Optimization of container ship route and speed in Public health emergency environment
Published Online: Mar 19, 2025
Received: Nov 03, 2024
Accepted: Feb 14, 2025
DOI: https://doi.org/10.2478/amns-2025-0487
Keywords
© 2025 Shengtong Guo et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
In container shipping business, route selection and transport speed optimization have been the core topics of concern for ship owners and shipping companies. With the continuous development of globalized trade, the demand for container transport between Chinese ports is increasing, and how to ensure that the cargoes arrive at their destinations safely, efficiently and on time through scientific decision-making has become the key to competition in the industry [1–4].
Route selection and transportation speed optimization are of great significance for ship owners and shipping companies. First of all, reasonable route selection can ensure that the ship avoids potential risk areas during navigation, such as the high incidence of piracy, bad weather areas, etc., so as to guarantee the safety of the cargo [5–8]. At the same time, optimizing the transport speed can reduce the waiting speed of the ship on the way, improve the turnover rate of the ship, and then reduce the operating costs. Secondly, route selection and transportation speed optimization are crucial to meet customer demand. In today’s competitive shipping market, customers’ needs are increasingly diversified, and higher requirements have been put forward for transportation speed, transportation cost, service quality and other aspects [9–12]. Shipowners and shipping companies need to optimize route selection and transportation speed to meet the different needs of customers, improve customer satisfaction, and thus win market share. Finally, route selection and transport speed optimization also help to promote the sustainable development of the entire shipping industry [13–16]. By reducing the speed of ships en route, energy consumption and carbon emissions can be reduced, which is conducive to environmental protection and energy saving. At the same time, optimizing route selection also helps to improve the transportation efficiency of ships, reduce logistics costs and promote the development of global trade [17–20].
Under the spread of coronavirus pandemic and the strict quarantine requirements set up in some ports, ships sailing from or passing through areas with severe pandemic may encounter a long waiting time for the quarantine in a certain port. Then, how to optimize the total operating costs by optimizing the ship’s routes and speed is an urgent problem for international voyage ships. Under the mentioned background, this study investigates the modeling of container ship routing and speed optimization under the pandemic situation, and puts forward a proposal of ship routing optimization, for shipping companies can better respond to the global scope of the region’s pandemic prevention and control policies.
Set the ship speed limit by complying with the design speed and the minimal speed, and set the minimal speed to avoid engine stall or non-optimal fuel consumption.
Highlighted that the calculation of optimal speed originates from discrete speed sets since shipping companies usually have fuel consumption data for a range of discrete speeds, instead of based on a function. In the section below, fuel consumption data from shipping companies at different speeds are fitted to give an approximate fuel consumption between these speeds to obtain a fuel consumption graph. There are minimal and maximal speed limits for ship speed. When the speed limit is lower than this minimum, the engine of the ship may stall or fuel consumption may become sub-optimal. The ship’s performance determines the maximum speed limit.
Assuming that the planned route of the shipping company is to leave from the pandemic focus area, and the port in the middle is a port with strict pandemic prevention and control measures (i.e., it will take ships 14 days to from the departure time of the key pandemic area to dock at the port on the 15th day), and finally arrive at the terminal port. The mentioned assumption originates from actual regulations in some regions (e.g., the Directorate General of Shipping (DGS) in India, Turkish ports and Bahraini ports where it is clearly stated that ships that have not exceeded the quarantine period (14 days) from the time of departure of the ship) from the pandemic focus nation or regions are prohibited from berthing in their ports. Furthermore, the mentioned ships will be required to berth at an anchorage away from the port till the 14-day period expires, without any restrictions if the arrival time at Bahraini ports from the pandemic focus nation’s port is longer than 14 days.
Sets
J: The set of sailing segments on the route where the ship sails along the curve, J = {1, 2, …, N}
P: The set of ports where ships call in the route of the voyage
V: The set of discrete speed points of ships
Parameter
Decision variables
On the whole, the cost of each route consists of fuel cost, in port cost (light oil + port disbursement account + shore power fee) as well as fixed cost. In addition, if the ship skips from the port restricted by pandemic situation, the skipping cost (mainly considering the freight transfer fee) of the ship will be generated. The total cost of each voyage is calculated in two cases, i.e., no port skipping and port skipping. Schematic diagram of a ship skipping over the port is shown in Figure 1.
Schematic diagram of ship skipping over the port
The mathematical model can be formulated as follows:
Among it
The constraints are as follows:
When rigorous quarantine measures are taken to cope with global health and safety emergencies in certain ports, ships can optimize their cost by adapting their port of call strategy to the actual route.
The objective function of this model is to minimize the total cost of ship sailing, as expressed in Eq. 1; Eq. 2 represents the total cost under the decision of choosing not to skip from the port; Eq. 3 represents the total cost under the decision that the ship should compensate for liquidated damages after choosing to skip port; Eq. 4–7 express the constraint conditions, Eq. 4 indicates that there is a maximal and minimal limit on the ship’s sailing speed, Eq. 5 indicates that the total time for a ship to sail from a port in a key pandemic area to a port with pandemic prevention and control measures plus the waiting time for quarantine at anchorage should be greater than or equal to 14 days; Eq. 6 and 7 express binary decision variables limited between 0, 1 respectively.
For the model above, Singapore port has been selected as the port with pandemic prevention and control treasures. The policy and regulations issued by Singapore point out that “for the arrival ships of crew / passengers going to mainland China, France, Germany, Iran, Italy, South Korea and Spain over the past 14 days”, Singapore will implement a 14-day quarantine measure. In other words, ships from the mentioned areas for less than 14 days from the port of departure need to be quarantined at the anchorage, and loading and unloading operations can only be carried out after 14 days. The model in the previous section analyzes whether a ship chooses to skip ports to optimize costs.
The selected sailing routes are presented below (Table 1 & Figure 2):
Map of route
Overview of case analysis route
| Route | Sailing route |
|---|---|
| Route 1 | Incheon-Qingdao-Shanghai-HongKong-Singapore-Port Klang |
| Route 2 | Incheon-Qingdao-Singapore-Port Klang |
The distance between each port applied in the case is listed in Table 2. This study selects a 4248TEU container ship, the maximal speed limit is 23.3 knots, with the minimal speed limit assumed to be 8 knots. When the container ship is below such a minimal speed limit, the engine of the ship may stall, or fuel consumption may turn non-optimal. Furthermore, the schedule of the ship should be given. The shift time is calculated as the sailing time between the two ports (Table 2) and the operating time in port (Table 3).
Distances of route legs in nautical miles
| Leg | Distance | Time (days) |
|---|---|---|
| Incheon-Qingdao | 377.2 | 1.1 |
| Qingdao-Shanghai | 484.4 | 1.4 |
| Shanghai-HongKong | 877.9 | 2.7 |
| HongKong-Singapore | 1477.8 | 4.5 |
| Singapore-Port Klang | 453.1 | 1.4 |
| Qingdao-Singapore | 2840.1 | 8.6 |
| Shanghai-Singapore | 2355.7 | 7.2 |
Port operation time and port disbursement account
| Port | Time in port (days) | Port disbursement account ($) | If shore power installed | Shore power unit consumption (kWh / time) |
|---|---|---|---|---|
| Incheon | 1.2 | 17729 | NO | - |
| Qingdao | 0.68 | 28325 | YES | 935.7 |
| Shanghai | 0.83 | 30126 | YES | 528.8 |
| HongKong | 0.98 | 18029 | NO | - |
| Singapore | 0.95 | 15028 | NO | - |
| Port Klang | 0.83 | 32444 | NO | - |
For the two sailing routes in the case, 120 containers are assumed to be loaded and unloaded in Singapore port. Moreover, if the cargo is unloaded in the port of Singapore, a penalty of $400 / TEU will be caused. The average price of fuel and light oil for the last six months is exploited. The daily fixed cost of the vessel includes numerous elements (e.g., crew wages, supplies, maintenance and insurance). Accordingly, all expenses in a year are averaged to $6,829 per day after the calculation.
In Table 2, the distance between two ports on the two routes and the planned sailing time between each port in the sailing schedule are listed. Table 3 lists the loading and unloading times, the port disbursement account, whether shore power equipment is installed, and the single consumption of shore power for the respective port involved in the case. In addition to the port disbursement account, the average cost of ship operation and fuel/shore power consumption costs are taken into account. Accordingly, the data basis is laid for the subsequent practical optimization.
As mentioned in the existing hypothesis, the fuel consumption of a ship is related to its sailing speed. The case study uses real data from an actual ship, and by fitting the fuel consumption data for the ship at different speeds to give an approximation of the fuel consumption between these speeds, a fuel consumption graph is obtained (Figure 3).
Fuel consumption per speed for ship sailing a given distance of 500 nautical miles
As listed in Table 4, due to the pandemic, it took 4.5 days to sail from Hong Kong Port to Singapore Port in Route 1. When the ship arrives in Singapore, it should be quarantined for 9.5 days at anchorage before berthing, with a total cost of $638279.27. By optimizing the sailing speed of the ship, the cost is reduced to $622610.12, saving US$15669.15. However, when the ship skips the port, even under a certain default cost, the total cost is $60,1010.02, thereby saving another $21,600 by optimizing the speed. Accordingly, in the sailing, the decision-making of skipping port will generate the optimal cost.
Calculation results of operating costs as impacted by pandemic situation
| Route | Cost (no port skipping) ($) | Cost (port skipping) | |
|---|---|---|---|
| Cost (under original speed) | Cost (under optimized speed) | ($) | |
| Route 1 | 638279.27 | 622610.12 | 601010.02 |
| Route 2 | 546390.81 | 516092.57 | 539193.25 |
As shown in Table 5, route 2 travels from Qingdao Port to Singapore Port, with 8.6 days en route and 5.4 days waiting in quarantine at anchor. The total cost of sailing and waiting at the original speed is suggested as US$546,390.81, which becomes US$539,193.25 after a port skipping, with a saving of US$7,197.56. However, if the speed is optimized during the voyage without skipping the port, the total cost will decrease to US$516,092.57, with a saving of US$23,100 compared with a port skipping. Thus, in Route 2, the optimal solution is to comply with the original route for the call after optimizing the speed. Thus, the choice of the optimal routes for a ship after being affected by the pandemic is associated with the voyage. The closer the ocean route is, the more likely it is to be affected. For this reason, a port skipping incident occurred, while the ocean route was relatively less affected.
Speed optimization and quarantine waiting time
| Route | Original speed | Waiting time for quarantine | Optimized speed | Waiting time for quarantine |
|---|---|---|---|---|
| Route 1 | 13.68 | 9.5 | 8 | 6.3 |
| Route 2 | 13.76 | 5.4 | 8.45 | 0 |
Table 6 shows that the total operating costs for Route 1, which is not affected by the pandemic, reaches US$568,600.95 and the total cost for Route 2 is US$506,784.19. As indicated from the comparison of Table 6 with Table 4, the optimal option for Route 1 under the effect of the pandemic is to skip the port, while the optimal option for Route 2 is to call at the original port and optimize the speed. This is an increase of US$32,409 compared to the cost without the pandemic. The cost of Route 2 has increased by US$9,308 due to the pandemic.
Cost calculation results of original voyage without pandemic situation
| Route | Time (days) | Cost ($) |
|---|---|---|
| Route 1 | 16.57 | 568600.95 |
| Route 2 | 14.76 | 506784.19 |
Analysis on the effect of loading and unloading volume
The model’s final decision will be influenced by the strict control of containers loaded and unloaded at the port in response to the pandemic. According to Table 7, the total cost of the corresponding voyage and the optimal scheme are determined by calculating the different loading and unloading volume of Singapore port in Route 1 In Route 1, with the increase in the container loading and the unloading volume, the total cost of the voyage under the decision of skipping port is suggested to rise, as well as the optimal decision. The optimal decision for loading and unloading 120 TEU refers to skipping the port, with a total cost of US$601,010.02. The optimal decision for loading and unloading 180 TEU is to optimize the speed without skipping the port, with the minimal total cost.
Analysis of fuel price impact
The present section analyzes whether the fluctuation of fuel prices impacts the optimization of ship routes or speeds. Route 1 is selected for the case analysis, and the mentioned fuel price of 610 $/ T is extended upward and downward to 510, 560, 660 and 710 $/ T. Table 8 lists the calculated results. With the fluctuation of fuel prices, the total cost of choosing a port-skipping strategy is suggested to be always optimal. However, with the increase in fuel prices, the difference between the total cost of the port skipping optimization plan and the speed optimization plan decreases continuously.
Analysis of the effect of the distance between the strictly controlled port and the next port
In the present section, the goods liquidated damages attributed to port skipping in the model is transformed into the cost of transporting goods to the destination port by other transshipment methods (e.g., trains and trucks). In such a case, the distance from the port with strict prevention and control measures to the next port will affect the cost of transshipment required in depth. Based on the example analysis, Table 9 indicates that the distance between the two ports will affect the choice of ship routing strategy. Under the distance between Singapore Port and Port Klang in Route 1 reaching 453.1 nautical miles or 600 nautical miles, the optimal strategy refers to skipping the port and unloading the cargo. Under the distance between the two ports reaching 750 nautical miles, the optimal strategy refers to optimizing the speed without skipping the port.
Analysis the range of port quarantine period
This section analyzes whether the quarantine period at the port has an impact on optimizing the ship’s path or speed. Route 1 is selected for case analysis, and the above port quarantine period of 14 day is extended upward and downward to 10 and 18 days. The calculation results are obtained in Table 10. Table 10 shows that the range of quarantine period will affect the choice of the best strategy. When the quarantine period is increased to 18 days, the greater the benefit of choosing to port skipping strategy; The quarantine period is reduced to 10 days, so choosing not skipping strategy for speed optimization is the best strategy.
Calculation results of operating costs under different loading and unloading volumes
| Route | volume | Cost (no port skipping) ($) | Cost (port skipping) | |
|---|---|---|---|---|
| Cost (under original speed) | Cost (under optimized speed) | ($) | ||
| Route 1 | 120 | 638279.27 | 622610.12 | 601010.02 |
| Route 1 | 150 | 638279.27 | 622610.12 | 613010.02 |
| Route 1 | 180 | 638279.27 | 622610.12 | 625010.02 |
Calculation results of operating costs under different fuel prices
| Route | Price of fuel oil | Cost (no port skipping) ($) | Cost (port skipping) | The difference of cost under the condition of skipping Port & optimizing speed | |
|---|---|---|---|---|---|
| ($/T) | Cost (under original speed) | Cost (under optimized speed) | ($) | ||
| Route 1 | 510 | 587327.15 | 573916.17 | 550057.90 | 23858.27 |
| Route 1 | 560 | 612803.21 | 598263.14 | 575533.96 | 22729.19 |
| Route 1 | 610 | 638279.27 | 622610.12 | 601010.02 | 21600.10 |
| Route 1 | 660 | 663755.33 | 646957.09 | 626486.07 | 20471.02 |
| Route 1 | 710 | 689231.39 | 671304.07 | 651962.13 | 19341.94 |
Optimization results at different distances
| Serial number | Distance between two ports | Cost (no port skipping) ($) | Cost (port skipping) | |
|---|---|---|---|---|
| (nautical miles) | Cost (under original speed) | Cost (under optimized speed) | ($) | |
| Route 1 | 453.1 | 638279.27 | 622610.12 | 601010.02 |
| Route 1 | 600 | 662413.06 | 646743.91 | 640705.93 |
| Route 1 | 750 | 701848.12 | 686178.97 | 696031.52 |
Optimization results under different port quarantine period
| Serial number | port quarantine period | Total voyage cost (no port skipping ($) | Total voyage cost (port skipping) | The difference of total cost under the condition of skipping Port & optimizing speed | |
|---|---|---|---|---|---|
| (day) | Cost (under original speed) | Cost (under optimized speed) | ($) | ||
| Route 1 | 10 | 608941.03 | 595642.12 | 601010.02 | -5367.90 |
| Route 1 | 14 | 638279.27 | 622610.12 | 601010.02 | 21600.10 |
| Route 1 | 18 | 667617.51 | 649578.12 | 601010.02 | 48568.10 |
When a serious health security emergency emerges and erupts on a large scale worldwide, the routing optimization strategy is critical for international ships sailing worldwide. Which is not only directly related to the prevention and control of the pandemic, but also has a significant impact on the financial cost of shipping companies. Different routes and pandemic characteristics will lead to different route optimization decisions. In this study, through mathematical programming and modeling, the optimization of shipping routes and speeds as impacted by the pandemic was analyzed. By combining the actual case data, the corresponding optimization results are achieved; on that basis, novel ideas and methods are proposed for investigating the optimal strategies of marine transportation under the sudden pandemic situation. And the responses to the effect of prevention and control measures brought about by the pandemic are suggested as skipping the port or speed optimization. Furthermore, different voyage distances and cargo volumes are subject to completely different response decisions.
The emergent safety and health incidents bring about the increase of the cost and the total voyage time. Relatively speaking, ocean shipping routes are less affected by the pandemic while near-sea shipping routes are more affected. In the face of quarantine measures taken to cope with health emergencies, ships will consider two options to reduce costs, i.e., skipping port or optimizing speed. The choice of option is significantly correlated with the distance of the voyage. Ships sailing in the ocean shipping route are less affected by the pandemic and can generally cope well with pandemic control measures after optimizing their speed. While near-ocean routes are more vulnerable to the pandemic, the cost optimization is more likely to be achieved through the choice of port skipping strategies. With the increase in the volume of containers loaded and unloaded, the amount of default, as well as the total operating costs in the port-skipping decision, thereby affecting the choice of the optimal decision. The lower the volume of containers loaded and unloaded, the more likely the port-hopping decision will occur. Moreover, the distance between a strictly controlled port and the next port will affect the choice of ship sailing strategy. The closer the distance, the more likely the port-skipping strategy will occur. The longer the distance, the more likely it will be to use a speed optimization strategy. The study reported that fuel prices slightly impact strategy choices. A sensitivity analysis has been conducted over a range of fuel price fluctuations over the last year, and the calculations reveal that the strategy remains unchanged. It is found that the range of port quarantine period will affect the choice of ship sailing strategy. The longer the port quarantine period, the better the skipping method is. The shorter the port quarantine period, the better the speed optimization method is.
At present, the World Health Organization has announced that the COVID-19 pandemic does not constitute a “public health emergency of international concern”, although the global health emergency of the new crown epidemic has ended, but in the future human beings may face similar or more serious public health emergencies, when facing major infectious disease epidemics, it will inevitably bring a higher risk of uncertainty to international shipping. Future research in this area can be expanded and diversified based on this study. On the one hand, we consider only one anti-pandemic port in the proposed model, in the future we should consider to the multiple anti-pandemic port; on the other hand, optimization model can be carried out not only from the perspective of shipping companies operating single ships, but also consider modeling studies in terms of the layout and optimization of shipping companies’ capacity networks. At the same time, more research on supply chain resilience can be conducted from the perspective of complex network planning.