With the global warming to the survival and development of mankind, more and more attention is paid to low-carbon, green and energy-saving production. As one of the main modes of international transportation, the wharf has been facing a serious problem of its high carbon-emission. In order to balance the relationship between port energy consumption and efficiency, it is necessary to study the berth allocation, loading and unloading of bulk terminal from the perspective of energy saving with the proposal of energy saving and emission reduction in China. Both energy saving and efficiency can be achieved at the bulk terminal in the study. First, the latest layout and basic operation process of the bulk terminal are obtained by analyzing its process system. Secondly, a new model of energy consumption is constructed through regression analysis, based on which a mathematical model of berth scheduling is then constructed toward the aim with the minimum cost of distance deviation, of delayed departure and of energy consumption. Finally, by taking Tianjin Port for example, the model is verified to be feasible and efficient in reducing the loading and unloading cost, the total cost of ship in port time, in improving its service quality and achieving a low-carbon production. Moreover, the model can serve as a reference for other ports to reduce mechanical energy consumption.
There has been an increasing recognition that more attention should be paid to energy saving and consumption reduction under the pressure of resource consumption on environment in China. Transportation is one of the most essential industries that consumes a large amount of energy. There are four forms of transportation: vehicle, ship, road and port. Port plays so important a role in transportation that it is of great significance to reduce its energy consumption for the whole energy consumption in transportation industry [
Both the bulk and the container terminals are important sections of the port system and play irreplaceable strategic roles in logistic industry. The Ministry of Transport of China has been drawing more and more attention to energy saving in port due to the fact there are a great deal of large-scaled equipment, which is complicated to handle and with high energy-consumption. With the improvement of informationization and the development of digitization and intellectualization, the port equipment is becoming much more large-scaled, integrated and automatic [
With the enlargement of the loading capacity and the improvement of infomationization, challenges have been raised in the scale of bulk terminal, automation and specialization of the equipment. Keys that affect the whole terminal’s system lie in how to coordinate all the parts and to distribute all the equipment evenly [
It has been several decades since the research on port began in the 1980s. Queuing theory, queuing network theory and computer simulation were commonly used in the research which involved predicting the throughput of the port, optimizing and configuring the equipment, optimizing the construction of the port, configuring the handling operation line for one-ship operation, port system simulation, analyzing and optimizing bottleneck, coordinating and configuring the container truck and operation line, berth scheduling and distributing and optimizing ship etc. Most of the research focused on the container terminal.
As one kind of multi-resource scheduling, the berth scheduling of bulk terminal has the same characteristic with scheduling. It differs greatly in equipment and process from the berth scheduling of the container terminal [
The core resources of bulk terminal are berthing position, loading and unloading machinery and stacking yard. Their allocation will directly influence the economic benefits [
At present, a large number researches of port focus on the optimization of cost, time and benefit in the allocation of core resources, especially on the modeling of port efficiency, but few on energy saving. In order to balance the relationship between energy consumption and efficiency [
This model is built on basis of the following assumptions: (1) the ship’s arrival time is known and it will arrive on time within the planned port time. (2) the berthing length is 1.2 times that of the ship. (3) regardless of shifting and only one chance is given to every ship to berth. (4) the depth of continuous shoreline is the same and greater than the drainage. (5) every ship has been assigned the minimum and maximum loading machinery respectively. (6) the loading machinery will move in orbit and won’t stride over. (7) the ratio of every loading machinery is a constant and regardless of the mutual interference between machinery. (8) the ship’s loading time is inversely proportional to the loading machinery numbers and there are a certain proportion.
Here, we aim to get the lowest berth scheduling costs that are made up of three parts, the lowest cost influenced by distance between the actual and the optimum berthing positions, the lowest delayed departure cost and the lowest energy consumption cost of cranes that serve for ship.
Since a simple mathematical formula can be used to describe the cost of berthing deviation distance and departure delay cost, a regressive analysis is employed to discuss the energy consumption of the portal crane, that is, different distribution numbers of crane, different operation time and non-operation time. Based on the relationship of energy consumption between the working time and the idle status, the crane’s energy consumption is thus computed by being converted into the cost of energy consumption.
There are two forms of energy consumption of machinery: the effective and the in-effective. The former is the energy consumed when the machinery is working properly, while the latter the energy consumed when the machinery is not working properly. Corresponding formulas are shown as follows:
Effective Energy Consumption for Per Unit:
In-effective Energy Consumption for Per Unit:
Just as the energy consumption of machinery, there are two forms of energy consumption of cranes: the effective and the in-effective. When the different crane operates on the same ship, there is interference between each other. So, the effective energy consumption of crane can’t be computed directly on the basis of the ratio of the single crane.
The more the crane numbers distributed to ship, the lower the efficiency of the single crane. According to some statics, when different crane numbers are assigned to the same ship, the ratio of nonworking to working time is as shown in
Machinery number | |||||||||
---|---|---|---|---|---|---|---|---|---|
Ratio of nonworking time to working time | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
0.786 | 0.889 | 0.921 | 0.934 | 0.96 | 0.949 | 0.964 | 0.98 | 0.969 | |
0.803 | 0.886 | 0.93 | 0.954 | 0.953 | 0.954 | 0.968 | 0.969 | 0.963 | |
0.804 | 0.897 | 0.911 | 0.943 | 0.953 | 0.963 | 0.965 | 0.962 | 0.972 | |
0.793 | 0.891 | 0.928 | 0.942 | 0.953 | 0.96 | 0.969 | 0.967 | 0.98 | |
0.797 | 0.901 | 0.917 | 0.942 | 0.948 | 0.948 | 0.976 | 0.977 | 0.968 | |
0.794 | 0.887 | 0.917 | 0.936 | 0.96 | 0.965 | 0.971 | 0.975 | 0.983 | |
0.8 | 0.889 | 0.914 | 0.933 | 0.949 | 0.973 | 0.964 | 0.959 | 0.971 | |
0.786 | 0.892 | 0.926 | 0.933 | 0.958 | 0.97 | 0.95 | 0.958 | 0.964 | |
0.797 | 0.901 | 0.918 | 0.943 | 0.962 | 0.953 | 0.964 | 0.973 | 0.967 | |
0.784 | 0.893 | 0.918 | 0.954 | 0.957 | 0.97 | 0.975 | 0.978 | 0.972 | |
0.806 | 0.885 | 0.919 | 0.939 | 0.958 | 0.951 | 0.96 | 0.965 | 0.968 | |
0.796 | 0.884 | 0.936 | 0.936 | 0.939 | 0.973 | 0.958 | 0.956 | 0.978 | |
0.799 | 0.897 | 0.936 | 0.949 | 0.947 | 0.96 | 0.952 | 0.963 | 0.975 | |
0.787 | 0.877 | 0.923 | 0.927 | 0.942 | 0.963 | 0.964 | 0.958 | 0.961 | |
0.794 | 0.897 | 0.931 | 0.953 | 0.941 | 0.96 | 0.953 | 0.977 | 0.971 | |
0.784 | 0.897 | 0.927 | 0.936 | 0.953 | 0.968 | 0.957 | 0.977 | 0.982 | |
0.79 | 0.901 | 0.931 | 0.941 | 0.945 | 0.964 | 0.966 | 0.981 | 0.984 |
By regressive analysis,
Machinery number | |||||||||
---|---|---|---|---|---|---|---|---|---|
Average ratio | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
0.794 | 0.889 | 0.924 | 0.941 | 0.953 | 0.960 | 0.965 | 0.968 | 0.972 |
A regression curve is obtained by use of the regression analysis module with a simulation software named eM-Plant, as shown in
It can be seen from the figure that the ratio of nonworking to working time follows the formula when assigned different numbers of crane to the single ship.
It shows that the correlation of the crane number assigned to one ship to the ratio of nonworking to working time reveals the third power function. According to the functional relation, we can build a ratio table of effective energy consumption of the crane when assigning different numbers of crane to one ship. It is shown in
Numbers Crane assigned to one ship | Ratio of effective energy consumption |
---|---|
1 | |
2 | |
3 | |
… | … |
Therefore, we can get the utilization ratio for per unit.
The objective function of this paper is as follows:
The minimum cost influenced by distance between the actual and the optimum berthing positions is:
The minimum delayed departure cost is:
The minimum energy consumption cost is:
Because there are differences in magnitude in the decision objective, it is necessary to normalize the destination function. By converting the destination function into a number with the same order of Magni-tude, the lowest cost can be computed directly according to weights of these three destination functions.
So, the total destination function integrates the berthing deviation cost, the delayed time cost for departure and the energy consumption cost for loading and unloading into the following formula:
In practice, the importance is different among the distance deviation cost for berthing, the delayed time cost for departure and the energy consumption cost for loading and unloading. Different weights will be given to these three costs by experts according to the actual requirement. Finally, the result is computed.
In order to solve problems of linear programming, constraint conditions must be taken into account. The constraint conditions of the destination function mentioned in Section 3.3 is as follows.
Formula
The shoreline is 1100 meters long in Tianjin Coal Terminal Port. Let assume that the coal terminal not only has a continuous berth, but also the same draught depth and berthing capacity. What’s more, the draught depth is less than the berthing capacity for all the ships. Let’s take 24-hour-data of ships that are waiting at port and expected to arrive ranging from 10th to 11th, October 2017. In order to satisfy the regulated time format and to calculate easily, the berthing time starts from 0:00 PM and the maximum waiting time is less than the loading and unloading time. Basic data is shown as in
Number | Length (unit: m) | Width (unit: m) | Maximum number of cranes | Loading capacity (unit: ton) | Optimum berthing position (unit: m) |
---|---|---|---|---|---|
V1 | 200 | 32 | 6 | 33000 | 650 |
V2 | 155 | 28 | 4 | 15800 | 447.5 |
V3 | 282 | 39 | 4 | 13000 | 921 |
V4 | 282 | 39 | 5 | 21000 | 361 |
V5 | 200 | 32 | 2 | 3500 | 650 |
V6 | 155 | 32 | 4 | 10800 | 447.5 |
V7 | 155 | 28 | 5 | 21000 | 1007.5 |
V8 | 155 | 28 | 3 | 8700 | 97.5 |
V9 | 200 | 32 | 2 | 5000 | 290 |
V10 | 272 | 32 | 2 | 5000 | 566 |
V11 | 155 | 32 | 4 | 14700 | 627.5 |
V12 | 200 | 32 | 2 | 5000 | 970 |
V13 | 155 | 28 | 2 | 5000 | 447.5 |
V14 | 155 | 28 | 2 | 5700 | 267.5 |
V15 | 155 | 32 | 3 | 8000 | 767.5 |
V16 | 155 | 28 | 7 | 37000 | 97.5 |
V17 | 155 | 28 | 4 | 13000 | 267.5 |
V18 | 200 | 32 | 2 | 5000 | 470 |
V19 | 200 | 32 | 4 | 13000 | 710 |
From the table above, it can be concluded that: number of ships, length and width of each ship, maximum number of machineries to be allocated, loading capacity and optimal berthing position. There are 4 loading machines and 4 cranes at Tianjin Port.
Type (1 represents crane, 2 represents loading machine) | Lower limit of ship | Upper limit of ship | Efficiency (unit: ton/hour) |
---|---|---|---|
2 | 15001 | 20000 | 1827 |
2 | 1000 | 5000 | 1623 |
2 | 5001 | 10000 | 1675 |
2 | 10001 | 15000 | 1829 |
2 | 15001 | 20000 | 1827 |
2 | 20001 | 25000 | 1870 |
2 | 25001 | 30000 | 1861 |
2 | 30001 | 35000 | 1933 |
2 | 35001 | 40000 | 1960 |
1 | 1 | 2000 | 472 |
1 | 2001 | 4000 | 661 |
1 | 4001 | 6000 | 707 |
1 | 6001 | 8000 | 637 |
1 | 10001 | 12000 | 690 |
The upper and lower bounds of tonnage range in the above table mainly distinguish the efficiency of different types of machinery. It is known that the penalty cost for the delay departure is 4944 yuan/h, the electricity charges for industrial use is 0.8 yuan/kwh, the operation efficiency of cranes is 40t/move, the unit energy consumption for cranes is 149.7 kwh. Preset the relevant experimental parameters as following: the coefficients of the penalty cost for the delay departure is
Simulation and optimization algorithm are used to solve the model. There are variations in berthing position, berthing time, departure time and cranes’ number before and after simulation optimization. The comparisons between initial data and optimized data are shown in
Ship number | Berthing deviation distance (m) | Penalty cost for delay (¥) | Operation time (h) | Cranes’ energy consumption (kwh) | ||||
---|---|---|---|---|---|---|---|---|
Before | After | Before | After | Before | After | Before | After | |
V1 | 0 | 0 | 0 | 0 | 6.62 | 6.62 | 5693.31 | 5693.31 |
V2 | 0 | 20.5 | 0 | 0 | 6.33 | 6.33 | 5600.7 | 5600.7 |
V3 | 21 | 1 | 824 | 1236 | 4.12 | 4.12 | 4500.6 | 4500.6 |
V4 | 80 | 40 | 0 | 0 | 9.99 | 9.25 | 10538.7 | 10500.7 |
V5 | 0 | 0 | 0 | 0 | 8.17 | 8.17 | 7860.7 | 7860.7 |
V6 | 147.5 | 10 | 12246 | 1483.2 | 11.19 | 8.17 | 13532.1 | 7860.7 |
V7 | 0 | 0 | 824 | 4944 | 10.02 | 8.02 | 12014.5 | 7821.2 |
V8 | 107 | 0 | 0 | 4944 | 2.9 | 2.9 | 1407.5 | 1407.5 |
V9 | 0 | 0 | 0 | 0 | 6.55 | 5.88 | 5538.1 | 4930.1 |
V10 | 80 | 0 | 9888 | 0 | 6.55 | 5.88 | 5538.1 | 4930.1 |
V11 | 27.5 | 0 | 0 | 0 | 5.77 | 5.77 | 4798.3 | 4798.3 |
V12 | 0 | 100 | 0 | 0 | 6.55 | 5.88 | 5538.1 | 4930.1 |
V13 | 27.5 | 0 | 1812.8 | 9888 | 6.55 | 5.88 | 5538.1 | 4930.1 |
V14 | 0 | 20.5 | 8548 | 0 | 7.21 | 7.21 | 6723.4 | 6723.4 |
V15 | 40 | 0.5 | 29664 | 0 | 7.55 | 7.55 | 6972.8 | 6972.8 |
V16 | 185 | 0 | 0 | 0 | 8.41 | 7.58 | 8712.2 | 6980 |
V17 | 232 | 11.5 | 0 | 0 | 10.03 | 8.15 | 12025.5 | 7860.7 |
V18 | 200 | 30 | 0 | 0 | 6.55 | 6.55 | 5538.1 | 5538.1 |
V19 | 0 | 289 | 12360 | 0 | 9.87 | 7.91 | 10420.3 | 7017.6 |
SUM | 1147.5 | 523 | 76166.8 | 22495.2 | 140.93 | 127.82 | 138491.1 | 116856.7 |
Referring to the above comparison, the established model can reduce the berthing deviation distance, reduce the penalty cost of departure delay, reduce the operation practice and reduce the mechanical energy consumption. It has suggested that the mathematical model is appropriate and reflects an actual bulk terminal. It’s an effective and feasible way to solve berth scheduling by combining simulation model and genetic algorithm.
This paper conducts a deep analysis on the characteristic and operation of the bulk terminal. And it constructs a new model of energy consumption through regression analysis. When different crane numbers are assigned to the ship, the working and nonworking time varies. A regression curve is then obtained for the effective and ineffective energy consumption.
With the combination of both linear and non-linear method in Operational Research, a mathematical model for berth scheduling is constructed. By simulation and taking data of one day from Tianjin Port for example, the model is verified according to the actual conditions, which includes the berthing deviation distances, the penalty cost for delay, the operation time and the cranes’ energy consumption before and after optimization.