online supplement to ‘methods for strategic liner shipping … · 2017. 6. 27. · online...
TRANSCRIPT
Online supplement to ‘Methods for strategic liner shippingnetwork design’
Judith Muldera,∗, Rommert Dekkera
aEconometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, P.O. Box 1738,3000 DR Rotterdam, Netherlands
Appendix A. Data
Ports
The ports considered in this study are obtained by merging all routes in the Asia-Europe trade lane of Maersk during spring 2010. Port Los Angeles is removed from thelist, because it is not on the Asia-Europe trade lane. The 58 remaining ports, countriesand regions can be found in natural order in Table A.1.
Distance
The distances between ports can be computed using distance calculators on the inter-net. The distances between the port combinations can be found in Table A.2.
Demand
In the cargo routing model it is important to know the demand between two ports.However, it is hard to achieve realistic data on the demand. The demand data is obtainedfrom Lachner & Boskamp (2011). First, they determine total demand to be allocated onthe Asia-Europe trade lane. This is done using annual reports of Maersk. Furthermore, agrowth percentage is included in the calculation and corrections are made for joint services.Thereafter, the total demand is divided over port combinations using port throughput.The port throughput of both the origin and the destination port is used to determine thedemand of a port combination. The demand that is generated in this way can be foundin Table A.4.
Revenue
The revenue data is also obtained from Lachner & Boskamp (2011). It is assumed thatthe revenue per unit only depends on the distance between the origin and destination portof the demand and on the direction in which the demand has to be transported. Thereto,
∗Corresponding author, e-mail address: [email protected]
Preprint submitted to Elsevier 29th April 2013
two revenue factors are introduced. The first factor gives the revenue of transportingone unit of cargo over one nautical mile in the westbound direction. The other revenuefactor gives the revenue of transporting one unit of cargo over one nautical mile in theeastbound direction. Then, for each port combination, it is checked whether cargo has tobe transported in westbound or eastbound direction. Finally, the corresponding revenuefactor is multiplied with the direct distance between origin and destination port, whichgives the revenue per unit of the considered port combination.
Lachner & Boskamp obtained the revenue by taking the 10-year average of historicaldata. This calculation gives the revenue in USD/TEU for both the eastbound and thewestbound direction. Thereafter, they divided these revenues by the average distancebetween Asian and European ports. This results in the two revenue factors. The rev-enue factor is 0.0838 USD/nm in eastbound direction and 0.1677 USD/nm in westbounddirection.
Available ships
In Francesetti & Foschi (2002) an overview of costs related to ships with different sizesis given. The ship sizes given in this article are also used in this study. Furthermore, someadditional ship sizes are added in this study. The costs of these added ships are obtainedby extrapolation on the costs given in Francesetti & Foschi (2002). The available shipsizes for both the main and feeder services can be found in Tables A.6 and A.7. In thisstudy, it is assumed that an unlimited number of feeder ships is available.
Speed
From Notteboom (2006) it is learned that the speed of container vessels varies between18 and 26 nautical miles per hour. Therefore, this range of speeds is also considered inthis study. Furthermore, it is assumed that the speed can each time be increased by 0.5nm per hour. Thus, seventeen different values for liner shipping vessels are considered inthis study.
Further, it is assumed that feeder ships sail at a constant speed. This speed is assumedto be 22 nautical miles per hour.
Capital and operating cost
In Francesett & Foschi (2002), the yearly capital costs are given by 10% of the purchaseprice of the ship. The factor of 10% is the amortization factor. The purchase prices aregiven for ships with different ship sizes. The purchase price of the ships considered in thisstudy, that are not given in Francesetti & Foschi (2002) are determined by extrapolation.
The operating costs are defined as 5% of the purchase price of the ship plus 1.5 timesthe number of crew members times the average yearly wage of the crew. The crew size ismultiplied by 1.5 to take illness and holidays into account. The factor 5% of the purchase
2
price of the ship is used to take cost of maintenance, repairs, etcetera into account. Onaverage, 18 crew members with an average yearly wage of about $50, 000 are present ona ship. The average yearly wage is obtained by correcting the yearly wage of Fraccesetti& Foschi (2002) for inflation.
An overview on the yearly capital and operating costs per ship size can be found inTables A.6 and A.7.
Fuel cost
The fuel consumption in ton per day is given for the different ship sizes in Francesetti& Foschi (2002) for a speed of 25 nm per hour. When this amount is divided by thedistance travelled per day, the fuel consumption in ton per nautical mile is obtained.Thereafter, the fuel consumption is multiplied by the oil price in USD/ton to obtain thefuel cost in USD per nautical mile for the different ship sizes. In this study an oil priceof 500 USD per ton is used in the calculations.
In Notteboom (2006) a figure is given that shows the fuel consumption in ton per dayfor different values of the sailing speed for a ship with capacity of almost 8500 TEU. Therelation between fuel consumption and sailing speed will be about the same for differentship sizes. Therefore, this figure can be used to determine factors that indicate how muchoil is consumed at different sailing speeds. Finally, these factors can be used to determinethe fuel cost in USD per nautical mile for the other sailing speeds of the considered ships.
In Table A.8 an overview of the fuel cost for the different liner ship sizes and sailingspeeds is given. The fuel costs for feeder ships are obtained in a similar way and are givenin Table A.7.
Port, (un)loading and transhipment cost
The port, (un)loading and transhipment cost are obtained from Lachner & Boskamp(2011). Port costs are incurred per port visit and usually vary between ports. Further-more, the port costs may depend on the ship size. However, the differences in port costsare relatively small, so they are assumed to be constant per route type. In this study,ships are charged 25,000 USD per port visit on a main route and 15,000 USD per port visiton a feeder route. Thus, when a port is visited on a main route 52 · 25, 000 = 1, 300, 000
USD is charged, because each route is performed once a week. For feeder routes, the portcost per year equals 52 · 15, 000 = 780, 000 USD.
(Un)loading and transhipment costs are incurred per TEU (un)loaded or transhippedin a port. These costs can differ between ports and for different ship sizes. However, it isagain assumed that these costs are constant per route type. The cost of (un)loading is 175USD per TEU on main routes and 125 USD per TEU on feeder routes. A transhipmentconsist of a unloading and a loading movement, so the cost of a transhipment is 2 · 175 =
3
350 USD on main routes. Because each port (except the cluster centers) are only visited onone feeder route and no demand exists between ports in the same cluster, no transhipmentswill take place on feeder routes.
Port and buffer time
The time a ship spends in a port depends on many factors like the number of containersthat have to be (un)loaded, the number of cranes available to (un)load, the arrival time,etcetera. However, these factors are uncertain, so it is difficult to determine these times.Therefore, port times are assumed to be constant. The data on these times are obtainedfrom Lachner & Boskamp (2011). In this study, it is assumed that a ship spends 20 hourin a port on a main route and 15 hours in a port on a feeder route.
The buffer time is an additional time that is added to the route time to cover delays.The causes of delays can be divided in four groups: terminal operations, port access,maritime passages and chance (Notteboom (2006)). Chance includes weather conditionsand mechanical problems. In this study, a buffer time of at least 2 days has to be allocatedto each main route. The buffer time on feeder routes is assumed to be 1 day.
4
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6302
6282
6109
4773
4149
3267
2007
Gio
iaTau
ro88
2287
6187
1486
2284
2683
7185
1986
6383
5183
0380
6779
9477
2777
5375
8175
5473
7973
5373
6373
6865
8767
6859
4359
2357
6244
2037
8529
0316
43G
enoa
9305
9244
9197
9105
8909
8854
9002
9146
8834
8786
8550
8477
8210
8237
8064
8037
7862
7836
7847
7852
7071
7252
6426
6406
6245
4903
4268
3386
2126
Fos
9405
9344
9297
9205
9009
8954
9102
9246
8934
8886
8650
8577
8310
8332
8164
8137
7962
7936
7946
7951
7166
7340
6526
6506
6345
5003
4368
3486
2226
Bar
celo
na
9476
9415
9368
9276
9080
9029
9173
9317
9005
8957
8721
8648
8381
8407
8235
8208
8033
8007
8034
8039
7241
7409
6597
6577
6416
5074
4439
3557
2297
Val
enci
a95
5694
9594
4893
5691
6091
0992
5393
9790
8590
3788
0187
2884
6184
8783
1582
8881
1380
8780
9781
0273
2174
8966
7766
5764
9651
5445
1936
3723
77M
alag
a97
5896
9096
5095
5893
6292
7594
5595
9993
2492
3990
4089
3086
6386
8485
1784
9083
1583
2683
3683
4175
1876
8368
7268
5966
7953
4347
5838
3925
79A
lgec
iras
9804
9743
9696
9604
9408
9340
9501
9645
9333
9285
9049
8976
8709
8735
8563
8536
8361
8335
8385
8390
7569
7736
6925
6905
6744
5402
4767
3885
2625
Tan
gier
s98
3597
6397
2896
2494
4093
4895
3396
7793
6593
0590
8190
0887
4187
5785
9585
5683
9383
6784
1084
1575
9177
5769
4569
3767
5254
1647
9939
1526
57Le
Hav
re10
933
1087
210
825
1073
610
540
1048
510
633
1077
410
462
1041
410
178
1010
598
4198
6496
9296
6894
9094
6794
7794
8286
9888
7980
5480
3478
7365
3458
9950
1437
57Fel
ixst
owe
1105
610
995
1094
810
856
1066
310
605
1075
610
897
1058
510
537
1030
110
228
9961
1001
398
1597
8896
1395
8796
4096
4588
4790
1481
7781
5779
9666
5760
1951
3738
77Zee
bru
gge
1108
311
022
1097
510
883
1068
710
624
1078
010
924
1061
210
564
1032
810
255
9988
1001
798
4298
1596
4096
1496
2496
2988
5190
1882
0481
8480
2366
8160
4651
6439
04A
ntw
erp
1117
011
109
1106
210
970
1077
410
711
1086
710
986
1069
910
626
1041
510
317
1007
510
078
9929
9902
9701
9701
9711
9716
8912
9077
8291
8246
8094
6758
6133
5234
3991
Rot
terd
am11
133
1107
211
025
1093
310
737
1068
810
830
1097
410
662
1061
410
378
1030
510
038
1008
198
9298
6596
9096
6496
7496
7989
1590
8282
5482
3480
8467
4261
0752
1439
65B
rem
erhav
en11
328
1126
711
220
1112
810
932
1087
711
025
1116
910
857
1080
910
573
1050
010
233
1028
610
087
1006
098
8598
5998
8998
9491
2092
8784
4984
2982
6869
2662
9154
0941
49H
amburg
1141
611
355
1132
211
216
1103
410
971
1114
211
242
1097
410
882
1069
010
573
1035
010
334
1017
510
148
9956
9976
9979
9984
9168
9332
8537
8502
8342
7006
6408
5490
4237
Got
hen
burg
1156
811
507
1146
011
368
1117
511
117
1126
811
409
1109
711
049
1081
310
740
1047
610
524
1032
710
300
1012
510
099
1014
110
146
9358
9525
8689
8669
8508
7169
6531
5649
4389
Aar
hus
1166
211
601
1155
411
462
1126
911
127
1141
911
391
1124
811
025
1096
410
721
1061
510
454
1042
110
394
1027
610
250
1025
810
263
9453
9620
8783
8763
8602
7263
6682
5626
4483
Gdan
sk11
792
1173
111
684
1159
211
386
1129
311
489
1163
311
321
1127
311
037
1096
410
697
1083
310
541
1052
410
349
1032
310
509
1051
497
2698
9389
0388
9287
2173
7567
5558
7346
13
Tab
leA
.2:
Dis
tanc
esbe
twee
npo
rts
6
Ori
gin
Destination
PortSaid
Damietta
Izmit
IstanbulAmbarli
Odessa
Ilyichevsk
Constantza
Piraeus
Rijeka
Koper
Trieste
GioiaTauro
Genoa
Fos
Barcelona
Valencia
Malaga
Algeciras
Tangiers
LeHavre
Felixstowe
Zeebrugge
Antwerp
Rotterdam
Bremerhaven
Hamburg
Gothenburg
Aarhus
Gdansk
Yok
oham
a78
9479
2587
1886
6990
1590
1388
7284
8191
3991
7891
8688
2293
0594
0594
7695
5697
5898
0498
3510
933
1105
611
083
1117
011
133
1132
811
416
1156
811
662
1179
2Shim
izu
7833
7864
8650
8608
8954
8941
8811
8420
9078
9117
9120
8761
9244
9344
9415
9495
9690
9743
9763
1087
210
995
1102
211
109
1107
211
267
1135
511
507
1160
111
731
Nag
oya
7786
7817
8617
8561
8907
8905
8764
8373
9031
9070
9078
8714
9197
9297
9368
9448
9650
9696
9728
1082
510
948
1097
511
062
1102
511
220
1132
211
460
1155
411
684
Kob
e76
9477
2585
1884
6988
1588
0986
7282
8189
3989
7889
8686
2291
0592
0592
7693
5695
5896
0496
2410
736
1085
610
883
1097
010
933
1112
811
216
1136
811
462
1159
2B
usa
n74
9875
1983
2982
7386
1986
1784
7680
8587
4387
8287
9084
2689
0990
0990
8091
6093
6294
0894
4010
540
1066
310
687
1077
410
737
1093
211
034
1117
511
269
1138
6K
wan
gyan
g74
4374
2682
7882
1985
3985
2684
2280
3386
9187
2787
3583
7188
5489
5490
2991
0992
7593
4093
4810
485
1060
510
624
1071
110
690
1087
710
971
1111
711
127
1129
3D
alia
n75
9176
2284
2283
6687
1287
3185
6981
7888
3688
7588
8385
1990
0291
0291
7392
5394
5595
0195
3310
633
1075
610
780
1086
710
830
1102
511
142
1126
811
419
1148
9X
inga
ng
7735
7766
8566
8510
8856
8869
8713
8322
8980
9019
9027
8663
9146
9246
9317
9397
9599
9645
9677
1077
410
897
1092
410
986
1097
411
169
1124
211
409
1139
111
633
Qin
gdao
7423
7454
8254
8198
8544
8563
8401
8010
8668
8707
8715
8351
8834
8934
9005
9085
9324
9333
9365
1046
210
585
1061
210
699
1066
210
857
1097
411
097
1124
811
321
Lia
ngy
unga
ng
7375
7406
8206
8150
8496
8494
8353
7962
8620
8659
8667
8303
8786
8886
8957
9037
9239
9285
9305
1041
410
537
1056
410
626
1061
410
809
1088
211
049
1102
511
273
Shan
ghai
7139
7170
7970
7914
8260
8279
8117
7726
8384
8423
8431
8067
8550
8650
8721
8801
9040
9049
9081
1017
810
301
1032
810
415
1037
810
573
1069
010
813
1096
411
037
Nin
gbo
7066
7097
7898
7841
8187
8185
8044
7653
8311
8350
8358
7994
8477
8577
8648
8728
8930
8976
9008
1010
510
228
1025
510
317
1030
510
500
1057
310
740
1072
110
964
Fuzh
ou67
9968
3076
3075
7479
2079
3977
7773
8680
4480
8380
9177
2782
1083
1083
8184
6186
6387
0987
4198
4199
6199
8810
075
1003
810
233
1035
010
476
1061
510
697
Tai
pei
6822
6842
7644
7591
7938
7935
7794
7412
8070
8109
8114
7753
8237
8332
8407
8487
8684
8735
8757
9864
1001
310
017
1007
810
081
1028
610
334
1052
410
454
1083
3X
iam
en66
5366
7474
8474
2877
7477
7276
3172
4078
9879
3779
4575
8180
6481
6482
3583
1585
1785
6385
9596
9298
1598
4299
2998
9210
087
1017
510
327
1042
110
541
Kao
hsi
ung
6626
6657
7450
7401
7747
7741
7604
7213
7871
7910
7918
7554
8037
8137
8208
8288
8490
8536
8556
9668
9788
9815
9902
9865
1006
010
148
1030
010
394
1052
4Shen
zhen
Yan
tian
6451
6482
7275
7226
7572
7592
7429
7038
7696
7735
7738
7379
7862
7962
8033
8113
8315
8361
8393
9490
9613
9640
9701
9690
9885
9956
1012
510
276
1034
9H
ong
Kon
g64
2564
5672
5672
0075
4675
6574
0370
1276
7077
0977
1773
5378
3679
3680
0780
8783
2683
3583
6794
6795
8796
1497
0196
6498
5999
7610
099
1025
010
323
Shen
zhen
Chiw
an64
3564
6672
6672
1075
5675
7374
1370
2276
8077
1977
2773
6378
4779
4680
3480
9783
3683
8584
1094
7796
4096
2497
1196
7498
8999
7910
141
1025
810
509
Shen
zhen
Da
Chan
Bay
6440
6471
7271
7215
7561
7578
7418
7027
7685
7724
7732
7368
7852
7951
8039
8102
8341
8390
8415
9482
9645
9629
9716
9679
9894
9984
1014
610
263
1051
4Vung
Tau
5656
5668
6478
6425
6772
6769
6628
6246
6904
6943
6948
6587
7071
7166
7241
7321
7518
7569
7591
8698
8847
8851
8912
8915
9120
9168
9358
9369
9726
Lae
mC
hab
ang
5837
5806
6654
6599
6964
6951
6818
6413
7071
7124
7116
6759
7243
7340
7409
7489
7683
7736
7757
8882
9014
9018
9077
9082
9287
9332
9525
9507
9893
Sin
gapor
e50
1550
3658
3257
9061
3661
2359
9356
0262
6062
9963
0259
4364
2665
2665
9766
7768
7269
2569
4580
5481
7782
0482
9182
5484
4985
3786
8987
8389
03Tan
jung
Pel
epas
4995
5025
5825
5770
6116
6114
5973
5582
6240
6279
6282
5923
6406
6506
6577
6657
6859
6905
6937
8034
8157
8184
8246
8234
8429
8502
8669
8763
8892
Por
tK
lang
4834
4854
5639
5609
5943
5930
5812
5421
6079
6117
6109
5762
6245
6345
6416
6496
6679
6744
6752
7873
7996
8023
8094
8084
8268
8342
8508
8602
8721
Col
ombo
3492
3508
4303
4267
4607
4594
4470
4079
4737
4776
4773
4420
4903
5003
5074
5154
5343
5402
5416
6534
6657
6681
6758
6742
6926
7006
7169
7263
7375
Jebel
Ali
2857
2888
3687
3632
3979
3996
3835
3444
4102
4141
4149
3785
4268
4368
4439
4519
4758
4767
4799
5899
6019
6046
6133
6107
6291
6408
6531
6682
6755
Sal
alah
1975
2006
2805
2750
3097
3094
2953
2562
3220
3259
3267
2903
3386
3486
3557
3637
3839
3885
3915
5014
5137
5164
5234
5214
5409
5490
5649
5626
5873
Jeddah
715
746
1539
1490
1837
1834
1693
1302
1960
1999
2007
1643
2126
2226
2297
2377
2579
2625
2657
3757
3877
3904
3991
3965
4149
4237
4389
4483
4613
Por
tSai
d0
3182
477
911
2611
1598
259
012
4812
8712
9493
114
1315
1315
8516
6518
6419
1319
4130
4231
6531
9532
7932
5634
3735
2536
7737
7138
98D
amie
tta
310
848
793
1150
1137
996
607
1265
1307
1310
962
1434
1536
1603
1683
1877
1930
1951
3073
3196
3212
3271
3276
3468
3526
3707
3701
3867
Izm
it82
484
80
5539
738
425
139
011
5011
8611
9083
713
2114
2015
0415
8817
6216
4316
7527
9831
2130
6231
4731
2633
7832
6134
3235
3538
00Is
tanbulA
mbar
li77
979
355
034
734
420
334
910
9711
3711
4579
012
7313
7314
6015
4217
3116
9817
3028
5329
7629
9230
7930
5332
4833
3634
8735
8238
29O
des
sa11
2611
5039
734
70
1317
069
414
4414
8414
9211
3716
2017
2018
0718
8920
7820
4021
5631
9533
9133
3434
2133
9536
6337
5139
0339
9742
44Ilyic
hev
sk11
1511
3738
434
413
016
068
114
4114
7714
8111
2816
1217
0717
9818
7920
7520
2720
5932
8033
0534
1833
9734
8236
8736
4538
1639
1141
84C
onst
antz
a98
299
625
120
317
016
00
552
1300
1340
1348
993
1476
1576
1663
1745
1934
1894
2012
3049
3247
3188
3359
3249
3519
3607
3759
3853
4100
Pir
aeus
590
607
390
349
694
681
552
079
082
983
748
396
610
6611
5312
3514
3214
8415
0526
1427
3727
7328
4728
3430
0930
9532
4933
4335
90R
ijek
a12
4812
6511
5010
9714
4414
4113
0079
00
103
110
581
1064
1164
1251
1338
1554
1603
1628
2732
2855
2892
2973
2953
3127
3215
3367
3461
3708
Kop
er12
8713
0711
8611
3714
8414
7713
4082
910
30
862
011
0312
0212
9013
7715
9316
4216
6727
7228
9429
3130
0929
9231
6632
5434
0635
0037
47Tri
este
1294
1310
1190
1145
1492
1481
1348
837
110
80
625
1109
1208
1296
1383
1598
1647
1672
2777
2925
2936
3014
3000
3205
3260
3436
3531
3804
Gio
iaTau
ro93
196
283
779
011
3711
2899
348
358
162
062
50
484
583
671
758
973
1022
1047
2152
2275
2311
2389
2372
2547
2635
2787
2881
3128
Gen
oa14
1314
3413
2112
7316
2016
1214
7696
610
6411
0311
0948
40
208
350
508
798
847
871
1997
2100
2136
2213
2197
2372
2460
2630
2706
2953
Fos
1513
1536
1420
1373
1720
1707
1576
1066
1164
1202
1208
583
208
017
233
164
168
071
218
3019
3219
6920
2920
3022
0422
8524
6225
3828
04B
arce
lona
1585
1603
1504
1460
1807
1798
1663
1153
1251
1290
1296
671
350
172
016
149
951
354
516
6317
8618
0218
8118
6320
5821
2922
9723
9226
39Val
enci
a16
6516
8315
8815
4218
8918
7917
4512
3513
3813
7713
8375
850
833
116
10
338
382
411
1512
1635
1672
1752
1712
1907
1995
2147
2241
2488
Mal
aga
1864
1877
1762
1731
2078
2075
1934
1432
1554
1593
1598
973
798
641
499
338
065
8712
1913
4313
5814
2914
2216
2716
7718
5419
4922
22A
lgec
iras
1913
1930
1643
1698
2064
2054
1894
1484
1603
1642
1647
1022
847
680
513
382
650
3211
5512
7812
9413
7013
5515
5016
1817
8918
8421
31Tan
gier
s19
4119
5116
7517
3020
7720
5919
3315
0516
2816
6716
7210
4787
171
254
541
187
320
1137
1273
1276
1347
1340
1545
1595
1786
1869
2154
Le
Hav
re30
4230
7327
9828
5331
9532
8030
4926
1427
3227
7227
7721
5219
9718
3016
6315
1212
1911
5511
370
163
171
252
232
431
500
674
769
1015
Fel
ixst
owe
3165
3196
3121
2976
3323
3332
3179
2737
2855
2894
2925
2275
2100
1932
1786
1635
1343
1278
1273
163
083
141
123
303
360
530
606
872
Zee
bru
gge
3195
3212
3062
2992
3334
3336
3188
2773
2892
2931
2936
2311
2136
1969
1802
1672
1358
1294
1276
171
830
8764
269
347
519
627
861
Antw
erp
3279
3271
3147
3079
3421
3397
3280
2847
2973
3009
3014
2389
2213
2029
1881
1752
1429
1370
1347
252
141
870
149
356
405
597
680
965
Rot
terd
am32
5632
7631
2630
5333
9534
0032
4928
3429
5329
9230
0023
7221
9720
3018
6317
1214
2213
5513
4023
212
364
149
021
530
546
758
480
9B
rem
erhav
en34
3734
6833
3132
4835
9536
0534
5130
0931
2731
6632
0525
4723
7222
0420
5819
0716
2715
5015
4543
130
326
935
621
50
117
344
456
686
Ham
burg
3525
3526
3261
3336
3683
3645
3539
3095
3215
3254
3260
2635
2460
2285
2129
1995
1677
1618
1595
500
360
347
405
305
117
040
248
577
0G
othen
burg
3677
3707
3432
3487
3834
3843
3690
3249
3367
3406
3436
2787
2630
2462
2297
2147
1854
1789
1786
674
530
519
597
467
344
402
015
136
8A
arhus
3771
3701
3527
3582
3929
3938
3785
3343
3461
3500
3531
2881
2706
2538
2392
2241
1949
1884
1869
769
606
627
680
584
456
485
151
037
9G
dan
sk38
9838
6738
0038
2941
7642
1140
3235
9037
0837
4738
0431
2829
5328
0426
3924
8822
2221
3121
5410
1587
286
196
580
968
677
036
837
90
Tab
leA
.3:
Dis
tanc
esbe
twee
npo
rts
(2)
7
Ori
gin
Destination
Yokohama
Shimizu
Nagoya
Kobe
Busan
Kwangyang
Dalian
Xingang
Qingdao
Liangyungang
Shanghai
Ningbo
Fuzhou
Taipei
Xiamen
Kaohsiung
ShenzhenYantian
HongKong
ShenzhenChiwan
ShenzhenDaChanBay
VungTau
LaemChabang
Singapore
TanjungPelepas
PortKlang
Colombo
JebelAli
Salalah
Jeddah
Yok
oham
a0
00
00
00
00
00
00
00
00
00
00
00
00
098
2630
8327
31Shim
izu
00
00
00
00
00
00
00
00
00
00
00
00
00
1756
551
488
Nag
oya
00
00
00
00
00
00
00
00
00
00
00
00
00
7419
2328
2062
Kob
e0
00
00
00
00
00
00
00
00
00
00
00
00
078
9124
7621
93B
usa
n0
00
00
00
00
00
00
00
00
00
00
00
00
041
983
1317
111
667
Kw
angy
ang
00
00
00
00
00
00
00
00
00
00
00
00
00
6358
1995
1767
Dal
ian
00
00
00
00
00
00
00
00
00
00
00
00
00
1598
650
1544
42X
inga
ng
00
00
00
00
00
00
00
00
00
00
00
00
00
3055
295
8584
90Q
ingd
ao0
00
00
00
00
00
00
00
00
00
00
00
00
036
031
1130
410
013
Lia
ngy
unga
ng
00
00
00
00
00
00
00
00
00
00
00
00
00
1060
833
2829
48Shan
ghai
00
00
00
00
00
00
00
00
00
00
00
00
00
8780
127
546
2439
9N
ingb
o0
00
00
00
00
00
00
00
00
00
00
00
00
036
884
1157
210
250
Fuzh
ou0
00
00
00
00
00
00
00
00
00
00
00
00
041
3212
9611
48Tai
pei
00
00
00
00
00
00
00
00
00
00
00
00
00
3512
1102
976
Xia
men
00
00
00
00
00
00
00
00
00
00
00
00
00
1643
651
5745
68K
aohsi
ung
00
00
00
00
00
00
00
00
00
00
00
00
00
3013
694
5583
74Shen
zhen
Yan
tian
00
00
00
00
00
00
00
00
00
00
00
00
00
4272
713
405
1187
4H
ong
Kon
g0
00
00
00
00
00
00
00
00
00
00
00
00
073
688
2311
820
477
Shen
zhen
Chiw
an0
00
00
00
00
00
00
00
00
00
00
00
00
016
023
5027
4453
Shen
zhen
Da
Chan
Bay
00
00
00
00
00
00
00
00
00
00
00
00
00
5341
1676
1484
Vung
Tau
00
00
00
00
00
00
00
00
00
00
00
00
00
6496
2038
1805
Lae
mC
hab
ang
00
00
00
00
00
00
00
00
00
00
00
00
00
1623
050
9245
10Sin
gapor
e0
00
00
00
00
00
00
00
00
00
00
00
00
090
837
2849
925
243
Tan
jung
Pel
epas
00
00
00
00
00
00
00
00
00
00
00
00
00
2107
166
1158
55Por
tK
lang
00
00
00
00
00
00
00
00
00
00
00
00
00
2567
080
5471
34C
olom
bo
00
00
00
00
00
00
00
00
00
00
00
00
00
1216
638
1733
81Je
bel
Ali
3215
575
2428
2582
1373
720
8052
3199
9711
790
3471
2873
012
069
1352
1149
5378
9861
1398
124
112
5243
1748
2126
5311
2972
368
9584
0039
810
00
Sal
alah
1009
180
762
810
4310
653
1641
3136
3699
1089
9014
3786
424
361
1687
3094
4386
7565
1645
548
667
1666
9325
2163
2635
1249
00
0Je
ddah
893
160
675
718
3818
578
1454
2778
3276
965
7984
3354
376
319
1495
2740
3885
6700
1457
486
591
1476
8260
1916
2334
1106
00
0Por
tSai
d10
0317
975
780
542
8564
916
3231
1836
7810
8389
6237
6542
235
816
7830
7643
6175
2116
3554
566
316
5792
7221
5126
2012
420
00
Dam
iett
a32
157
242
257
1370
207
522
997
1176
346
2865
1203
135
115
536
983
1394
2404
523
174
212
530
2964
687
838
397
00
0Iz
mit
539
4042
226
3486
164
194
5747
219
822
1988
162
230
396
8629
3587
489
113
138
6521
066
58Is
tanbulA
mbar
li62
111
146
949
926
5340
210
1019
3122
7767
055
4923
3126
122
210
3919
0427
0046
5710
1333
841
110
2657
4113
3216
2276
924
6977
568
6O
des
sa42
731
3317
827
6813
015
345
373
156
1815
7012
818
131
368
2328
6938
589
109
5216
652
46Ilyic
hev
sk32
624
2613
721
5210
011
835
287
121
1411
5499
140
241
5217
2153
297
6984
4012
840
36C
onst
antz
a20
136
152
161
859
130
327
625
737
217
1796
754
8572
336
616
874
1507
328
109
133
332
1858
431
525
249
799
251
222
Pir
aeus
475
8535
838
120
2830
777
214
7617
4151
242
4117
8220
017
079
414
5620
6435
6077
425
831
478
443
8810
1812
4058
818
8759
252
4R
ijek
a49
937
3921
032
8015
318
053
438
184
2118
8215
021
336
880
2732
8145
310
512
861
195
6154
Kop
er11
621
8893
496
7518
936
142
612
510
3743
649
4119
435
650
587
018
963
7719
210
7324
930
314
446
114
512
8Tri
este
9417
7175
400
6115
229
134
410
183
735
239
3315
728
740
770
315
351
6215
586
620
124
511
637
211
710
3G
ioia
Tau
ro94
716
971
576
140
4661
315
4129
4534
7310
2284
6235
5539
833
815
8429
0441
1871
0215
4451
562
615
6487
5520
3124
7411
7337
6511
8110
46G
enoa
519
9339
241
722
1633
684
416
1319
0256
046
3519
4721
818
586
815
9122
5638
9084
628
234
385
747
9511
1213
5564
220
6264
757
3Fos
299
5322
524
012
7519
348
692
810
9532
226
6711
2112
610
749
991
612
9822
3948
716
219
749
327
6064
078
037
011
8737
233
0B
arce
lona
609
109
460
489
2601
394
991
1893
2233
657
5441
2285
256
218
1018
1867
2648
4566
993
331
403
1006
5629
1306
1591
754
2421
759
673
Val
enci
a12
3622
193
399
252
8080
020
1138
4345
3213
3411
043
4639
520
442
2067
3790
5374
9268
2015
672
817
2041
1142
526
5032
2915
3049
1315
4113
65M
alag
a98
1874
7941
963
160
305
360
106
876
368
4135
164
301
426
735
160
5365
162
906
210
256
121
390
122
108
Alg
ecir
as10
2918
477
782
643
9766
616
7432
0037
7411
1191
9638
6343
336
817
2131
5644
7577
1816
7855
968
017
0095
1422
0726
8912
7440
9212
8411
37Tan
gier
s33
860
255
272
1445
219
550
1052
1240
365
3022
1270
142
121
566
1037
1471
2536
552
184
224
559
3127
725
884
419
1345
422
374
Le
Hav
re74
413
356
259
831
7948
112
1123
1427
2880
366
4927
9331
326
612
4522
8232
3655
8012
1340
449
212
2968
7915
9619
4492
129
5892
882
2Fel
ixst
owe
1048
187
792
842
4480
678
1706
3260
3845
1132
9369
3936
441
375
1754
3216
4559
7863
1710
570
693
1732
9693
2248
2739
1298
4168
1308
1158
Zee
bru
gge
787
141
595
632
3364
510
1281
2448
2887
850
7036
2956
331
281
1317
2415
3424
5905
1284
428
521
1301
7280
1689
2057
975
3131
982
870
Antw
erp
2472
442
1867
1985
1056
316
0040
2276
8790
6626
6922
091
9280
1040
884
4135
7582
1075
018
540
4031
1344
1634
4084
2285
553
0264
5930
6198
2930
8427
31R
otte
rdam
3295
589
2488
2646
1408
021
3253
6110
247
1208
435
5829
446
1237
013
8611
7855
1210
107
1433
024
713
5374
1791
2179
5443
3046
570
6786
0940
8013
102
4110
3641
Bre
mer
hav
en15
3427
411
5812
3265
5599
324
9647
7056
2516
5613
708
5759
645
548
2566
4705
6671
1150
525
0283
410
1425
3414
182
3290
4008
1899
6099
1914
1695
Ham
burg
2371
424
1790
1904
1013
015
3438
5773
7286
9425
6021
186
8900
997
847
3966
7271
1031
017
780
3866
1289
1567
3916
2191
850
8461
9429
3694
2629
5726
19G
othen
burg
277
4920
922
211
8217
945
086
010
1429
924
7110
3811
699
463
848
1202
2074
451
150
183
457
2556
593
722
342
1099
345
306
Aar
hus
231
4117
418
698
714
937
671
884
724
920
6486
797
8338
670
810
0517
3237
712
615
338
221
3649
560
428
691
828
825
5G
dan
sk81
1561
6534
853
132
253
298
8872
730
534
2913
625
035
461
013
344
5413
475
217
521
310
132
410
290
Tab
leA
.4:
Dem
and
betw
een
port
s
8
Ori
gin
Destination
PortSaid
Damietta
Izmit
IstanbulAmbarli
Odessa
Ilyichevsk
Constantza
Piraeus
Rijeka
Koper
Trieste
GioiaTauro
Genoa
Fos
Barcelona
Valencia
Malaga
Algeciras
Tangiers
LeHavre
Felixstowe
Zeebrugge
Antwerp
Rotterdam
Bremerhaven
Hamburg
Gothenburg
Aarhus
Gdansk
Yok
oham
a30
6598
013
816
2210
984
525
1240
128
303
245
2473
1355
780
1590
3228
256
2688
883
1943
2738
2057
6457
8606
4007
6192
722
603
213
Shim
izu
548
175
2529
019
1594
222
2354
4444
224
213
928
457
746
480
158
347
489
368
1154
1538
716
1107
129
108
38N
agoy
a23
1474
010
412
2582
6339
693
697
229
185
1868
1023
589
1201
2437
193
2029
667
1467
2068
1553
4875
6499
3025
4676
545
456
160
Kob
e24
6278
711
113
0287
6742
299
610
324
319
619
8610
8862
612
7725
9220
621
5870
915
6121
9916
5251
8569
1232
1849
7358
048
417
1B
usa
n13
096
4186
590
6929
465
359
2243
5297
547
1295
1045
1056
757
8833
3167
9413
790
1094
1148
437
7483
0311
700
8787
2758
736
772
1711
826
456
3086
2578
908
Kw
angy
ang
1983
634
8910
4970
5434
080
283
196
158
1600
877
504
1029
2088
166
1739
572
1257
1772
1331
4178
5569
2592
4006
467
390
138
Dal
ian
4986
1594
225
2638
177
137
854
2017
208
493
398
4024
2204
1268
2587
5251
417
4373
1437
3161
4455
3346
1050
414
001
6518
1007
411
7598
134
6X
inga
ng
9530
3047
429
5043
339
261
1632
3854
398
943
761
7690
4212
2424
4944
1003
579
683
5727
4760
4285
1463
9420
076
2676
012
458
1925
322
4618
7666
1Q
ingd
ao11
239
3593
506
5947
399
308
1925
4546
470
1112
897
9069
4967
2859
5831
1183
593
998
5532
3971
2610
041
7541
2367
631
558
1469
222
705
2648
2212
779
Lia
ngy
unga
ng
3309
1058
149
1751
118
9156
713
3813
832
726
426
7014
6384
217
1734
8527
629
0295
420
9829
5622
2069
7192
9243
2666
8578
065
122
9Shan
ghai
2738
887
5512
3414
491
973
751
4691
1107
711
4427
0921
8622
100
1210
569
6614
209
2884
022
8824
016
7893
1736
424
468
1837
657
694
7690
335
801
5532
964
5353
9118
99N
ingb
o11
505
3678
518
6087
409
315
1970
4653
481
1138
918
9284
5085
2926
5969
1211
596
110
089
3316
7294
1027
977
1924
236
3230
515
039
2324
327
1122
6579
8Fuzh
ou12
8941
258
682
4635
221
521
5412
710
310
4057
032
866
913
5710
811
3037
181
711
5186
527
1536
1916
8526
0430
425
489
Tai
pei
1095
350
4958
039
3018
844
346
108
8788
448
427
956
811
5492
961
316
695
979
735
2308
3076
1432
2213
258
216
76X
iam
en51
2716
3923
127
1318
214
187
820
7421
450
740
941
3722
6613
0426
6053
9942
844
9614
7832
5145
8034
4010
800
1439
667
0210
358
1208
1009
356
Kao
hsi
ung
9400
3005
423
4974
334
258
1610
3802
393
930
750
7585
4155
2391
4877
9899
785
8243
2709
5960
8398
6307
1980
226
395
1228
818
990
2215
1850
652
Shen
zhen
Yan
tian
1332
842
6060
070
5247
336
522
8353
9055
713
1810
6410
755
5891
3390
6914
1403
411
1311
687
3841
8450
1190
789
4228
076
3742
317
422
2692
531
4026
2392
4H
ong
Kon
g22
986
7348
1035
1216
281
663
039
3792
9696
122
7318
3518
548
1015
958
4611
925
2420
419
2020
156
6624
1457
320
535
1542
248
420
6454
130
046
4643
554
1645
2415
94Shen
zhen
Chiw
an49
9815
9822
526
4417
813
785
620
2120
949
439
940
3322
0912
7125
9352
6341
843
8314
4031
6944
6533
5310
528
1403
465
3310
097
1178
984
347
Shen
zhen
Da
Chan
Bay
1666
533
7588
159
4628
567
470
165
133
1344
736
424
864
1754
139
1461
480
1056
1488
1118
3509
4678
2178
3366
393
328
116
Vung
Tau
2026
648
9110
7272
5634
782
085
200
162
1635
896
515
1051
2134
169
1777
584
1285
1810
1360
4268
5690
2649
4093
477
399
141
Lae
mC
hab
ang
5063
1618
228
2679
180
139
867
2048
212
501
404
4085
2238
1288
2627
5331
423
4439
1459
3210
4523
3397
1066
514
216
6618
1022
811
9399
735
1Sin
gapor
e28
335
9058
1276
1499
210
0777
748
5311
460
1184
2802
2262
2286
412
523
7207
1470
029
837
2367
2484
781
6617
965
2531
419
012
5968
979
562
3703
957
242
6676
5577
1965
Tan
jung
Pel
epas
6573
2101
296
3478
233
180
1126
2658
275
650
525
5304
2905
1672
3410
6921
549
5763
1894
4167
5872
4410
1384
618
455
8592
1327
815
4912
9445
6Por
tK
lang
8007
2560
361
4237
284
220
1371
3239
335
792
639
6461
3539
2037
4154
8432
669
7022
2308
5077
7154
5373
1686
822
484
1046
716
177
1887
1576
555
Col
ombo
3795
1213
171
2008
135
104
650
1535
159
375
303
3062
1677
965
1969
3996
317
3328
1094
2406
3390
2546
7994
1065
649
6176
6789
474
726
3Je
bel
Ali
00
180
2110
142
109
683
1613
167
394
318
3217
1762
1014
2069
4199
333
3496
1149
2528
3562
2675
8400
1119
652
1280
5594
078
527
7Sal
alah
00
5666
244
3421
450
652
124
100
1009
553
318
649
1317
105
1097
361
793
1118
839
2635
3513
1635
2527
295
246
87Je
ddah
00
5058
639
3019
044
846
110
8889
449
028
257
511
6793
972
319
703
990
743
2334
3111
1448
2239
261
218
77Por
tSai
d0
056
658
4434
213
503
5212
399
1004
550
316
645
1310
104
1091
358
789
1111
835
2620
3492
1626
2513
293
245
86D
amie
tta
00
1821
014
1168
161
1739
3232
117
610
120
641
933
349
115
252
355
267
838
1116
520
803
9478
28Iz
mit
6621
00
00
00
00
00
00
00
00
00
00
00
00
00
0Is
tanbulA
mbar
li77
024
60
00
00
00
00
00
00
00
00
00
00
00
00
00
Odes
sa52
170
00
00
00
00
00
00
00
00
00
00
00
00
00
Ilyic
hev
sk40
130
00
00
00
00
00
00
00
00
00
00
00
00
00
Con
stan
tza
249
800
00
00
00
00
00
00
00
00
00
00
00
00
00
Pir
aeus
589
188
00
00
00
00
00
00
00
00
00
00
00
00
00
0R
ijek
a61
190
00
00
00
00
00
00
00
00
00
00
00
00
00
Kop
er14
446
00
00
00
00
00
00
00
00
00
00
00
00
00
0Tri
este
116
370
00
00
00
00
00
00
00
00
00
00
00
00
00
Gio
iaTau
ro11
7437
50
00
00
00
00
00
00
00
00
00
00
00
00
00
Gen
oa64
320
60
00
00
00
00
00
00
00
00
00
00
00
00
00
Fos
370
118
00
00
00
00
00
00
00
00
00
00
00
00
00
0B
arce
lona
755
241
00
00
00
00
00
00
00
00
00
00
00
00
00
0Val
enci
a15
3349
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Mal
aga
122
390
00
00
00
00
00
00
00
00
00
00
00
00
00
Alg
ecir
as12
7640
80
00
00
00
00
00
00
00
00
00
00
00
00
00
Tan
gier
s41
913
40
00
00
00
00
00
00
00
00
00
00
00
00
00
Le
Hav
re92
329
50
00
00
00
00
00
00
00
00
00
00
00
00
00
Fel
ixst
owe
1300
416
00
00
00
00
00
00
00
00
00
00
00
00
00
0Zee
bru
gge
977
312
00
00
00
00
00
00
00
00
00
00
00
00
00
0A
ntw
erp
3066
980
00
00
00
00
00
00
00
00
00
00
00
00
00
0R
otte
rdam
4087
1306
00
00
00
00
00
00
00
00
00
00
00
00
00
0B
rem
erhav
en19
0360
80
00
00
00
00
00
00
00
00
00
00
00
00
00
Ham
burg
2940
940
00
00
00
00
00
00
00
00
00
00
00
00
00
0G
othen
burg
343
110
00
00
00
00
00
00
00
00
00
00
00
00
00
0A
arhus
286
920
00
00
00
00
00
00
00
00
00
00
00
00
00
Gdan
sk10
132
00
00
00
00
00
00
00
00
00
00
00
00
00
0
Tab
leA
.5:
Dem
and
betw
een
port
s(2
)
9
Ship Ship Capacity Total Capacity Capital Cost Operating Cost Nr availableName (TEU) (TEU/year) ($/year) ($/year)M1 4000 208000 4500000 3600000 5M2 5000 260000 5400000 4050000 5M3 6000 312000 6000000 4350000 5M4 7000 364000 6500000 4600000 5M5 8000 416000 7000000 4850000 5M6 9000 468000 7500000 5100000 5M7 10000 520000 8000000 5350000 2M8 14000 728000 10000000 7850000 1
Table A.6: Liner ship characteristics
Ship Ship Capacity Total Capacity Capital Cost Operating Cost Fuel costName (TEU) (TEU/year) ($/year) ($/year) ($/nm)F1 200 10400 800000 1450000 16.667F2 350 18200 950000 1525000 20.833F3 500 26000 1100000 1600000 25.000F4 700 36400 1400000 1750000 26.667F5 800 41600 1500000 1800000 29.167F6 900 46800 1600000 1850000 31.667F7 1000 52000 1750000 1925000 33.333F8 1250 65000 2100000 2100000 41.667F9 1500 78000 2300000 2200000 50.000F10 1750 91000 2500000 2300000 58.333F11 2000 104000 2700000 2400000 66.667F12 2250 117000 2950000 2525000 75.000F13 2500 130000 3200000 2650000 83.333F14 4000 208000 4500000 3600000 91.626F15 5000 260000 5400000 4050000 104.264
Table A.7: Feeder ship characteristics
10
Ship
Spee
dN
ame
1818
.519
19.5
2020
.521
21.5
2222
.523
23.5
2424
.525
25.5
26M
185
.637
84.9
2584
.250
83.6
1083
.002
83.8
7084
.696
88.2
4291
.626
94.8
6010
1.82
010
8.48
311
4.86
912
0.99
512
6.87
513
2.52
513
7.95
7M
297
.449
96.6
3995
.871
95.1
4394
.451
95.4
3896
.379
100.
413
104.
264
107.
944
115.
864
123.
447
130.
713
137.
684
144.
375
150.
804
156.
986
M3
109.
261
108.
353
107.
492
106.
675
105.
900
107.
006
108.
061
112.
584
116.
902
121.
028
129.
908
138.
410
146.
557
154.
372
161.
875
169.
083
176.
014
M4
121.
073
120.
067
119.
113
118.
208
117.
348
118.
575
119.
743
124.
755
129.
540
134.
112
143.
952
153.
373
162.
401
171.
061
179.
375
187.
363
195.
043
M5
132.
886
131.
780
130.
734
129.
740
128.
797
130.
143
131.
425
136.
927
142.
178
147.
196
157.
996
168.
336
178.
245
187.
750
196.
875
205.
642
214.
071
M6
144.
698
143.
494
142.
354
141.
273
140.
245
141.
711
143.
107
149.
098
154.
816
160.
280
172.
040
183.
299
194.
090
204.
439
214.
375
223.
921
233.
100
M7
156.
510
155.
208
153.
975
152.
805
151.
694
153.
280
154.
790
161.
269
167.
454
173.
364
186.
084
198.
263
209.
934
221.
128
231.
875
242.
200
252.
129
M8
203.
758
202.
063
200.
458
198.
935
197.
488
199.
553
201.
519
209.
954
218.
007
225.
701
242.
261
258.
115
273.
310
287.
884
301.
875
315.
317
328.
243
Tab
leA
.8:
Fuel
cost
for
diffe
rent
spee
dsan
dsh
ipsi
zes
11
Appendix B. Reference network
Table B.9 shows the routes in the reference network during spring 2010. Next, TableB.10 shows the different types of ships used on each of the routes.
AE1/AE10 AE10/AE1 AE2 AE3 AE6Yokohama Shenzhen Yantian Busan Dalian YokohamaHong Kong Hong Kong Xingang Xingang NagoyaShenzhen Yantian Tanjung Pelepas Dalian Busan ShanghaiTanjung Pelepas Le Havre Qingdao Shanghai NingboFelixstowe Zeebrugge Kwangyang Ningbo XiamenRotterdam Hamburg Shanghai Taipei Hong KongHamburg Gdansk Bremerhaven Shenzhen Chiwan Shenzhen YantianBremerhaven Gothenburg Hamburg Shenzhen Yantian Tanjung PelepasTangiers Aarhus Rotterdam Tanjung Pelepas JeddahJeddah Bremerhaven Felixstowe Port Klang BarcelonaJebel Ali Rotterdam Antwerp Port Said ValenciaShenzhen Da Chan Bay Singapore Tanjung Pelepas Damietta AlgecirasNingbo Hong Kong Busan Izmit TangiersShanghai Kobe Istanbul Ambarli Tanjung PelepasKaohsiung Nagoya Constantza Vung TauYokohama Shimizu Ilyichevsk Shenzhen Yantian
Yokohama Odessa Hong KongShenzhen Yantian Damietta Yokohama
Port SaidPort KlangTanjung PelepasDalian
AE7 AE9 AE11 AE12Shanghai Laem Chabang Qingdao ShanghaiNingbo Tanjung Pelepas Shanghai BusanXiamen Port Klang Fuzhou Hong KongHong Kong Colombo Hong Kong Shenzhen ChiwanShenzhen Yantian Zeebrugge Shenzhen Chiwan Tanjung PelepasAlgeciras Felixstowe Shenzhen Yantian Port KlangTangiers Bremerhaven Tanjung Pelepas Port SaidRotterdam Rotterdam Port Klang PiraeusFelixstowe Le Havre Salalah KoperBremerhaven Tangiers Port Said RijekaMalaga Salalah Gioia Tauro TriesteShenzhen Yantian Colombo Genoa DamiettaHong Kong Port Klang Fos Port SaidShanghai Singapore Genoa Jeddah
Laem Chabang Damietta Port KlangPort Said SingaporeSalalah ShanghaiPort KlangSingaporeLiangyungangQingdao
Table B.9: Routes in the Maersk network
12
AE1/AE10 Capacity AE10/AE1 Capacity AE2 CapacitySofie Maersk 8160 A.P. Moller 8160 Maersk Seville 8478Albert Maersk 8272 Skagen Maersk 8160 Maersk Saigon 8450Carsten Maersk 8160 Sally Maersk 8160 Adrian Maersk 8272Maersk Singapore 8478 Arnold Maersk 8272 Maersk Salina 8600Clementine Maersk 8648 Svendborg Maersk 8160 Maersk Savannah 8600Maersk Seoul 8450 Svend Maersk 8160 Anna Maersk 8272Maersk Taurus 8400 Columbine Maersk 8648 Arthur Maersk 8272Sine Maersk 8160 Maersk Tukang 8400 Maersk Stepnica 8600Axel Maersk 8272 Clifford Maersk 8160 Maersk Semarang 8400Cornelia Maersk 8650 Maersk Salalah 8600 Maersk Stralsund 8450
Maersk Stockholm 8600Average 8365 8316 8439
AE3 AE6 AE7Maersk Kinloss 6500 Mathilde Maersk 9038 Eugen Maersk 14770CMA CGM Debussy 6627 Maersk Antares 9200 Elly Maersk 14770Maersk Kuantan 6500 Gunvor Maersk 9074 Evelyn Maersk 14770Maersk Kowloon 6500 Mette Maersk 9038 Edith Maersk 14770CMA CGM Corneille 6500 Marit Maersk 9038 Estelle Maersk 14770Maersk Kelso 6500 Gerd Maersk 9074 Maersk Algol 9200CMA CGM Musset 6540 Maersk Altair 9200 Ebba Maersk 14770Maersk Kwangyang 6500 Gudrun Maersk 9074 Eleonora Maersk 14770CMA CGM Bizet 6627 Marchen Maersk 9038 Emma Maersk 14770Maersk Kensington 6500 Maren Maersk 9038 Gjertrud Maersk 9074CMA CGM Baudelaire 6251 Georg Maersk 9074
Grete Maersk 9074Maersk Alfirk 9200Margrethe Maersk 9038
Average 6504 9086 13643
AE9 AE11 AE12Maersk Sembawang 6478 Charlotte Maersk 8194 Maersk Kyrenia 6978Maersk Sebarok 6478 Maersk Surabaya 8400 Safmarine Komati 6500Maersk Serangoon 6478 Maersk Santana 8478 CMA CGM Belioz 6627SL New York 6420 CMA CGM Faust 8204 Safmarine Kariba 6500Maersk Seletar 6478 Soroe Maersk 8160 CMA CGM Balzac 6251Maersk Kendal 6500 Susan Maersk 8160 Maersk Karachi 6930Maersk Sentosa 6478 Caroline Maersk 8160 CMA CGM Ravel 6712Maers Semakau 6478 Cornelius Maersk 8160 CMA CGM Flaubert 6638Maersk Senang 6478 Chastine Maersk 8160 CMA CGM Voltaire 6456Average 6474 8230 6621
Table B.10: Ships and capacities on the Maersk network
13
Appendix C. Cluster design
Table C.11 shows the composition of the ten clusters obtained after aggregation inthis study.
Shanghai Hong Kong Singapore Colombo Jebel AliYokohama Xiamen Vung Tau Colombo Jebel AliShimizu Kaohsiung Laem Chabang SalalahNagoya Shenzhen Yantian SingaporeKobe Hong Kong Tanjung PelepasBusan Shenzhen Chiwan Port KlangKwangyang Shenzhen Da Chan BayDalianXingangQingdaoLiangyungangShanghaiNingboFuzhouTaipei
Port Said Valencia Rotterdam Antwerp HamburgIzmit Gioia Tauro Zeebrugge Antwerp BremerhavenOdessa Genoa Le Havre HamburgJeddah Fos Felixstowe GothenburgPort Said Barcelona Rotterdam AarhusDamietta Valencia GdanskIstanbul Ambarli MalagaIlyichevsk AlgecirasConstantza TangiersPiraeusRijekaKoperTrieste
Table C.11: Design of the ten clusters
14
Appendix D. Best Network
15
M1 M2 M3 M4Tanjung Pelepas Shenzhen Yantian Busan NingboSingapore Shenzhen Chiwan Qingdao BusanPort Klang Shenzhen Da Chan Bay Xingang QingdaoColombo Hong Kong Dalian XingangGioia Tauro Xiamen Shanghai DalianValencia Kaohsiung Ningbo LiangyungangAlgeciras Singapore Hong Kong ShanghaiFelixstowe Tanjung Pelepas Shenzhen Chiwan FuzhouZeebrugge Port Klang Shenzhen Yantian Hong KongRotterdam Port Said Jeddah Shenzhen YantianBremerhaven Felixstowe Port Said XiamenHamburg Le Havre Bremerhaven KaohsiungRotterdam Rotterdam Hamburg AlgecirasDamietta Zeebrugge Aarhus TangiersPort Said Port Klang Gothenburg MalagaJeddah Tanjung Pelepas Antwerp ValenciaTanjung Pelepas Singapore Algeciras Fos
Shenzhen Yantian Valencia GenoaGioia Tauro BarcelonaPort Said Gioia TauroJeddah NingboColomboShenzhen ChiwanHong KongShenzhen YantianBusan
9000 10000 14000 9000M5 M6 M7Shenzhen Yantian Ningbo Shenzhen YantianShenzhen Chiwan Qingdao Shenzhen ChiwanHong Kong Busan Shenzhen Da Chan BayXiamen Xingang Hong KongKaohsiung Dalian XiamenJebel Ali Shanghai KaohsiungSalalah Jebel Ali JeddahAntwerp Valencia Port SaidHamburg Felixstowe DamiettaBremerhaven Le Havre Shenzhen YantianRotterdam RotterdamZeebrugge ZeebruggeAlgeciras AntwerpValencia Port SaidBarcelona SingaporeGioia Tauro Hong KongPort Said NingboPort KlangTanjung PelepasSingaporeVung TauShenzhen Yantian14000 TEU 9000 TEU 9000 TEU 8000 TEU
Table D.12: Main routes of the best network
16
Rou
teC
apac
ityPor
tsvi
site
dF01
350
Rot
terd
amLe
Hav
reFe
lixst
owe
Rot
terd
amF02
900
Shan
ghai
Lian
gyun
gang
Shan
ghai
F03
2000
Shan
ghai
Nin
gbo
Nag
oya
Yok
oham
aSh
angh
aiF04
500
Shan
ghai
Fuzh
ouSh
imiz
uSh
angh
aiF05
2000
Shan
ghai
Taip
eiK
obe
Kw
angy
ang
Shan
ghai
F06
1250
Hon
gK
ong
Xia
men
Kao
hsiu
ngSh
enzh
enD
aC
han
Bay
Hon
gK
ong
F07
2250
Sing
apor
eV
ung
Tau
Laem
Cha
bang
Sing
apor
eF08
1250
Ham
burg
Aar
hus
Gda
nsk
Got
henb
urg
Ham
burg
F09
200
Por
tSa
idJe
ddah
Por
tSa
idF10
1750
Por
tSa
idIs
tanb
ulA
mba
rli
Izm
itPor
tSa
idF11
200
Por
tSa
idIly
iche
vsk
Ode
ssa
Por
tSa
idF12
1750
Por
tSa
idP
irae
usC
onst
antz
aPor
tSa
idF13
200
Por
tSa
idR
ijeka
Dam
iett
aPor
tSa
idF14
700
Por
tSa
idTr
iest
eK
oper
Por
tSa
idF15
2250
Val
enci
aTa
ngie
rsG
enoa
Fos
Bar
celo
naV
alen
cia
F16
200
Val
enci
aM
alag
aV
alen
cia
Tab
leD
.13:
Feed
erro
utes
ofth
ebe
stne
twor
k
17
Appendix E. Solution approach
In this section, some solution methods are discussed in more detail.
Appendix E.1. Aggregation
First, we will describe the methods used to aggregate ports into port clusters. Thereto,we will first create lists of central, noncentral and intermediary ports. Thereafter, initialclusters will be designed, which are updated in the next step. After this step, the finalclusters are known and the cluster data have to be constructed.
Appendix E.1.1. Lists of central, noncentral and intermediary ports
First, construct the lists of central, noncentral and intermediary ports:
Hc := {h ∈ H : xh ≥ Mx̄} central ports.
Hnc := {h ∈ H : xh ≤ mx̄} noncentral ports.
Hm := {h ∈ H : h /∈ Hc ∪Hnc} intermediary ports.
In this definitions, H is the set containing all ports, m and M are the minimum andmaximum factor respectively. In our case study, we used m = 0.2 and M = 2. Further,when da,b is the demand from port a to port b, we have:
xh =∑h′∈H
dh,h′ +∑h′∈H
dh′,h throughput of port h;
x̄ =1
|H|∑h∈H
xh average throughput per port.
Appendix E.1.2. Initial clusters
Next, we create initial clusters. For each hi ∈ Hc, create a new cluster Ci := {hi}(with i = 1, . . . , |Hc|) only containing port hi and the central port of the cluster is ci = hi.
Let I denote the number of clusters. Then, we have I = |Hc| initial clusters all containingexactly one port. Next, we will add intermediary and noncentral ports to the nearestexisting cluster if they are within the maximum cluster distance. We will only comparethe distance between the considered port and the central port of the cluster with themaximum cluster distance, because this distance has to be covered on the feeder lines.Thus, it is possible that the distance between two ports in the same cluster exceeds themaximum cluster distance, but these ports will then not be visited on the same feederservice. Thus, for each h ∈ Hnc ∪Hm, we will have
Ci = Ci ∪ {h} if Dh,ci = min1≤j≤I
Dh,cj ≤ Dmax
Ci = Ci else,
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where Da,b is the distance between port a and b and Dmax the maximum distance allowedbetween ports in a cluster. In our case study we used Dmax = 1250 nm, such that directfeeder lines between a port in the cluster and the central port of the cluster can alwaysbe served within one week.
Appendix E.1.3. Update clusters
Let
Ha := {h ∈ Hnc ∪Hm : h ∈ ∪iCi} allocated ports.
Hmna := {h ∈ Hm : h /∈ ∪iCi} nonallocated intermediary ports.
Hncna := {h ∈ Hnc : h /∈ ∪iCi} nonallocated noncentral ports.
As long as Hmna ̸= ∅, take port h ∈ Hm
na with the largest throughput (xh = maxh′∈Hmnaxh′).
Create a new cluster, I = I + 1 and CI = {h}, cI = h. Add intermediary and noncentralports to the new cluster if they are nearest to this cluster and their distance is within themaximum distance allowed. That is, for each h ∈ Hnc ∪Hm, we will have
CI = CI ∪ {h} if Dh,cI = minj≤I
Dh,cj ≤ M
CI = CI else,
where Da,b is again the distance between port a and b and M the maximum distanceallowed between ports in a cluster. For all port h ∈ CI check whether they were alreadyallocated to a cluster, that is check whether
h ∈ ∪1≤i≤I−1Ci.
If the port was already allocated to a cluster, remove it from the cluster, so if h ∈ Cj with1 ≤ j ≤ I − 1, then let Cj = Cj \ {h}. Update the sets with allocated and nonallocatedports and repeat this procedure until Hm
na = ∅.If Hnc
na ̸= ∅, then determine for each h ∈ Hncna to which cluster it is closest and add it
to this cluster:
Ci = Ci ∪ {h} if Dh,ci = min1≤j≤I
Dh,cj ≤ M
Ci = Ci else.
The clusters Ci for 1 ≤ i ≤ I are the final clusters that will be used as input for the cargorouting model. It only remains to determine the relevant port cluster data, which will beexplained in the next section.
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Appendix E.1.4. Determine cluster data
To determine the profitability of a given network, the demand, distance and revenuebetween port pairs are needed. Furthermore, the (un)loading, transhipment and visitcosts are needed for each port, as is the time of a port visit. The distance, costs and porttime of a cluster are all incurred in the central port of the cluster, so we set:
DCi,Cj= Dci,cj 1 ≤ i, j ≤ I;
cCi= cci 1 ≤ i ≤ I;
tCi= tci 1 ≤ i ≤ I,
where Da,b is the distance between port/cluster a and b, ca denote the relevant costs ofport/cluster a and ta is the port time of port/cluster a. Furthermore, Ci denotes cluster i,while ci is the central port of cluster i. Since it is not possible to determine the origin anddestination port of a cargo flow between clusters when solving the cargo routing model,we let the revenue between port pairs be equal to the revenue between the central portsof the relevant clusters. That is, we let:
rCi,Cj= rci,cj 1 ≤ i, j ≤ I.
The demand between clusters depend on the demand between the ports in the clusters.Cluster demand equals the sum of all individual port demands in the cluster:
dCi,Cj=
∑h∈Ci
∑h′∈Cj
dh,h′ 1 ≤ i, j ≤ I,
with da,b the demand between ports/clusters a and b.
Appendix E.2. Disaggregation
In practice, it is necessary to know the exact origin and destination port of each cargoflow. Therefore, the cargo flows between port clusters have to be disaggregated into cargoflows between ports. This section will describe the method to obtain these disaggregatedflows.
The disaggregation process can be performed for each combination of port clustersseparately. Thus, select two port clusters Ci and Cj and the corresponding total flow overthe network
f =∑s∈S
xtotCi,Cj ,s
.
So, the total cargo flow from cluster Ci to cluster Cj over the network is equal to f. Now,we want to determine the origin and destination ports of the flow. Repeat the followinguntil f = 0. Select the combination (h, h′) with h ∈ Ci and h′ ∈ Cj with the largest
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expected revenue. Now, allocate as much flow as possible to the combination (h, h′), so
fh,h′ = min(dh,h′ , f),
where dh,h′ is the demand between port h and h′ and fh,h′ is the allocated flow from porth to port h′. Update the flow to be allocated:
f = f − fh,h′ .
Appendix E.3. Feeder network
In the disaggregation phase, cargo flows between ports are determined. We will usefeeder services to ship the cargo from and to ports in the cluster. After an initial feedernetwork is constructed, some methods are described to improve the network. Thesemethods include reallocating demand in order to reduce the capacity on the feeder lines,exchanging ports between feeder lines and adding ports to the main route network. Inthis section, a description of these methods will be given.
Appendix E.3.1. Initial feeder network
In first instance, for each port in the cluster (except the central port) a direct feederservice is constructed between this port and the central port of the cluster. Let FC beset of feeder services in cluster C, then
FC := {(c, h, c) : h ∈ C \ {c}} initial feeder network of cluster C,
where c is the central port of cluster C. The capacity of a line F ∈ FC is given by
bf = min {b ∈ B : b ≥ max(fc,h, fh,c)} .
Appendix E.3.2. Reduce feeder capacity
The method to reduce the capacity is performed for each cluster separately. Therefore,we describe the method for a given cluster C. In the algorithm, we will determine andstore the difference in profit of reducing the feeder capacity for each feeder service in thecluster separately. Thus, we select one by one the feeder services in the cluster.
Flow over legs.Let F be the selected feeder line. For this service, we first determine the flow on each legof the feeder line. Let the legs of the line be given by l1, . . . , ln, where n is the number oflegs of the service and let the feeder route be given by p1, . . . , pn, p1 (leg l1 corresponds tothe leg between ports p1 and p2). Furthermore, let
f opi=
∑h∈H
fpi,h
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be the total flow with origin port pi and
fdpi=
∑h∈H
fh,pi
be the total flow with destination port pi Then, the flow on leg 1 ≤ i ≤ n is given by
fli =∑j>i
fdpj+∑j≤i
f opj.
Reduce capacity.Let bc be the current capacity of the feeder service and bn the capacity when we reducethis capacity by one size. Then, the reduction needed on leg li is equal to
yli = max(fli − bn, 0).
That is, we only need to reduce the flow over a leg if it is currently larger than the newcapacity of the service.
Valid combinations to exchange demand.The flow over a leg can be reduced by changing the origin and/or destination port of acargo flow. Since cargo flows between ports are obtained from cargo flows between clusters,there are multiple feasible allocations of the flow to the port pairs. We determine the portcombinations between which cargo flows can be exchanged in order to reduce the flowover F.
Lo := {((h1, h2), (h3, h2)) : h1 ∈ F, h2 /∈ C, h3 ∈ C \ F} combinations with origin in C.
Ld := {((h1, h2), (h1, h3)) : h1 /∈ C, h2 ∈ F, h3 ∈ C \ F} combinations with destination in C.
L := Lo ∪ Ld valid port combinations.
The set L consists of all valid combinations of port pairs between which cargo can beexchanged to reduce the cargo flow on feeder line F. If ((h1, h2), (h3, h4)) ∈ L, then thecargo flow over F can be reduced by increasing the satisfied demand between ports h3
and h4 and at the same time reducing the demand between ports h1 and h2 with the sameamount. In this way, the total demand satisfied between clusters does not change as longas ports h1 and h3 belong to the same cluster and ports h2 and h4 belong to the samecluster. Furthermore, we only want to change the flow over the feeder network in clusterC, so we will add the restriction that the port that does not belong to C is not allowedto be changed. In Lo the origin port belongs to C and thus we see that the destinationport in both port pairs is the same (namely h2) and, similarly, for Ld the origin port (h1)is the same for both pairs. Furthermore, we want to reduce the cargo flow over line F, sowe do not want to shift cargo from one leg of service F to another leg. Therefore, we add
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the restriction that the new port in cluster C is not allowed to be on line F. Thus, porth3 in the definition of both Lo and Ld is an element of C \ F (all ports in C that are notvisited on line F ).
Exchange demand between port pairs.For each combination ((h1, h2), (h3, h4)) of port pairs in L, the revenue decrease per unitof exchanging cargo from the first demand pair to the second is given by rh1,h2 − rh3,h4 ,
where ra,b denotes the revenue of satisfying one unit of demand from port a to port b.
Select the combination with the lowest decrease in revenue. We want to exchange asmuch cargo as possible from the first port pair to the second pair. Clearly, the maximumamount that can be exchanged is bounded by the amount of cargo that is currentlytransported between the first port pair and the unsatisfied demand between the new portpair. Furthermore, it is bounded by the free capacity of the feeder line over which thenew flow has to be transported.
Let po denote the port in C of the first port pair, pn the port in C of the secondport pair and p′ the port not in C that is part of both port pairs. Furthermore, let Da,b
and Dsata,b be the demand and satisfied demand between ports a and b respectively. The
demand to be exchanged is bounded by
Dexd =
{min(Dsat
p′,po , Dp′,pn −Dsatp′,pn) if p′ is the origin port,
min(Dsatpo,p′ , Dpn,p′ −Dsat
pn,p′) if p′ is the destination port.
Exchanging demand will also change the flow on the feeder lines containing po and pn,
but only the flow on the new feeder line is relevant in this case, because this flow will beincreased. Let Fn be the new feeder service. The definition of L guarantees that Fn ̸= F.
If p′ is the origin ports of the pairs, then the flow between the port pairs will be on thefeeder line for all legs before port pn, while it will be on the feeder line for all legs afterport pn if p′ is the destination ports Let pn be the k-th port of feeder line Fn and let n
the length of the feeder line. Furthermore, let fnli
be the flow on feeder line Fn over leg li.
Then, the amount of cargo that can at most be exchanged is bounded by
Dexf =
min1≤i<k
bFn − fnli
if p′ is the origin port,
mink≤i≤n
bFn − fnli
if p′ is the destination port.
Thus, the maximum amount of cargo that can be exchanged between the combinationsof port pairs is given by:
Dex = min(Dexd , Dex
f ).
The flow over the feeder services has to be updated when we exchange this amount.
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Thereto,
f oli=
{f oli−Dex 1 ≤ i < j if p′ is the origin port,
f oli−Dex j ≤ i ≤ m if p′ is the destination port,
where port po is the j-th port on feeder line F and f oli
is the flow over leg li of feeder lineF and m is the length of feeder service F. Similarly,
fnli=
{fnli+Dex 1 ≤ i < j if p′ is the origin port,
fnli+Dex j ≤ i ≤ m if p′ is the destination port.
The costs of exchanging the demand is given by:
Cex = Cex +
{(rp′,po − rp′,pn + chpn − chpo)D
ex if p′ is the origin port,
(rpo,p′ − rpn,p′ + chpn − chpo)Dex if p′ is the destination port,
where chp is the handling cost per unit in port p and Cex is initialized at 0 each time weconsider a new feeder service F.
Next, we can update the reduction needed on each leg and repeat this procedure untileither all valid combinations of port pairs are considered or the reduction needed equalszero on each leg. If the capacity of the feeder service can be reduced (the reduction neededequals zero for each leg of the service), then the profit is given by
P ex = ccbc + cfbc − (ccbn + cfbn)− Cex,
where ccb is the capital and operating costs on the feeder line F when a ship with capacityb is used and cfb is the fuel costs on F for a ship with capacity b.
Appendix E.3.3. Exchange port between feeder services
Next, we describe the method to exchange a port between two feeder services. Thecargo allocation is not changed in this method, so we can consider the different clustersseparately. Thereto, we first select a cluster C. For each combination of two feeder linesin cluster C and each port on the first feeder line, we will consider the increase in profitwhen we exchange this port from the first service to the second service. Thus, we selecttwo feeder service F1 and F2 in C. Furthermore, let q be a noncentral port on feeder lineF1. Then, we will determine at which location it is most profitable to add port q to lineF2 and how large the profit increase is.
Let (p, p′) be a consecutive port combination on feeder service F2. First, determine thecost of the feeder services F1 and F2 as they are before we exchange a port:
Cold = ccbf1+ cfbf1
+ ccbf2+ cfbf2
,
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where bf1 and bf2 are the capacities of F1 and F2 respectively and ccb and cfb are the capitaland operating and fuel costs for a ship with capacity b respectively.
Let q now be visited in between ports p and p′ on feeder service F2, that is, removeleg (p, p′) from F2 and add legs (p, q) and (q, p′) to F2. Since q will now be visited on lineF2, we remove it from line F1. The method described in Section Appendix E.3.2 can beused to determine the new flows on the feeder services F1 and F2, because the satisfieddemand between port pairs is known. When the flow over each leg is known, the capacityof the feeder service can be determined by:
bf = min
{b ∈ B : b ≥ max
1≤i≤nfli
},
where the feeder service is given by l1, . . . , ln.
The costs of the feeder services F1 and F2 after exchanging port q can again be calcu-lated by:
Cnew = ccbf1+ cfbf1
+ ccbf2+ cfbf2
,
where bf1 and bf2 are now the new capacities on the feeder lines. The increase in profit isgiven by:
P q = Cold − Cnew.
Repeat this procedure until all consecutive port combinations on F2 are considered. Then,repeat until all noncentral ports on F1 are considered.
Appendix E.3.4. Add ports to main routes
In the aggregation phase, we decided to create port clusters in order to reduce thecomputation time of the cargo-routing model. Central ports of the clusters are visitedon the main route network, while all other ports are currently only visited on the feedernetwork. However, it might be profitable to visit some of those ports on the main network.Ports are clustered based on distance to the central port, so if the central port is visited ona main route, the additional distance that has to be sailed in order to include a noncentralport to the main route will in general be quite small. In this section, we describe a methodto add noncentral ports to the main routes.
First, select a main route R and determine the clusters C1, . . . , Cn that are visited onR. If a cluster is visited twice on a route, we consider it to be two different clusters. So,a distinction is made between the cluster when it is visited on the eastbound part of theroute and the cluster when it is visited on the westbound part of the route. So, eachcluster that is visited on a route is unique for the route. Consider a cluster C on routeR and let q be a port that belongs to cluster C and is not yet visited on route R, thatis, q ∈ C \ R. Let (p, p′) be a consecutive port combination on main route R, satisfying
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p ∈ C and/or p′ ∈ C. Furthermore, let F be the feeder service on which port q is currentlyvisited (q ∈ F ).
Cargo reallocation.Let q now be visited in between ports p and p′ on main route R′, that is, let R′ = R
and remove leg (p, p′) from R′ and add legs (p, q) and (q, p′) to R′. Since it is probablynot feasible to (un)load all cargo from/to port q on route R (some cargo might be on adifferent route, or the ship capacity will not suffice to transport all cargo directly via routeR), we cannot remove port q from the feeder line F . We want to reallocate as much cargoas possible from feeder service F to main route R, because the handling and transhipmentcosts will be reduced in this way. The amount of cargo that can be reallocated is firstof all restricted by the total amount of cargo from/to port q that is present on the ship.Furthermore, it depends on the unused capacity of the ship on the additional legs. Todetermine how much cargo can be reallocated according to the unused capacity of theship, first the position of the inserted port q with respect to the center of the cluster hasto be determined.
Two situations can be distinguished: the central port of the cluster is already visitedwhen port q is visited on the main route, or the central port of the cluster has still to bevisited when port q is visited. Figure E.1 shows the two possibilities. In the figures, onlythe central ports of the clusters and port q are considered, but all conclusions that willbe drawn, will also hold when more ports are on the route.
Now, consider the left figure, where port q belongs to cluster C and is visited afterthe central port of the cluster. In the original route, the ship visits first the central port cof cluster C and directly thereafter the central port c′ of the cluster C ′. Thus, the cargoflows from and to port q are (un)loaded in c. Now, let fc,c′ be the flow from port c to portc′. The cargo flow with destination port q will be unloaded in port c, so this flow is notincluded in flow fc,c′ . On the other hand, the cargo flow with origin port q is included inflow fc,c′ , because it is loaded in port c.
When port q is added to the main route after the central port c in the cluster, flows fc,qand fq,c′ have to be determined. The difference with the original situation is that the cargoflow from and to port q is now (un)loaded in port q instead of in port c. Thus, the cargoflow to port q is included in flow fc,q, while the flow from port q is not included. Combiningthis with the flows included in flow fc,c′ , it can be seen that fc,q = fc,c′ − qoutf + qinf , whereqinf is the amount of cargo flow unloaded in port q (flow with port q as destination) andqoutf is the amount of cargo flow loaded in port q (flow with origin port q). In flow fq,c′ thecargo flow to port q is not included, where the flow from port q is included, so it holdsthat fq,c′ = fc,c′ . Thus, qoutf is not included in fc,q and included in both fc,c′ and fq,c′ , soall cargo with origin port q on ship route R can be loaded in port q, without exceeding
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the capacity of the ship. However, the amount of cargo that can be unloaded in port q isbounded by qinf ≤ bR − fc,c′ + qoutf , since this cargo is included in the new flow fc,q but notin the old flow fc,c′ .
fc,q fq,c′
fc,c′
C
C ′
q qfc′,q
fq,c
fc′,c
C ′
C
Port q is visited after the center of the cluster Port q is visited before the center of the cluster
c
c′
c
c′
Figure E.1: Example of the positioning of port q with respect to the central port c and c′ ofthe cluster
The other situation is shown in the right figure. In this case, port q belonging tocluster C is visited before the central port c of the cluster. The flow on the initial routebetween central ports c′ and c is denoted by fc′,c. In this case, the flow to port q is includedin flow fc′,c, while the flow from port q is not included, because it will be loaded in thecentral port c of cluster C. Now, consider flow fc′,q between central port c′ and port q.
In this flow, the cargo flow to port q is included and the cargo flow from port q is notincluded. Thus, in this case fc′,q = fc′,c. The cargo flow to port q is now unloaded in portq, so this flow is not included in fq,c. However, the flow from port q is already loaded inport q, so is included in fq,c. Together with the flows included in fc′,c, it can be found thatfq,c = fc′c − qinf + qoutf , where qinf and qoutf have the same definitions as above. Now, allcargo to port q can be unloaded without exceeding the capacity of the ship when sailingto port q, but the amount of flow that is loaded is bounded by qout ≤ bR−fc′,c+ qinf , sincethis cargo is included in the new flow fq,c but not in the old flow fc′,c.
The amounts of flow (un)loaded in port q are equal to
qout = min(qoutf , qouts )
andqin = min(qinf , qins ),
where qouts and qins are the amounts of cargo present on the ship on route R with port q
respectively as origin and destination port. Thereafter, the new flows can be determinedusing the formulas for fa,b given above. Furthermore, qin and qout can be used to updatethe flows on the feeder service visiting port q by subtracting the flows from the legs overwhich it should be transported. When no flows are loaded and unloaded anymore in portq on the feeder service, the port can be deleted from the feeder service.
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Cost reduction.Which costs incurred at the main and feeder network are relevant in this method depend onwhere in the solution algorithm this procedure is executed. When the methods to reducethe feeder network are not yet performed, only the handling costs on the feeder networkare considered to be relevant. However, when these methods are already performed alsothe capital, operating, fuel and port costs of the feeder network are relevant. The handling,port, capital, operating and fuel costs of the main network are relevant in both cases.
The route costs crR and crR′ consisting of the capital, operating, port visit and fuel costsof the main routes R and R′ can be obtained from the method to determine the optimalspeed, which is described in Section 3.2.2. The new capacity needed on the feeder route canbe obtained from the method described in Section Appendix E.3.2. Thereafter, the newroute costs of the feeder route can easily be computed by adding the capital, operating,port visit and fuel costs, because the route duration and speed are fixed. Furthermore,the difference in handling costs can be obtained using qin and qout.
After the cost reduction is determined, repeat this procedure for a new consecutiveport combination (p, p′) on route R with p ∈ C and/or p′ ∈ C until as long as they arenot all considered yet. Next, repeat until all noncentral ports q ∈ C \R are considered, allclusters C ∈ R are considered and finally until all routes R are considered. Then, add theport for which the cost reduction is largest to the main route and at the location wherethis cost reduction will be obtained. This method is repeated until no cost reduction canbe obtained anymore by adding a port to a main route.
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