The following presents results of our approach on LINERLIB dataset.
LINERLIB
The LINERLIB benchmark suite presents industry-standard instances for shipping network design problems. Introduced by Brouer et al. (2013), the suite offers extensive documentation and comprises seven instances, gradually increasing in complexity based on the number of ports, demands, and vessels. This work focuses on the base case, where no modifications to the original data are made. The data was parsed into the format of our API. The following table summarizes the characteristics of each instance after parsing.
| Instance | Baltic | WAF | Mediterranean | Pacific | World Small | Europe Asia | World Large |
|---|---|---|---|---|---|---|---|
| # Ports | 12 | 19 | 39 | 45 | 47 | 111 | 197 |
| # Demands
# Containers |
22
4 904 |
38
8 541 |
369
7 545 |
722
44 180 |
1 764
138 247 |
4 000
76 944 |
9 630
138 914 |
| # Vessels | 6 | 42 | 21 | 100 | 263 | 176 | 501 |
Assumptions
To ensure a fair comparison with previous work, parameters were set as follows:
- Minimum port stay time: 24 hours for all ports
- Minimum transshipment time: 48 hours for all ports
- Bunker cost: 600 USD per metric ton
- Demand rejection penalty (or opportunity cost): 1000 USD for all demands
As suggested by the LINERLIB authors, we only present results using revised transit times.
We only report results on the 5 largest instances, as Baltic and WAF are usually used for tuning purposes.
One of the key advantages of the API is its ability to clearly define leg candidates in terms of time and costs. This leaves all cost modeling to the user, eliminating ambiguity in the definition of optimality. However, this advantage comes at the cost of time discretization. Unless otherwise stated, leg candidates' durations are generated with a 12-hour discretization.
Baseline
To ensure a fair evaluation, our techniques are compared with the most recent publicly available vessel services from LINERLIB. It is important to note that the LINERLIB services were optimized without regard to demand transit times. Considering transit times significantly complicates the problem, requiring joint scheduling of all vessel services and demands.
To better align with LINERLIB's vessel services, we included additional leg candidates with the closest rounded hour in the input. Our approach, however, does not utilize these additional legs and initiates the process anew.
To account for transit times in the LINERLIB vessel services, demands were routed using a column generation-based optimization assuming a maximum of three transshipments.
Metrics
When comparing methods, the following metrics are considered:
- Cost related metrics:
- Profit: The objective to be maximized, defined as revenue minus vessel services and transshipment costs.
- Revenue: Sum of the revenue of fulfilled containers. The revenue of a container is its freight rate minus the loading and unloading costs plus the opportunity cost (or demand rejection penalty).
- Vessel service costs: Operating costs of vessels deployed on all services, including bunker, charter and port stay costs.
- Transshipment costs: Handling costs related to transshipments.
- Other key metrics:
- Number of shipped containers
- Number of vessels used
For comparison with existing work, where the opportunity cost of each container is set to 1000$, conversion formulas to compute the profits presented in this page are:
- from LINERLIB:
total_container_count* 1000 -linerlib_half_yearly_objective* 7 / 180. - from Koza:
total_container_count* 1000 -koza_objective.
Results
The next table presents a comparison of our approach with the baseline. Solution files for our approach and the baseline are available to download on github.
| Mediterranean | Pacific | World Small | Europe Asia | World Large | ||
|---|---|---|---|---|---|---|
| # Containers
# Vessels |
7 545
21 |
44 180
100 |
138 247
263 |
76 944
176 |
138 914
501 |
|
| Our approach | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
5.23 M$
7.47 M$ 2.05 M$ 0.20 M$ 5 391 16 |
43.21 M$
66.88 M$ 22.68 M$ 0.98 M$ 39 621 96 |
173.11 M$
266.78 M$ 86.89 M$ 6.78 M$ 106 861 236 |
88.50 M$
140.56 M$ 47.86 M$ 4.20 M$ 55 493 146 |
119.38 M$
209.07 M$ 81.76 M$ 7.93 M$ 78 983 311 |
| Baseline | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
2.63 M$
5.83 M$ 3.07 M$ 0.14 M$ 4 097 21 |
22.52 M$
47.81 M$ 24.78 M$ 0.51 M$ 29 343 99 |
70.78 M$
173.84 M$ 98.90 M$ 4.17 M$ 76 829 259 |
40.63 M$
115.04 M$ 70.77 M$ 3.64 M$ 46 434 172 |
|
| Delta / baseline | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
99%
28% -33% 47% 32% -24% |
92%
40% -8% 93% 35% -3% |
145%
53% -12% 63% 39% -9% |
118%
22% -32% 16% 20% -15% |
Considering transit times in optimization significantly increases the potential profit of a shipping network. Across all instances, the profit increase is nearly 100%. Most of the profit increase comes from additional revenue as more containers are shipped. However, it can also be achieved with a decrease in vessel services costs by deploying only profitable services. This can potentially unlock additional revenue from chartering out these vessels.
The following table compares profit numbers made available by Koza et al. (2020). We would like to emphasize that due to the lack of publicly available data, this comparison is not made in depth and we are not fully confident that the same assumptions were made for both studies.
| Mediterranean | Pacific | World Small | Europe Asia | World Large | |
|---|---|---|---|---|---|
| Our approach | 5.23 M$ | 43.21 M$ | 173.11 M$ | 88.50 M$ | 119.38 M$ |
| Koza et al. (2020) | 4.80 M$ | 41.40 M$ | 170.85 M$ | 79.89 M$ | |
| Delta / Koza et al. (2020) | 9% | 4% | 1% | 11% |
Comparison in the case with no transit time
We compared our approach to LINERLIB's vessel services in a simplified scenario without considering transit times. It is worth noting that even on the specific criteria that LINERLIB's services were designed to optimize, our approach demonstrates superior results in terms of profitability, as indicated in the final table. Solution files for our approach and the baseline are available to download on github.
| Mediterranean | Pacific | World Small | Europe Asia | ||
|---|---|---|---|---|---|
| # Containers
# Vessels |
7 545
21 |
44 180
100 |
138 247
263 |
76 944
176 |
|
| Our approach | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
6.49 M$
9.46 M$ 2.67 M$ 0.30 M$ 7 003 19 |
48.56 M$
68.55 M$ 19.09 M$ 0.90 M$ 41 089 99 |
204.11 M$
293.52 M$ 82.48 M$ 6.93 M$ 116 474 263 |
109.84 M$
169.94 M$ 54.62 M$ 5.48 M$ 67 134 173 |
| Baseline | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
6.21 M$
9.57 M$ 3.07 M$ 0.29 M$ 7 075 21 |
47.24 M$
72.87 M$ 24.78 M$ 0.85 M$ 43 459 99 |
195.48 M$
302.26 M$ 98.90 M$ 7.88 M$ 123 056 259 |
107.30 M$
183.57 M$ 70.77 M$ 5.50 M$ 73 614 172 |
| Delta / baseline | Profit (objective)
Container revenue Vessel service costs Transshipment costs # Shipped containers # Used vessels |
5%
-1% -13% 4% -1% -10% |
3%
-6% -23% 6% -5% 0% |
4%
-3% -17% -12% -5% 2% |
2%
-7% -23% 0% -9% 1% |