An evolutionary approach to a combined mixed integer programming model of seaside operations as arise in container ports

This paper puts forward an integrated optimisation model that combines three distinct problems, namely berth allocation, quay crane assignment, and quay crane scheduling that arise in container ports. Each one of these problems is difficult to solve in its own right. However, solving them individually leads almost surely to sub-optimal solutions. Hence, it is desirable to solve them in a combined form. The model is of the mixed-integer programming type with the objective being to minimize the tardiness of vessels and reduce the cost of berthing. Experimental results show that relatively small instances of the proposed model can be solved exactly using CPLEX. Large scale instances, however, can only be solved in reasonable times using heuristics. Here, an implementation of the genetic algorithm is considered. The effectiveness of this implementation is tested against CPLEX on small to medium size instances of the combined model. Larger size instances were also solved with the genetic algorithm, showing that this approach is capable of finding the optimal or near optimal solutions in realistic times

Container Terminal Berth-Quay Crane Capacity Planning Based on Markov Chain

This paper constructs a berth-quay crane capacity planning model with the lowest average daily cost in the container terminal, and analyzes the influence of the number of berths and quay cranes on the terminal operation. The object of berth-quay crane capacity planning is to optimize the number of berths and quay cranes to maximize the benefits of the container terminal. A steady state probability transfer model based on Markov chain for container terminal is constructed by the historical time series of the queuing process. The current minimum time operation principle (MTOP) strategy is proposed to correct the state transition probability of the Markov chain due to the characteristics of the quay crane movement to change the service capacity of a single berth. The solution error is reduced from 7.03% to 0.65% compared to the queuing theory without considering the quay crane movement, which provides a basis for the accurate solution of the berth-quay crane capacity planning model. The proposed berth-quay crane capacity planning model is validated by two container terminal examples, and the results show that the model can greatly guide the container terminal berth-quay crane planning

Barge Prioritization, Assignment, and Scheduling During Inland Waterway Disruption Responses

Inland waterways face natural and man-made disruptions that may affect navigation and infrastructure operations leading to barge traffic disruptions and economic losses. This dissertation investigates inland waterway disruption responses to intelligently redirect disrupted barges to inland terminals and prioritize offloading while minimizing total cargo value loss. This problem is known in the literature as the cargo prioritization and terminal allocation problem (CPTAP). A previous study formulated the CPTAP as a non-linear integer programming (NLIP) model solved with a genetic algorithm (GA) approach. This dissertation contributes three new and improved approaches to solve the CPTAP. The first approach is a decomposition based sequential heuristic (DBSH) that reduces the time to obtain a response solution by decomposing the CPTAP into separate cargo prioritization, assignment, and scheduling subproblems. The DBSH integrates the Analytic Hierarchy Process and linear programming to prioritize cargo and allocate barges to terminals. Our findings show that compared to the GA approach, the DBSH is more suited to solve large sized decision problems resulting in similar or reduced cargo value loss and drastically improved computational time. The second approach formulates CPTAP as a mixed integer linear programming (MILP) model improved through the addition of valid inequalities (MILP\u27). Due to the complexity of the NLIP, the GA results were validated only for small size instances. This dissertation fills this gap by using the lower bounds of the MILP\u27 model to validate the quality of all prior GA solutions. In addition, a comparison of the MILP\u27 and GA solutions for several real world scenarios show that the MILP\u27 formulation outperforms the NLIP model solved with the GA approach by reducing the total cargo value loss objective. The third approach reformulates the MILP model via Dantzig-Wolfe decomposition and develops an exact method based on branch-and-price technique to solve the model. Previous approaches obtained optimal solutions for instances of the CPTAP that consist of up to five terminals and nine barges. The main contribution of this new approach is the ability to obtain optimal solutions of larger CPTAP instances involving up to ten terminals and thirty barges in reasonable computational time

Genetic algorithm for integrated model of berth allocation problem and quay crane scheduling with noncrossing safety and distance constraint

Berth Allocation and Quay Crane Scheduling are the most important part of container terminal operations since berth and quay cranes are an interface of ocean-side and landside in any port container terminal operation. Their operations significantly influence the efficiency of port container terminals and need to be solved simultaneously. Based on the situation, this study focuses on an integrated model of Continuous Berth Allocation Problem and Quay Crane Scheduling Problem. A comprehensive analysis of safety distance for vessel and non-crossing constraint for quay crane is provided. There are two integrated model involved. For the first integrated model, non-crossing constraints are added wherein quay cranes cannot cross over each other since they are on the same track. The second integrated model is focused on the safety distance between vessels while berthing at the terminal and at the same time, quay crane remains not to cross each other. These two constraints were selected to ensure a realistic model based on the real situation at the port. The objective of this model is to minimise the processing time of vessels. A vessel's processing time is measured between arrival and departure including the waiting time to be berthed and servicing time. A new algorithm is developed to obtain the good solution. Genetic Algorithm is chosen as a method based on flexibility and can apply to any problems. There are three layers of algorithm that provide a wider search to the solution space for vessel list, berth list, and hold list developed in this study. The new Genetic Algorithm produced a better solution than the previous research, where the objective function decreases 5 to 12 percent. Numerical experiments were conducted and the results show that both integrated models are able to minimize the processing time of vessels and can solve problem quickly even involving a large number of vessels. Studies have found that the safety distance set as 5 percent of vessel length gives the best solution. By adding safety distance to the integrated model with non-crossing constraint, the result indicates no improvement in the model objective function due to increasing distance between vessels. The objective function increases in the range of 0.4 to 8.6 percent. However, the safety distance constraint is important for safety and realistic model based on the port’s real situation

Mathematical Models of Seaside Operations in Container Ports and their Solution

Operational Research and Optimization are fundamental disciplines which, for decades, provided the real-world with tools for solving practical problems. Many such problems arise in container ports. Container terminals are important assets in modern economies. They constitute an important means of distributing goods made overseas to domestic markets in most countries. They are expensive to build and difficult to operate. We describe here some of the main operations which are faced daily by decision makers at those facilities. Decision makers often use Operational Research and Optimization tools to run these operations effectively. In this thesis, we focus on seaside operations which can be divided into three main problems: 1- the Berth Allocation Problem (BAP), 2- the Quay Crane Assignment Problem (QCAP), 3- the Quay Crane Scheduling Problem (QCSP). Each one of the above is a complex optimization problem in its own right. However, solving them individually without the consideration of the others may lead to overall suboptimal solutions. For this reason we will investigate the pairwise combinations of these problems and their total integration In addition, several important factors that affected on the final solution. The main contributions of this study are modelling and solving of the: 1- Robust berth allocation problem (RBAP): a new efficient mathematical model is formulated and a hybrid algorithm based on Branch-and-Cut and the Genetic Algorithm is used to find optimal or near optimal solutions for large scale instances in reasonable time. 2- Quay crane assignment and quay crane scheduling problem (QCASP): a new mathematical model is built to simultaneously solve QCASP and a heuristic based on the Genetic Algorithm is developed to find solutions to realistic instances in reasonable time. 3- Berth allocation, quay crane assignment and quay crane scheduling problem (BACASP): an aggregate model for all three seaside operations is proposed and to solve realistic instances of the problem, an adapted variant of the Genetic Algorithm is implemented. Keywords: berth allocation; quay crane assignment; quay crane scheduling; terminal operations; genetic algorith

Flexible ship loading problem with transfer vehicle assignment and scheduling

This paper presents the flexible containership loading problem for seaport container terminals. The integrated management of loading operations, planning of the transport vehicles to use and their scheduling is what we define as the Flexible Ship Loading Problem (FSLP). The flexibility comes from a cooperative agreement between the terminal operator and the liner shipping company, specifying that the terminal has the right to decide which specific container to load for each slot obeying the class-based stowage plan received from the liner. We formulate a mathematical model for the problem. Then we present various modelling enhancements and a mathematical model to obtain strong lower bounds. We also propose a heuristic algorithm to solve the problem. It is shown that enhancements improve the performance of formulation significantly, and the heuristic efficiently generates high-quality solutions. Results also point out that substantial cost savings can be achieved by integrating the ship loading operations

Container Terminal Management:Integrated Models and Large-Scale Optimization Algorithms

This thesis deals with models and methods for large scale optimization problems; in particular, we focus on decision problems arising in the context of seaport container terminals for the efficient management of terminal operations. Large-scale optimization problems are both difficult to handle and important in many concrete contexts. They usually originate from real world applications, such as telecommunication, transportation and logistics, and their combinatorial complexity often represents a major issue; therefore, optimization models are crucial to support the decision making process. In particular, column generation and branch-and-price schemes currently represent one of the most advanced and efficient exact optimization approaches to solve large scale combinatorial problems. However, the increasing size and complexity of practical problems arising in real-world applications motivates the design of new solution approaches able to tackle current optimization challenges. In this thesis, we address two complementary research streams where both methods and applications play an important role. On the one hand, we focus on the specific application of container terminals: we propose a new model for the integrated planning of operations and we provide a heuristic and an exact solution algorithm; the broader objective is to devise solution methods that can be generalized and extended to other applications and domains. On the other hand, we aim to develop new methods and algorithms for general large scale problems and, in this context, we investigate a new column generation framework that exploits the relationship between compact and extensive formulation. In particular, we focus on a class of split delivery vehicle routing problems that generalizes a large number of applications arising in the real world, such as transportation and logistics, including container terminal management. In the context of container terminals, we propose a model for the integrated planning of berth allocation and quay crane assignment: the two decision problems are usually solved hierarchically by terminal planners, whereas in the Tactical Berth Allocation Problem we optimize the two problems simultaneously. We firstly present a mixed integer programming formulation that is embedded into a two-level heuristic algorithm based on tabu search and mathematical programming techniques: our heuristic proves to be very efficient, providing good-quality solutions in a reasonable time. The problem is reformulated via Dantzig-Wolfe decomposition and solved via column generation: we propose an exact branch-and-price algorithm and our implementation, that includes state-of-the-art techniques for the master and the pricing problem, outperforms commercial solvers. Furthermore, the exact approach allows us to provide an interesting experimental comparison between hierarchical and integrated planning: computational tests confirm the added value of integration in terms of cost reduction and efficient use of resources. From a methodological point of view, this dissertation investigates a new column generation concept for difficult large scale optimization problems. In particular, we study a class of split delivery vehicle routing problems that generalizes some interesting features of Tactical Berth Allocation Problem, which are relevant also to other applications such as transportation, logistics and telecommunication. The problem, called Discrete Split Delivery Vehicle Routing Problem with Time Windows, presents two main modeling features: demand is discrete and delivered in discrete orders, opposite to the usual assumption of continuously splittable demand; the service time is dependent on the delivered quantity, opposite to the usual assumption of constant service time, regardless of the quantity. The problem is used to validate and test the new column generation approach studied in this thesis. The proposed framework, called Two-stage column generation, represents a novel contribution to recent advances in column generation: the basic idea is to simultaneously generate columns both for the compact and the extensive formulation. We propose to start solving the problem on a subset of compact formulation variables, we apply Dantzig-Wolfe decomposition and we solve the resulting master problem via column generation. At this point, profitable compact formulation variables are dynamically generated and added to the formulation according to reduced cost arguments, in the same spirit of standard column generation. The key point of our approach is that we evaluate the contribution of compact formulation variables with respect to the extensive formulation: indeed, we aim at adding compact formulation variables that are profitable for the master problem, regardless of the optimal solution of the linear relaxation of the compact formulation. We apply two-stage column generation to the Discrete Split Delivery Vehicle Routing Problem with Time Windows. Computational results show that our approach significantly reduces the number of generated columns to prove optimality of the root node. Furthermore, suboptimal compact formulation variables are detected correctly and a large number of variables is not taken into account during the solution process, thus reducing the size of the problem. However, the additional effort required by such a sophisticated approach makes the method competitive in terms of computational time only for instances of a certain difficulty. To conclude, two-stage column generation is a promising new approach and we believe that further research in this direction may contribute to solve more and more complex large scale optimization problems