l L z Z ( M z o u t Q o z o w n + c z l T z l + M z i n Q z i n ) R l z Z T z l × D z ρ , l L z Z q z o w n Q o w n , z Z z Z q z i n Q i n , z Z T z l M l , l L T z l ( Q o w n + Q i n ) × [ ( 365 τ z ) / t z l ] , z Z , l L

The model follows the total income minus the total cost to obtain the total profit. The total income includes the ship rental income ( z Z M z o u t q z o w n ) + the freight income of the ship ( f l R l ), and the total cost includes the cost of the ship through the canal ( z Z ( p 1 z R 1 + 2 p 2 z q z 2 ) ) + charter cost ( l L z Z M z o u t Q o z o w n ) + voyage operating cost ( l L z Z c z l T z l ) + ship rental expenses ( l L z Z M z i n Q z i n ). The following explains the parameters of the model and the variables.

Qown: the number of own z-type ships assigned to route l;

Qin: the number of rented z-type ships assigned to route l;

Tzl: the number of flights of the z-type ship on the l route during the planning period;

L = {1, 2} is the liner route collection. L = {1} is the route through the Panama Canal, that is, directly to the East Coast through the Panama Canal; L = {2} is the route through the Suez Canal, that is, to cross the Atlantic Ocean through the Suez Canal to reach the East.

z = {1, 2, 3, 4, 5} is a collection of container types. z = {1} specifically refers to a container ship of 6500 TEU; z = {2} specifically refers to a container ship of 8500 TEU; z = {3} specifically refers to a container ship of 10,500 TEU; z = {4} specifically refers to a container of 12,500 TEU Ship; z = {5} specifically refers to a 15,000 TEU container ship.

Mzin: rented rent for z-type container ships;

Mzout: rental and rental of z-type container ships;

Qzown: the number of own z-type container ships;

Qzin: the number of ships that can be rented into z-type containers;

fl: the average freight rate of containers on the Panama Canal route (unit: USD/TEU);

Rl: The total annual transportation demand of l route (unit: TEU);

P1z: Panama Canal toll for z-type container ships on the eastbound route (unit: USD/TEU);

P2z: Suez Canal navigation fee for z-type container ships on the westbound route (in US dollars);

Czl: the operating cost of a single round-trip voyage on the Z-type container ship on the l route;

Tzl: the sailing time of a single round-trip voyage of a Z-type container ship on the l route;

τz: the number of idle days of Z-type container ships;

Ml: the minimum number of flights required to meet the weekly service and route;

Dz: single ship capacity of Z-type container ships;

Vz: economical speed of Z-type container ships (Note: 1 knot = 1 nautical mile/hour = 1.852 km/h).

3. Empirical Analysis

The widening of the Panama Canal has an impact on container liner shipping in the American East-Far East. The largest container ship that can be passed before the Panama Canal was widened was 4500 TEU. The smallest ship type applied after widening has reached 6500 TEU, The largest ship type that can be passed is 15,000 TEU. Data collection based on the parameters mentioned in the model established in the previous section.

3.1. Various Types of Ship Parameters

From Table 1, the economies of scale brought about by the large-scale ship can be intuitively obtained, Although container ships with larger payloads are slower in service speed than container ships with smaller payloads, there is an absolute advantage in container ships with a larger average daily fuel consumption. This advantage is not only reflected in the economy, but also in the environmental protection. Large ships can guarantee energy consumption based on reduced energy consumption.

3.2. Various Types of Ship Operating Hours

Table 2 and Table 3 show the timing of the two types of routes through the Panama Canal and the Suez Canal, which are needed in the final distribution model.

3.3. Route Cost of Various Ship Types

Based on the actual situation, the following assumptions are made.

1) The liner shipping company does not change the original port of call. The reduced capacity is only used for renting. The increased capacity is only from renting.

2) Do not consider other types of costs mentioned in the text.

3) The costs and profits in the route are all divided according to the two routes given in the article.

4) All types of ships are economical service speeds when serving on the route, regardless of the difference between ballast and heavy load.

Table 4 presents the various cost calculation rules, including fixed costs and variable costs through the Panama Canal and the Suez Canal.

Table 5 shows the specific values of fixed costs, which are needed in the distribution model.

Table 6 shows the variable cost of the route through the Panama Canal, which is part of the final total cost and is needed in the distribution model. Specifically, it can be searched from the parameters in the ship model, and the data in the table is used for calculation.

Table 7 shows the variable cost of the route through the Suez Canal, which is part of the final total cost and is needed in the distribution model. Specifically, it can be searched from the parameters in the ship model, and the data in the table is used for calculation.

In order to meet the calculation requirements of the distribution ship, the average freight rates of the two routes of the Panama Canal and the Suez Canal were calculated, the average freight rate of the Panama Canal is p1: 3087.5 US dollars/TEU; the average freight rate over the Suez Canal is p2: 1647 US dollars/TEU.

Source: http://www.sofreight.com/freight_from__to__l0d0s0t0w0p1_by_0_carrier__c0.html.

Ships also need to pay the corresponding river crossing fees through the canal. The cost of passing the Panama Canal is shown in Table 8, and the cost of passing the Suez Canal is shown in Table 9.

Table 1. Ship parameters of various types.

Source: Clarkson research

Table 2. Operation time of the route through the Panama Canal.

Table 3. Operating time of the route through the Suez Canal.

Table 4. The source of the route cost of each type of ship is summarized as follow [13] .

Table 5. Annual fixed costs for various ship types ($).

Source: Clarkson research.

Table 6. Variable costs of various types of ships on the Panama Canal route ($).

Source: Clarkson research.

Table 7. Variable costs of various ship types on the Suez Canal route ($).

Table 8. Panama Canal navigation fee ($/TEU).

Table 9. Suez Canal container ship navigation fee ($).

Explain: 1 SDR = 1.406 USD, Source: Suez Canal official website.

Table 10. The result of matching ships.

Since the east-west loading rate is different, it is assumed that the average cargo loading rate is 70%, that is, ρ = 70% in the model, which simplifies the calculation and transforms a double-objective problem into a single-objective integer programming problem. It can be solved with the optimization software lingo [14] [15] .

Table 10 shows the distribution of the Panama Canal and the Suez Canal. This type of distribution plan can maximize economic benefits.

4. Conclusions

It can be seen from the results of the ship distribution that after the expansion of the Panama Canal, the large container ships will be deployed on the routes through the Panama Canal to obtain greater economic benefits [16] [17] [18] . However, due to the resource constraints of large ships, the 15,000 TEU container ships were not deployed on routes passing the Suez Canal with a longer distance. The reason for this result is that: first, the effect of large-scale ships after the expansion of the Panama Canal is obvious. And the impact on the Suez Canal after the expansion of the Panama Canal, the Suez Canal’s ability to collect goods is insufficient, so this has happened. Secondly, as the Panama Canal expands the development of ports along Central America and the Caribbean, many liners need to be transited in ports in Central America and the Caribbean. This is the reason why the smaller ship type is configured in the Panama Canal. Subject to the limitations of ship-type resources, the liner transfer business through the Suez Canal can only be completed by the ship type 2 (8500 TEU), which is the maximum benefit allocation.

After the expansion of the Panama Canal, the most direct impact is that it can pass the larger ship type, and the 15,000 TEU option can be added to the ship plan. At the same time, the mileage of the large ship is reduced, thereby reducing the time of the round trip and finally reducing the single box cost. For the shipping company, it is necessary to make corresponding adjustments according to the distribution plan, such as adjusting the chartering plan, renting a 15,000 TEU ship type on the route through the Panama Canal to obtain greater economic benefits, while strengthening the route through the Panama Canal. At the same time, we will strengthen our ability to collect cargo on the Panama Canal route and maximize the benefits of large-scale ships.

In addition, in order to adapt to the current trend of large-scale ships, the infrastructure of the East Coast Port Group should also follow the development trend. At present, the US East Port can only provide services for traditional Panamax vessels. The capacity of the US East Port Group cannot support the docking of 15,000 TEU container ships. As the volume of cargo increases, the collection and distribution system of the US East Port Group also needs to be upgraded to match the increase in the volume of goods. The follow-up can further study the collection and distribution system of the US East Port and to be perfect the impact of the Panama Canal widening on shipping.

Cite this paper
Fan, H.X. and Gu, W.H. (2019) Study on the Impact of the Panama Canal Expansion on the Distribution of Container Liner Routes. Journal of Transportation Technologies, 9, 204-214. doi: 10.4236/jtts.2019.92013.
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