Abstract
The employment of quay cranes assumes a variety of functions. Due to this, problems concerning scheduling and assignment of quay cranes arise. Cranes are to perform a variety of tasks when they are assigned to vessels.
The main issues researched in this matter are safety during the operation of quay cranes, algorithm of vessel priority and the pattern of assignment of cranes to new vessels when their previous tasks are complete.
Literature Review
In the contemporary world international trade is vital for the development of the world’s economy. Maritime transportation is one of the most cost-effective and popular means of international trade. Goods are handled at ports, where the container traffic experiences rapid growth lately.
For the optimisation of container traffic quay cranes are utilised. Currently there are three main problems considering the operation of cranes: assignment of cranes to vessels, the issue of quay time and service assignment, and the problem with scheduling of containers handles by quay cranes and their sequence.
This paper provides a literature review of seven papers studying these issues.
In the article called “Quay crane scheduling problem” the authors recognise the problem with quay crane scheduling due to the growth of container traffic. The sequence of discharging needs to be determined for a set number of cranes, which will shorten the time of task completion [1].
The important aspect of scheduling is the creation of balance between the stacks of loads and the number of bays. It is suggested that more thorough approach towards stacks and loads planning in each bay will optimize the operation of quay cranes.
The paper titled “The dynamic berth allocation problem: A linearised formulation” by Simrin and Diabat suggests that a progress in quay crane utilisation can be achieved by means of optimisation of container terminal operations [5]. Berth allocation problem or BAP is viewed as one of the major challenges in this sphere.
The problem was addressed through an application of genetic algorithm heuristic which was used for various aspects of the problem. The obtained results were tested in order to identify the best, worst and average outcomes.
The authors of the study called “A joint quay crane assignment and scheduling problem: formulation, solution algorithm and computational results” offer a simplified approach towards the problem of quay crane scheduling and integrated assignment. The problem is viewed from the perspective of a crane-to-bay assignment [6].
As a result a Lagrangian relaxation algorithm is developed in order to solve the problem. After that the relaxed problem is solved through the constraint generation method and the performance of the Lagrangian heuristic is evaluated.
In the paper called “An integrated quay crane assignment and scheduling problem” Theodorou and Diabat view container handling efficiency as the productivity of quay cranes responsible for such operations as loading and unloading of containers [7].
The authors develop a formulation for quay crane assignment. Quay crane scheduling problem is addressed with the help of genetic algorithm and the results obtained after the application of the algorithm are evaluated to determine the efficiency of calculations.
Fu and Diabat, the authors of the paper titled “A Lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem” offer an alternative approach to the problems of quay crane integrated assignment and scheduling.
It is recognised that these two issues are always addressed independently from each other. As an alternative, Fu and Diabat suggest addressing them simultaneously this time and offer a mathematical formulation for these problems [2]. The calculations take into consideration quay crane interference.
The proposed model is addressed with the help of Lagrangian relaxation and the results are evaluated.
In the paper by Fu, Diabat, and Tsai called “A multi-vessel quay crane assignment and scheduling problem: Formulation and heuristic solution approach” the authors approach the problem with the assignment of quay cranes to vessels and the tasks fulfilled by cranes in a sequence [3].
Important factors such as safety of distances between operating quay cranes, priority of vessels and ordering conditions are taken into consideration in the course of calculations. Since the problem is complex and has many layers, a genetic algorithm is applied to it. The evaluation of the obtained results confirms their validity.
The study by Simrin, Alkawaleet and Diabat titled “A Lagrangian Relaxation Based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method” maintains that there is a variety of approaches to the solution of berth allocation problem.
The difference between these approaches is the way they view berth allocation, as a static or dynamic problem [4]. The layout applied to quays is also different – it can be continuous, discrete or hybrid.
Berth allocation problem is viewed as a vital aspect of optimization of work of quay cranes just like in the article called “The dynamic berth allocation problem: A linearised formulation” by Simrin and Diabat.
In the present article the authors use Lagrangian relaxation with the application of cutting plane method and ran it on various aspects of the problem.
References
[1] N. Al-Dhaheri and A. Diabat. “Quay crane scheduling problem,” JMSY, pp1-8, Feb. 2015.
[2] Y. Fu and A. Diabat. A Lagrangian relaxation approach for solving the integrated quay crane assignment and scheduling problem. Applied Mathematical Modeling, vol. 39, pp1194–1201, Mar. 2015
[3] Y. Fu, A. Diabat, and I. Tsai. “A multi-vessel quay crane assignment and scheduling problem: Formulation and heuristic solution approach,” Expert Systems with Applications, vol. 41, pp6959–6965, May. 2014.
[4] A. Simrin, N. Alkawaleet and A. Diabat. “A Lagrangian Relaxation Based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method,” Science and Technology Publications, vol 1, pp565-569, 2013
[5] A. Simrin and A. Diabat. “The dynamic berth allocation problem: A linearised formulation.” RAIRO-Oper. Res., vol. 49, pp473-494, Jul. 2015.
[6] E. Theodorou and A. Diabat. “A joint quay crane assignment and scheduling problem: formulation, solution algorithm and computational results,” Optim Lett, vol. 9, pp799-817, Aug. 2014.
[7] E. Theodorou and A. Diabat. “An integrated quay crane assignment and scheduling problem, “ Computers & Industrial Engineering, vol. 73, 115–123, Mar. 2014.