1 HMFVRP 4.2 (Sequential) Farthest Neighbor 28

40 HMFVRP HMFVRP2 29

41 OPT Or-OPT (Selection strategy) Best First () 2-OPT 2-OPT OPT (a) (1,2)(3,4) (1,3)(2,4) (2,3) (b) Depot (a) Depot (b) 4.3 (2-OPT) () Or-OPT Or-OPT 4.4 Or-OPT p=3 p=2 p=1 Or-OPT 30

42 (p=1) (p=2) Depot (a) 3 4 Depot (b) Depot Depot (p=3) (a) (b) Depot Depot (a) (b) 4.4 (Or-OPT) 31

43 () (1-0) (a) A 3 B 8 5 B (b) B 5 B A 4 7 A Depot Depot (a) (B) 4.5 (1-0) () (1-1) (a) A 3 B 8 A B (b) B 5 B A 4 7 A Depot (a) Depot (b) 4.6 (1-1) 32

44 Solomon HMFVRP HMFVRP1 HMFVRP2 5.1 HMFVRP The VRP Web34 VRP Solomon(1983) VRPTW Taillard VRP Homberger VRP Solomon C ( )R ( ) RC ( ) C R RC 100Taillard VRP Homberger VRP (1) (2) (3) (4)

45 C R RC C

46 HMFVRP 5.5 HMFVRP ( ) 42 ( ) HMFVRP OPT Or-OPT = x 100% 5.7 (24 ) N1-1:Or_OPT+1_0+1_1 N3-1:1_1+Or_OPT+2_OPT N1-2:Or_OPT+1_1+1_0 N3-2:1_1+2_OPT+Or_OPT N1 N3 N1-3:1_1+Or_OPT+1_0 N3-3:Or_OPT+1_1+2_OPT 2_OPT 1_0 N1-4:1_1+1_0+Or_OPT N3-4:Or_OPT+2_OPT+1_1 N1-5:1_0+Or_OPT+1_1 N3-5:2_OPT+1_1+Or_OPT N1-6:1_0+1_1+Or_OPT N3-6:2_OPT+Or_OPT+1_1 N2-1:1_0+1_1+2_OPT N4-1:1_0+Or_OPT+2_OPT N2-2:1_0+2_OPT+1_1 N4-2:1_0+2_OPT+Or_OPT N2 N4 N2-3:1_1+1_0+2_OPT N4-3:Or_OPT+1_0+2_OPT Or_OPT 1_1 N2-4:1_1+2_OPT+1_0 N4-4:Or_OPT+2_OPT+1_0 N2-5:2_OPT+1_0+1_1 N4-5:2_OPT+1_0+Or_OPT N2-6:2_OPT+1_1+1_0 N4-6:2_OPT+Or_OPT+1_0 35

47 4 Solomon VRPTW Taillard VRP Homberger VRP ( )HMFVRP1 HMFVRP ( ) _OPT Or_OPT 1_0 1_1 24 2_OPT 2_OPT 1_0 1_0 1_1 Or_OPT ( ) ( ) HMFVRP1 (%) (%) 2_OPT+Or_OPT+1_0+1_ _OPT+Or_OPT+1_1+1_ _OPT+1_1+Or_OPT+1_ _OPT+1_1+1_0+Or_OPT _OPT+1_0+Or_OPT+1_ _OPT+1_0+1_1+Or_OPT Or_OPT+1_0+1_1+2_OPT

48 5.8 HMFVRP1 () Or_OPT+1_0+2_OPT+1_ Or_OPT+1_1+1_0+2_OPT Or_OPT+1_1+2_OPT+1_ Or_OPT+2_OPT+1_0+1_ Or_OPT+2_OPT+1_1+1_ _0+1_1+Or_OPT+2_OPT _0+1_1+2_OPT+Or_OPT _0+Or_OPT+1_1+2_OPT _0+Or_OPT+2_OPT+1_ _0+2_OPT+1_1+Or_OPT _0+2_OPT+Or_OPT+1_ _1+1_0+Or_OPT+2_OPT _1+1_0+2_OPT+Or_OPT _1+Or_OPT+1_0+2_OPT _1+Or_OPT+2_OPT+1_ _1+2_OPT+1_0+Or_OPT _1+2_OPT+Or_OPT+1_ HMFVRP2 (%) (%) 2_OPT+Or_OPT+1_0+1_ _OPT+Or_OPT+1_1+1_ _OPT+1_1+Or_OPT+1_ _OPT+1_1+1_0+Or_OPT _OPT+1_0+Or_OPT+1_ _OPT+1_0+1_1+Or_OPT Or_OPT+1_0+1_1+2_OPT Or_OPT+1_0+2_OPT+1_ Or_OPT+1_1+1_0+2_OPT Or_OPT+1_1+2_OPT+1_ Or_OPT+2_OPT+1_0+1_ Or_OPT+2_OPT+1_1+1_ _0+1_1+Or_OPT+2_OPT

49 5.9 HMFVRP2 () 1_0+1_1+2_OPT+Or_OPT _0+Or_OPT+1_1+2_OPT _0+Or_OPT+2_OPT+1_ _0+2_OPT+1_1+Or_OPT _0+2_OPT+Or_OPT+1_ _1+1_0+Or_OPT+2_OPT _1+1_0+2_OPT+Or_OPT _1+Or_OPT+1_0+2_OPT _1+Or_OPT+2_OPT+1_ _1+2_OPT+1_0+Or_OPT _1+2_OPT+Or_OPT+1_ ( ) HMFVRP1 HMFVRP1 ( ) HMFVRP % 50% N3 N4( ) HMFVRP1 N3-1(1_0+1_1+Or_OPT+2_OPT) HMFVRP2 N3-5(1_0+2_OPT+1_1+Or_OPT) ( ) HMFVRP1 HMFVRP1 ( ) (N3 N4) 38

50 (N1 N2) 5.1 HMFVRP1 HMFVRP2 HMFVRP1 N3-1(1_0+1_1+Or_OPT+2_OPT) HMFVRP2 N3-5(1_0+2_OPT+1_1+Or_OPT) 5.1 HMFVRP1 HMFVRP2 5.2 HMFVRP1 HMFVRP2 39

51 5.3 HMFVRP1 5.4 HMFVRP Z α= 0.05HMFVRP1( ) HMFVRP2() ( ) Z Z HMFVRP2 40

52 5.10 HMFVRP1 HMFVRP2 (HMFVRP1HMFVRP2) Z Z Z HMFVRP HMFVRP1 HMFVRP2 (HMFVRP1HMFVRP2) Z Z Z HMFVRP HMFVRP1 HMFVRP2 (HMFVRP1HMFVRP2) Z Z Z HMFVRP HMFVRP1 HMFVRP2 (HMFVRP1HMFVRP2) Z ( ) ( ) HMFVRP2 HMFVRP1 HMFVRP2 41

53 6.1 HMFVRP HMFVRP SolomonTaillard Homberger HMFVRP1 HMFVRP2 HMFVRP HMFVRP1 HMFVRP2 VRP HMFVRP2 HMFVRP1 ( ) ( ) HMFVRP2 HMFVRP1 HMFVRP2 HMFVRP1 HMFVRP2 HMFVRP1 HMFVRP2 HMFVRP1 HMFVRP 72% 50% N3 N4 42

54 N3 N4( ) HMFVRP1 N3-1(1_0+1_1+Or_OPT+2_OPT) HMFVRP2 N3-5(1_0+2_OPT+1_1+Or_OPT) ( ) (HMFVRP) HMFVRP2 HMFVRP1 HMFVRP (Heterogeneous Multi-temperature Fleet Vehicle Routing Problem, HMFVRP) 6.2 HMFVRP HMFVRP HMFVRP (2-OPT Or-OPT ) ( ) Starbucks HMFVRP2 43

55 HMFVRP1 HMFVRP1 44

56 1. IEK (2004) 2. (2000) 3. (2001) 4. (2005) (2003) 6. (2003) 7. (2001) 8. (2005) 9. (2003) 10. (2004) (2004) IEK 12. (2005) 13. (1998) 14. (2002) st century Logistics (2004) - () (2004) - () (1994) 18. (1998) 19 (2001) TSP VRP (2001) 45

57 21. Bodin, L., Golden, B.L., Assad, A. and Ball, M. (1983), Routing and schedule of vehicle and crew: the state of art, Computers and Operations Research, Vol. 10, No. 2, pp Dullaert, W., Janssens, GK., Sorensen, K., and Vernimmen, B. (2002), New heuristics for the Fleet Size and Mix Vehicle Routing Problem With Time Window Journal of the Operational Research Society, Vol 53, pp Gendreau, M., Laporte, G., Musaraganyi, C., and Taillard, E.D. (1999), A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers & Operations Research, Vol 26, pp Ghetsens, Filip, Golden, Bruce, and Assad, Arjang (1986), A new heuristic for determining fleet size and composition Mathematical Programming Studies,Vol.26,pp Golden, B.L., Assad, A., Levy, L., and Gheysens, F.G. (1984), The Fleet Size and Mix Vehicle Routing Problem, Computers & Operations Research, Vol.11, pp Koo, Pyung Hoi, Lee, Woon Seek, Jang, and Dong Won, (2004), Fleet sizing and vehicle routing for containet transportation in a static environment OR Spectrum, Vol.26, pp Liu, F-H, Shen, S-Y (1999), The fleet size and mix vehicle routing problem with time window Journal of the Operational Research Society, Vol.50, pp.721-pp Ochi, Luiz S., Vianna, Dalessandro S., Drummond, Lucia M., Andre, A. and Victor, O. (1998), A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet Future Generation Computer System, Vol.14, pp.285-pp Renaud, Jacques and Boctor, Fayez F. (2002), A sweep-based algorithm for the fleet size and mix vehicle routing problem European Journal of Operation Research, Vol.140, pp Salhi, S. and G..K. Rand (1993), "Incorporating Vehicle Routing into the Vehicle Fleet Composition Problem," European Journal of Operational Research, Vol.66, pp Solomon, M.M. (1983), Vehicle routing and Scheduling with Time Window ConstraintsModels and Algorithms, Ph.D. Dissertation, Dept. of Decision Sciences, University of Pennsylvania. 32. Tarantilis,C.D and. Kiranoudis, C.T. (2001), A meta-heuristic algorithm for the efficient distribution of perishable food, Journal of Food 46

58 Engineering, Vol.50, pp Tarantilis,C.D.and Kiranoudis, C.T. (2002), Dstribution of Fresh Meat Journal of food engineering, Vol.51, pp Tarantilis, C.D., Kiranoudis, C.T., and V.S. Vassiliadis (2003), A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem Journal of the operational research society, Vol.54, pp Tarantilis, C.D., Kiranoudis, C.T., and V.S. Vassiliadis (2004), A threshold acceptin metaheuristic for the heterogeneous fixed fleet vehicle routing problem European Journal of Operation Research, Vol.152, pp

59 HMFVRP1 TMHMFVRP2 MSB HMFVRP1 TM (1) TM-H TM HMFVRP1 H Homberger (2) TM-S100-C TM HMFVRP1 S Solomon 100 C101 C (3) TM-T TM HMFVRP1 T Taillard (1) TM-H TM HMFVRP1 H Homberger Solomon C (2) TM-S100-C TM HMFVRP1 S Solomon 100 C101 C Solomon R (3) TM-T TM HMFVRP1 T Taillard Solomon RC (1) TM-H TM HMFVRP1 H Homberger %80% (2) TM-S100-C TM HMFVRP1 S Solomon 100 C101 C %70% (3) TM-T TM HMFVRP1 T Taillard %60% 48

60 (1) TM-H TM HMFVRP1 H Homberger %20% (2) TM-S100-C TM HMFVRP1 S Solomon 100 C101 C %30% (3) TM-T TM HMFVRP1 T Taillard %40% 49

61 HMFVRP1 (1) 80 TM-S100-R TM-S100-R N

62 (2) 80 TM-S100-R TM-S100-R N

63 (3) 80 TM-S100-R TM-S100-R N

64 (4) 80 TM-S100-R TM-S100-R N

65 HMFVRP2 (1) 80 MSB-S100-R MSB-S100-R N

66 (2) 80 MSB-S100-R MSB-S100-R N

67 (3) 80 MSB-S100-R MSB-S100-R N

68 (4) 80 MSB-S100-R MSB-S100-R N

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