Pickup and Delivery Problem
with Time Windows and Two-Dimensional Loading for Shipbuilding Block
Transportation
Ohhyun Kweona,
Jun Kima, Sang Hun Kimb Byung-In
Kima*
aDepartment of Industrial and
Management Engineering, Pohang University of Science and Technology (POSTECH). dhgus5676@gmail.com, jun1209@postech.ac.kr, bkim@postech.ac.kr
bSamsung Heavy Industries Co. sh2105.kim@samsung.com
*Corresponding
author. Tel.: +82 54 279 2371; Fax: +82 54 279 2870.
Benchmark Instances (click)
Last updated: 2026/01/16
1. Introduction
The many-to-many pickup and delivery problem with time
windows (M2MPDPTW) is a variant of the pickup and delivery problem with time
windows (PDPTW), as classified by request types in Berbeglia
et al. (2007). The M2MPDPTW deals with many-to-many (M-M) requests, in which
pickup and delivery locations can be chosen from multiple alternatives. This
flexibility allows decision-makers to generate more feasible and adaptable
routing schedules.
In the steelmaking industry, M-1 and 1-M requests have
been applied to the transportation of non-motorized Torpedo Ladle Cars, which
are containers used for molten iron, as discussed by Kweon and Kim (2024). In
addition, the shipbuilding industry has adopted M-M requests for transporting
subassemblies. These subassemblies are transferred between quays by barges,
subject to specific time windows. However, unlike land transportation, quay
availability may be restricted due to tidal conditions. To accommodate this,
the shipbuilding industry allows subassemblies to be picked up from or
delivered to alternative quays. These subassemblies are then transported over
land by specialized transporters, and an additional charge is incurred when
such alternatives are used.
Since subassemblies often have irregular shapes, they
are stacked on top of rectangular blocks. Therefore, when loaded onto barges,
these subassemblies can be treated as rectangular items due to the uniform
shape of the blocks beneath them. Accordingly, each request that involves
transporting a subassembly is associated with a rectangular item, referred to
as a block.
The many-to-many pickup and delivery problem with time
windows and two-dimensional (2D) loading constraints (2L-M2MPDPTW) has not yet
been investigated in the literature. The objective of the 2L-M2MPDPTW is to
minimize the total travel cost and additional charges, while accounting for 2D
loading constraints. Reflecting the block transportation characteristics of the
shipbuilding industry, the following assumptions are made:
1) Barges are
heterogeneous.
2) Each barge has
two types of capacity constraints: total weight and unit weight capacity.
3) Some barges may
not have predefined initial locations; if not specified, they are assumed to be
available anywhere at the start of the schedule.
4) Each barge has a
fixed rectangular loading area.
5) All distances
satisfy the triangle inequality.
6) Each request
involves only one item (i.e., one block)
7) Each request may
have alternative pickup and delivery quays, each
associated with different time windows and additional charges.
2.
Benchmark Problems
To the best of our knowledge, the
2L-M2MPDPTW has not been studied yet. Therefore, we introduce 180 new benchmark
instances generated to reflect real-world conditions, including quay
utilization and barge specifications. The generated instances
are categorized based on the number of requests and the number of alternative
combinations. The numbers of requests considered are 10, 25, 50, 75, 100, and
125, labeled as XXS, XS, SS, MM, LL, and XL, respectively. Alternatives for
each pickup and delivery quay are generated based on a binomial distribution
with two trials and probabilities of 25%, 50%, and 75%, labeled as
"25", "50", and "75". The additional charges
incurred by using alternative quays are set identical to the corresponding
travel distances. The number of barges is fixed at 30% of the number of
requests, each with a workhour limit of 400 minutes. All pickup and delivery
time windows are set to 60 minutes. A service time of 5 minutes is required for
loading or unloading a block.
Table 1. Summary of new benchmark instances.
|
Data Group |
Num |
Requests |
Alternatives |
Barges |
|
XXS25 |
10 |
10 |
23.3 |
3 |
|
XS25 |
10 |
25 |
54.8 |
7 |
|
SS25 |
10 |
50 |
112.1 |
13 |
|
MM25 |
10 |
75 |
165.1 |
19 |
|
LL25 |
10 |
100 |
219.8 |
25 |
|
XL25 |
10 |
125 |
288.5 |
32 |
|
XXS50 |
10 |
10 |
42.7 |
3 |
|
XS50 |
10 |
25 |
98.5 |
7 |
|
SS50 |
10 |
50 |
201.2 |
13 |
|
MM50 |
10 |
75 |
286.7 |
19 |
|
LL50 |
10 |
100 |
383.9 |
25 |
|
XL50 |
10 |
125 |
495.2 |
32 |
|
XXS75 |
10 |
10 |
61.5 |
3 |
|
XS75 |
10 |
25 |
152.0 |
7 |
|
SS75 |
10 |
50 |
310.7 |
13 |
|
MM75 |
10 |
75 |
469.7 |
19 |
|
LL75 |
10 |
100 |
628.1 |
25 |
|
XL75 |
10 |
125 |
789.1 |
32 |
Table 1 presents a summary of
the generated data. The second column of Table 1 indicates the number of
instances belonging to each data group. The third column indicates the number
of requests, while the fourth column shows the number of combinations of all
possible pickup and delivery quays. The fifth column presents the number of
barges.
Four input
files are provided in .txt format: "Barge.txt",
"Block.txt", "OD.txt", and "Filelist.txt". All
values in different columns are separated using tab delimiters. The
"Barge.txt" file contains the following four columns:
-
ID:
Identifier of the barge
-
Starting:
Initial quay assigned to the barge
-
TW:
Working hours of the barge
-
Spec
(M, L, W, UM): Capacity specifications of the barge, where each value denotes
mass (or weight), length, width, and unit mass (or weight) capacity,
respectively.
The
"Block.txt" file contains the following four columns:
-
ID:
Identifier of the block
-
Spec
(M, L, W): Specifications of the block, where each value denotes mass (or
weight), length, and width, respectively
-
Pickup
Info: This column contains the list of possible pickup quays. Different quays
are separated using space delimiters. Each quay entry includes, in order, the
quay ID, pickup time window, and the associated additional charge,
sequentially.
-
Delivery
Info: This column contains the list of possible delivery quays. Different quays
are separated using space delimiters. Each quay entry includes, in order, the
quay ID, delivery time window, and the associated additional charge,
sequentially.
All distances
are recorded in an adjacency list format in the "OD.txt" file. The
"OD.txt" file contains the following three columns:
-
From:
departure quay
-
To:
arrival quay
-
Travel
time: travel time between the departure and arrival quays
The
"Filelist.txt" file contains the names of the above three types of
files for each instance.
3.
Computational results
A total of 180 benchmark instances
were tested using the hybrid ALNS algorithm and the MILP model. The detailed
results are presented in Table 2. The ¡°C0,¡± ¡°C1,¡± and ¡°C2¡± denote the objective
value, the total travel time required by the barges, and the additional charges
incurred by selecting alternative quays, respectively. The ¡°L.¡± and ¡°T(s)¡±
represent the lower bound provided by the solver and the computational time,
respectively. The ¡°–¡± indicates that no result was obtained within the time
limit, and the bolded letters indicate the optimal solution. The MILP was not
tested on instances with more than 50 requests, because it was unlikely to
provide either a meaningful lower bound or any incumbent solution.
Table 2. Results of benchmark instances.
|
Data |
ALNS |
MILP |
Data |
ALNS |
MILP |
||||||||||||||
|
C0 |
C1 |
C2 |
T(s) |
L. |
C0 |
C1 |
C2 |
T(s) |
C0 |
C1 |
C2 |
T(s) |
L. |
C0 |
C1 |
C2 |
T(s) |
||
|
XXS2501 |
525 |
430 |
95 |
1.3 |
525 |
525 |
430 |
95 |
578.7 |
MM5001 |
2665 |
2270 |
395 |
84.2 |
|
|
|
|
|
|
XXS2502 |
585 |
550 |
35 |
1.4 |
585 |
585 |
520 |
65 |
1080.2 |
MM5002 |
2850 |
2120 |
730 |
104.2 |
|
|
|
|
|
|
XXS2503 |
575 |
530 |
45 |
1.3 |
575 |
575 |
530 |
45 |
438.3 |
MM5003 |
2725 |
2000 |
725 |
130.4 |
|
|
|
|
|
|
XXS2504 |
580 |
550 |
30 |
1.7 |
575 |
575 |
470 |
105 |
14539.6 |
MM5004 |
2585 |
2490 |
95 |
106.9 |
|
|
|
|
|
|
XXS2505 |
550 |
550 |
0 |
1.2 |
550 |
550 |
540 |
10 |
222.8 |
MM5005 |
2520 |
2070 |
450 |
204.3 |
|
|
|
|
|
|
XXS2506 |
590 |
570 |
20 |
2.4 |
590 |
590 |
570 |
20 |
2140.3 |
MM5006 |
2550 |
1900 |
650 |
191.2 |
|
|
|
|
|
|
XXS2507 |
655 |
600 |
55 |
1.7 |
655 |
655 |
600 |
55 |
2632.7 |
MM5007 |
2775 |
1830 |
945 |
148.5 |
|
|
|
|
|
|
XXS2508 |
575 |
490 |
85 |
2.7 |
575 |
575 |
490 |
85 |
340.0 |
MM5008 |
2640 |
1860 |
780 |
136.7 |
|
|
|
|
|
|
XXS2509 |
560 |
500 |
60 |
3.0 |
560 |
560 |
500 |
60 |
387.6 |
MM5009 |
2780 |
2140 |
640 |
151.9 |
|
|
|
|
|
|
XXS2510 |
525 |
480 |
45 |
3.4 |
525 |
525 |
480 |
45 |
347.5 |
MM5010 |
2365 |
2140 |
225 |
173.6 |
|
|
|
|
|
|
XS2501 |
1170 |
1010 |
160 |
10.0 |
597 |
¡¡ |
¡¡ |
¡¡ |
7207.5 |
LL5001 |
3120 |
2450 |
670 |
245.0 |
|
|
|
|
|
|
XS2502 |
1170 |
990 |
180 |
10.4 |
377 |
|
|
|
7211.7 |
LL5002 |
2725 |
2090 |
635 |
435.4 |
|
|
|
|
|
|
XS2503 |
1175 |
1100 |
75 |
11.1 |
436 |
|
|
|
7210.3 |
LL5003 |
3080 |
2780 |
300 |
282.2 |
|
|
|
|
|
|
XS2504 |
1120 |
1030 |
90 |
13.0 |
403 |
|
|
|
7202.3 |
LL5004 |
2710 |
2050 |
660 |
633.3 |
|
|
|
|
|
|
XS2505 |
1015 |
940 |
75 |
10.8 |
373 |
|
|
|
7210.5 |
LL5005 |
2910 |
2250 |
660 |
412.0 |
|
|
|
|
|
|
XS2506 |
1175 |
1050 |
125 |
10.3 |
452 |
|
|
|
7202.5 |
LL5006 |
3445 |
2400 |
1045 |
492.6 |
|
|
|
|
|
|
XS2507 |
1105 |
1010 |
95 |
14.4 |
356 |
|
|
|
7204.2 |
LL5007 |
3145 |
2170 |
975 |
472.9 |
|
|
|
|
|
|
XS2508 |
1175 |
1050 |
125 |
10.3 |
449 |
|
|
|
7203.1 |
LL5008 |
3600 |
2450 |
1150 |
305.6 |
|
|
|
|
|
|
XS2509 |
1215 |
1020 |
195 |
9.0 |
442 |
|
|
|
7210.2 |
LL5009 |
3085 |
2530 |
555 |
393.0 |
|
|
|
|
|
|
XS2510 |
1230 |
1100 |
130 |
11.1 |
441 |
|
|
|
7215.3 |
LL5010 |
3630 |
2740 |
890 |
199.3 |
|
|
|
|
|
|
SS2501 |
1815 |
1660 |
155 |
52.0 |
|
|
|
|
|
XL5001 |
3695 |
2810 |
885 |
411.4 |
|
|
|
|
|
|
SS2502 |
2085 |
1840 |
245 |
37.1 |
|
|
|
|
|
XL5002 |
3505 |
2380 |
1125 |
863.2 |
|
|
|
|
|
|
SS2503 |
2125 |
1870 |
255 |
34.8 |
|
|
|
|
|
XL5003 |
3540 |
3300 |
240 |
373.3 |
|
|
|
|
|
|
SS2504 |
2065 |
1800 |
265 |
33.6 |
|
|
|
|
|
XL5004 |
3740 |
2650 |
1090 |
344.9 |
|
|
|
|
|
|
SS2505 |
1960 |
1710 |
250 |
30.7 |
|
|
|
|
|
XL5005 |
3690 |
3100 |
590 |
513.2 |
|
|
|
|
|
|
SS2506 |
1910 |
1630 |
280 |
35.1 |
|
|
|
|
|
XL5006 |
3450 |
3110 |
340 |
595.1 |
|
|
|
|
|
|
SS2507 |
1785 |
1660 |
125 |
40.7 |
|
|
|
|
|
XL5007 |
3840 |
3590 |
250 |
555.1 |
|
|
|
|
|
|
SS2508 |
1645 |
1480 |
165 |
54.0 |
|
|
|
|
|
XL5008 |
3845 |
3410 |
435 |
387.2 |
|
|
|
|
|
|
SS2509 |
1845 |
1710 |
135 |
32.5 |
|
|
|
|
|
XL5009 |
3450 |
3120 |
330 |
790.7 |
|
|
|
|
|
|
SS2510 |
2195 |
2000 |
195 |
34.6 |
|
|
|
|
|
XL5010 |
3530 |
3460 |
70 |
233.2 |
|
|
|
|
|
|
MM2501 |
2330 |
2060 |
270 |
78.7 |
|
|
|
|
|
XXS7501 |
440 |
380 |
60 |
7.7 |
200 |
605 |
460 |
145 |
5408.4 |
|
MM2502 |
2775 |
2560 |
215 |
53.6 |
|
|
|
|
|
XXS7502 |
520 |
400 |
120 |
3.4 |
313 |
605 |
520 |
85 |
5401.7 |
|
MM2503 |
2705 |
2390 |
315 |
71.3 |
|
|
|
|
|
XXS7503 |
525 |
420 |
105 |
3.7 |
350 |
570 |
440 |
130 |
5401.2 |
|
MM2504 |
2210 |
1980 |
230 |
114.9 |
|
|
|
|
|
XXS7504 |
565 |
370 |
195 |
3.9 |
367 |
|
|
|
5407.0 |
|
MM2505 |
2520 |
2270 |
250 |
86.2 |
|
|
|
|
|
XXS7505 |
520 |
410 |
110 |
4.2 |
336 |
575 |
440 |
135 |
5401.0 |
|
MM2506 |
2385 |
2120 |
265 |
94.7 |
|
|
|
|
|
XXS7506 |
525 |
410 |
115 |
5.2 |
284 |
935 |
650 |
285 |
5402.1 |
|
MM2507 |
2625 |
2170 |
455 |
78.3 |
|
|
|
|
|
XXS7507 |
580 |
430 |
150 |
6.4 |
321 |
840 |
640 |
200 |
5405.3 |
|
MM2508 |
2670 |
2270 |
400 |
61.3 |
|
|
|
|
|
XXS7508 |
525 |
330 |
195 |
3.5 |
305 |
715 |
550 |
165 |
5401.5 |
|
MM2509 |
2685 |
2460 |
225 |
65.4 |
|
|
|
|
|
XXS7509 |
595 |
480 |
115 |
3.8 |
318 |
745 |
620 |
125 |
5449.3 |
|
MM2510 |
2725 |
2300 |
425 |
53.5 |
|
|
|
|
|
XXS7510 |
485 |
370 |
115 |
5.1 |
236 |
705 |
510 |
195 |
5402.5 |
|
LL2501 |
3340 |
2750 |
590 |
127.7 |
|
|
|
|
|
XS7501 |
1225 |
950 |
275 |
17.3 |
412 |
|
|
|
7258.6 |
|
LL2502 |
3135 |
2810 |
325 |
131.5 |
|
|
|
|
|
XS7502 |
1135 |
810 |
325 |
13.3 |
344 |
|
|
|
7246.0 |
|
LL2503 |
3310 |
2800 |
510 |
275.0 |
|
|
|
|
|
XS7503 |
1280 |
860 |
420 |
15.3 |
359 |
|
|
|
7265.3 |
|
LL2504 |
2740 |
2590 |
150 |
96.7 |
|
|
|
|
|
XS7504 |
1010 |
750 |
260 |
19.1 |
268 |
|
|
|
7261.4 |
|
LL2505 |
3295 |
3080 |
215 |
165.9 |
|
|
|
|
|
XS7505 |
985 |
760 |
225 |
19.3 |
292 |
|
|
|
7258.2 |
|
LL2506 |
3460 |
2900 |
560 |
101.4 |
|
|
|
|
|
XS7506 |
1045 |
670 |
375 |
26.2 |
191 |
|
|
|
7274.9 |
|
LL2507 |
3125 |
2910 |
215 |
217.1 |
|
|
|
|
|
XS7507 |
990 |
840 |
150 |
19.5 |
317 |
|
|
|
7242.5 |
|
LL2508 |
2780 |
2390 |
390 |
160.7 |
|
|
|
|
|
XS7508 |
1230 |
800 |
430 |
16.0 |
363 |
|
|
|
7267.3 |
|
LL2509 |
3110 |
2900 |
210 |
137.4 |
|
|
|
|
|
XS7509 |
1030 |
820 |
210 |
20.7 |
221 |
|
|
|
7257.6 |
|
LL2510 |
3655 |
3150 |
505 |
155.7 |
|
|
|
|
|
XS7510 |
1040 |
590 |
450 |
23.5 |
261 |
|
|
|
7271.5 |
|
XL2501 |
3785 |
2990 |
795 |
308.8 |
|
|
|
|
|
SS7501 |
1785 |
1490 |
295 |
69.6 |
|
|
|
|
|
|
XL2502 |
3485 |
3270 |
215 |
310.9 |
|
|
|
|
|
SS7502 |
1980 |
1110 |
870 |
62.2 |
|
|
|
|
|
|
XL2503 |
4045 |
3080 |
965 |
322.2 |
|
|
|
|
|
SS7503 |
2200 |
1260 |
940 |
86.8 |
|
|
|
|
|
|
XL2504 |
3460 |
3410 |
50 |
188.9 |
|
|
|
|
|
SS7504 |
1810 |
1160 |
650 |
135.3 |
|
|
|
|
|
|
XL2505 |
3965 |
3530 |
435 |
347.6 |
|
|
|
|
|
SS7505 |
1945 |
1290 |
655 |
73.3 |
|
|
|
|
|
|
XL2506 |
3770 |
3070 |
700 |
255.1 |
|
|
|
|
|
SS7506 |
2020 |
1420 |
600 |
78.3 |
|
|
|
|
|
|
XL2507 |
4080 |
3460 |
620 |
233.7 |
|
|
|
|
|
SS7507 |
1720 |
1380 |
340 |
64.8 |
|
|
|
|
|
|
XL2508 |
4000 |
3860 |
140 |
200.5 |
|
|
|
|
|
SS7508 |
2025 |
1390 |
635 |
86.8 |
|
|
|
|
|
|
XL2509 |
3480 |
3120 |
360 |
223.4 |
|
|
|
|
|
SS7509 |
1820 |
1020 |
800 |
155.8 |
|
|
|
|
|
|
XL2510 |
3680 |
3230 |
450 |
278.7 |
|
|
|
|
|
SS7510 |
1840 |
1280 |
560 |
120.7 |
|
|
|
|
|
|
XXS5001 |
455 |
420 |
35 |
2.8 |
345 |
475 |
420 |
55 |
5408.7 |
MM7501 |
2390 |
1450 |
940 |
521.6 |
|
|
|
|
|
|
XXS5002 |
570 |
460 |
110 |
1.9 |
357 |
590 |
480 |
110 |
5400.7 |
MM7502 |
2470 |
1510 |
960 |
513.7 |
|
|
|
|
|
|
XXS5003 |
625 |
490 |
135 |
2.3 |
625 |
625 |
490 |
135 |
4293.4 |
MM7503 |
2635 |
1470 |
1165 |
202.2 |
|
|
|
|
|
|
XXS5004 |
495 |
310 |
185 |
2.8 |
375 |
515 |
390 |
125 |
5400.7 |
MM7504 |
3005 |
1540 |
1465 |
199.1 |
|
|
|
|
|
|
XXS5005 |
580 |
490 |
90 |
2.2 |
355 |
675 |
550 |
125 |
5400.9 |
MM7505 |
2715 |
1640 |
1075 |
249.0 |
|
|
|
|
|
|
XXS5006 |
540 |
440 |
100 |
3.5 |
540 |
540 |
440 |
100 |
4821.0 |
MM7506 |
2660 |
1760 |
900 |
395.5 |
|
|
|
|
|
|
XXS5007 |
515 |
390 |
125 |
3.3 |
396 |
595 |
440 |
155 |
5401.2 |
MM7507 |
2625 |
1670 |
955 |
217.8 |
|
|
|
|
|
|
XXS5008 |
625 |
550 |
75 |
3.6 |
404 |
960 |
770 |
190 |
5401.1 |
MM7508 |
2815 |
1550 |
1265 |
271.1 |
|
|
|
|
|
|
XXS5009 |
465 |
390 |
75 |
1.6 |
385 |
455 |
400 |
55 |
5401.1 |
MM7509 |
2770 |
1500 |
1270 |
212.9 |
|
|
|
|
|
|
XXS5010 |
515 |
410 |
105 |
3.5 |
420 |
530 |
390 |
140 |
5400.7 |
MM7510 |
2730 |
1500 |
1230 |
513.2 |
|
|
|
|
|
|
XS5001 |
1095 |
880 |
215 |
16.3 |
278 |
|
¡¡ |
¡¡ |
7219.1 |
LL7501 |
3060 |
2860 |
200 |
521.1 |
|
|
|
|
|
|
XS5002 |
1140 |
900 |
240 |
15.2 |
373 |
|
|
|
7225.0 |
LL7502 |
3030 |
1880 |
1150 |
687.1 |
|
|
|
|
|
|
XS5003 |
990 |
810 |
180 |
16.3 |
284 |
|
|
|
7212.0 |
LL7503 |
3200 |
2290 |
910 |
884.0 |
|
|
|
|
|
|
XS5004 |
1120 |
980 |
140 |
14.1 |
386 |
|
|
|
7219.6 |
LL7504 |
3705 |
2070 |
1635 |
877.3 |
|
|
|
|
|
|
XS5005 |
1085 |
800 |
285 |
18.8 |
249 |
|
|
|
7219.0 |
LL7505 |
2865 |
1860 |
1005 |
913.8 |
|
|
|
|
|
|
XS5006 |
1205 |
1080 |
125 |
31.0 |
319 |
|
|
|
7214.7 |
LL7506 |
3665 |
2280 |
1385 |
442.3 |
|
|
|
|
|
|
XS5007 |
1235 |
930 |
305 |
17.8 |
484 |
|
|
|
7211.4 |
LL7507 |
3110 |
3050 |
60 |
275.8 |
|
|
|
|
|
|
XS5008 |
1045 |
940 |
105 |
11.9 |
257 |
|
|
|
7211.8 |
LL7508 |
3500 |
2190 |
1310 |
510.0 |
|
|
|
|
|
|
XS5009 |
895 |
880 |
15 |
11.0 |
308 |
|
|
|
7210.0 |
LL7509 |
3500 |
1970 |
1530 |
876.8 |
|
|
|
|
|
|
XS5010 |
1210 |
820 |
390 |
12.7 |
378 |
|
|
|
7218.2 |
LL7510 |
3195 |
3080 |
115 |
307.2 |
|
|
|
|
|
|
SS5001 |
1915 |
1510 |
405 |
41.8 |
|
|
|
|
|
XL7501 |
3825 |
2480 |
1345 |
924.0 |
|
|
|
|
|
|
SS5002 |
1920 |
1380 |
540 |
64.8 |
|
|
|
|
|
XL7502 |
3615 |
2960 |
655 |
921.4 |
|
|
|
|
|
|
SS5003 |
1975 |
1370 |
605 |
41.3 |
|
|
|
|
|
XL7503 |
4060 |
2790 |
1270 |
857.9 |
|
|
|
|
|
|
SS5004 |
1970 |
1640 |
330 |
57.5 |
|
|
|
|
|
XL7504 |
3845 |
2360 |
1485 |
923.6 |
|
|
|
|
|
|
SS5005 |
1915 |
1440 |
475 |
90.1 |
|
|
|
|
|
XL7505 |
3835 |
3720 |
115 |
751.3 |
|
|
|
|
|
|
SS5006 |
1750 |
1420 |
330 |
52.7 |
|
|
|
|
|
XL7506 |
3555 |
3450 |
105 |
528.6 |
|
|
|
|
|
|
SS5007 |
1815 |
1260 |
555 |
43.3 |
|
|
|
|
|
XL7507 |
3715 |
3000 |
715 |
914.1 |
|
|
|
|
|
|
SS5008 |
1795 |
1520 |
275 |
86.7 |
|
|
|
|
|
XL7508 |
3870 |
3730 |
140 |
666.9 |
|
|
|
|
|
|
SS5009 |
1815 |
1340 |
475 |
81.0 |
|
|
|
|
|
XL7509 |
3340 |
3250 |
90 |
920.4 |
|
|
|
|
|
|
SS5010 |
1830 |
1580 |
250 |
37.4 |
|
|
|
|
|
XL7510 |
4000 |
2290 |
1710 |
928.2 |
|
|
|
|
|
Reference
Berbeglia, G., Cordeau, J. F., Gribkovskaia, I., & Laporte, G. 2007. Static pickup and
delivery problems: a classification scheme and survey. TOP 15:
1–31.
Kweon, O., & Kim, B. I. 2024.
Many-to-many locomotive routing problem for the steel industry. International
Journal of Production Research: 1–24.