A Branch-and-Price Algorithm to Solve a Quay Crane Scheduling Problem

AbstractAs the maritime industry grows rapidly in size, more attention is being paid to to a wide range of aspects of problems faced at ports with respect to the efficient allocation of resources. A very important seaside planning problem that has received large attention in literature lately is the quay crane scheduling problem (QCSP). The problem involves the creation of a work schedule for the available quay cranes at the port to empty the containers from a vessel or given set of vessels. These optimization problems can be very complex and since they involve a large number of variables and constraints, the use of a commercial solver is impractical. In this paper, we reformulate a problem currently available in the literature to a Dantzig-Wolfe formulation that can be solved by column generation. We then develop a branch-and-price algorithm, which is an exact method, to effectively solve mixed integer programs with very large instances. The algorithm is first tested on a formulation currently available in literature with a small instance and will then be tested on large instances

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

Integrated Berth Allocation and Quay Crane Assignment Problem: Set partitioning models and computational results

Most of the operational problems in container terminals are strongly interconnected. In this paper, we study the integrated Berth Allocation and Quay Crane Assignment Problem in seaport container terminals. We will extend the current state-of-the-art by proposing novel set partitioning models. To improve the performance of the set partitioning formulations, a number of variable reduction techniques are proposed. Furthermore, we analyze the effects of different discretization schemes and the impact of using a time-variant/invariant quay crane allocation policy. Computational experiments show that the proposed models significantly improve the benchmark solutions of the current state-of-art optimal approaches

Multiship Crane Sequencing with Yard Congestion Constraints

Crane sequencing in container terminals determines the order of ship discharging and loading jobs that quay cranes (QCs) perform, so that the duration of a vessel's stay is minimized. The ship's load profile, berthing time, number of available bays, and QCs are considered. More important, clearance and yard congestion constraints need to be included, which, respectively, ensure that a minimum distance between adjacent QCs is observed and yard storage blocks are not overly accessed at any point in time. In sequencing for a single ship, a mixed-integer programming (MIP) model is proposed, and a heuristic approach based on the model is developed that produces good solutions. The model is then reformulated as a generalized set covering problem and solved exactly by branch and price (B&P). For multiship sequencing, the yard congestion constraints are relaxed in the spirit of Lagrangian relaxation, so that the problem decomposes by vessel into smaller subproblems solved by B&P. An efficient primal heuristic is also designed. Computational experiments reveal that large-scale problems can be solved in a reasonable computational time

The synergistic effect of operational research and big data analytics in greening container terminal operations: a review and future directions

Container Terminals (CTs) are continuously presented with highly interrelated, complex, and uncertain planning tasks. The ever-increasing intensity of operations at CTs in recent years has also resulted in increasing environmental concerns, and they are experiencing an unprecedented pressure to lower their emissions. Operational Research (OR), as a key player in the optimisation of the complex decision problems that arise from the quay and land side operations at CTs, has been therefore presented with new challenges and opportunities to incorporate environmental considerations into decision making and better utilise the ‘big data’ that is continuously generated from the never-stopping operations at CTs. The state-of-the-art literature on OR's incorporation of environmental considerations and its interplay with Big Data Analytics (BDA) is, however, still very much underdeveloped, fragmented, and divergent, and a guiding framework is completely missing. This paper presents a review of the most relevant developments in the field and sheds light on promising research opportunities for the better exploitation of the synergistic effect of the two disciplines in addressing CT operational problems, while incorporating uncertainty and environmental concerns efficiently. The paper finds that while OR has thus far contributed to improving the environmental performance of CTs (rather implicitly), this can be much further stepped up with more explicit incorporation of environmental considerations and better exploitation of BDA predictive modelling capabilities. New interdisciplinary research at the intersection of conventional CT optimisation problems, energy management and sizing, and net-zero technology and energy vectors adoption is also presented as a prominent line of future research

Adaptive autotuning mathematical approaches for integrated optimization of automated container terminal

With the development of automated container terminals (ACTs), reducing the loading and unloading time of operation and improving the working efficiency and service level have become the key point. Taking into account the actual operation mode of loading and unloading in ACTs, a mixed integer programming model is adopted in this study to minimize the loading and unloading time of ships, which can optimize the integrated scheduling of the gantry cranes (QCs), automated guided vehicles (AGVs), and automated rail-mounted gantries (ARMGs) in automated terminals. Various basic metaheuristic and improved hybrid algorithms were developed to optimize the model, proving the effectiveness of the model to obtain an optimized scheduling scheme by numerical experiments and comparing the different performances of algorithms. The results show that the hybrid GA-PSO algorithm with adaptive autotuning approaches by fuzzy control is superior to other algorithms in terms of solution time and quality, which can effectively solve the problem of integrated scheduling of automated container terminals to improve efficiency.info:eu-repo/semantics/publishedVersio

Sequence-Based Simulation-Optimization Framework With Application to Port Operations at Multimodal Container Terminals

It is evident in previous works that operations research and mathematical algorithms can provide optimal or near-optimal solutions, whereas simulation models can aid in predicting and studying the behavior of systems over time and monitor performance under stochastic and uncertain circumstances. Given the intensive computational effort that simulation optimization methods impose, especially for large and complex systems like container terminals, a favorable approach is to reduce the search space to decrease the amount of computation. A maritime port can consist of multiple terminals with specific functionalities and specialized equipment. A container terminal is one of several facilities in a port that involves numerous resources and entities. It is also where containers are stored and transported, making the container terminal a complex system. Problems such as berth allocation, quay and yard crane scheduling and assignment, storage yard layout configuration, container re-handling, customs and security, and risk analysis become particularly challenging. Discrete-event simulation (DES) models are typically developed for complex and stochastic systems such as container terminals to study their behavior under different scenarios and circumstances. Simulation-optimization methods have emerged as an approach to find optimal values for input variables that maximize certain output metric(s) of the simulation. Various traditional and nontraditional approaches of simulation-optimization continue to be used to aid in decision making. In this dissertation, a novel framework for simulation-optimization is developed, implemented, and validated to study the influence of using a sequence (ordering) of decision variables (resource levels) for simulation-based optimization in resource allocation problems. This approach aims to reduce the computational effort of optimizing large simulations by breaking the simulation-optimization problem into stages. Since container terminals are complex stochastic systems consisting of different areas with detailed and critical functions that may affect the output, a platform that accurately simulates such a system can be of significant analytical benefit. To implement and validate the developed framework, a large-scale complex container terminal discrete-event simulation model was developed and validated based on a real system and then used as a testing platform for various hypothesized algorithms studied in this work

An exact algorithm for the integrated planning of berth allocation and quay crane assignment

In this paper we study the simultaneous optimization of berth allocation and quay crane assignment in seaport container terminals. We propose a model based on an exponential number of variables that is solved via column generation. An exact branch-and-price algorithm is implemented to produce optimal integer solutions to the problem. In particular, we present several accelerating techniques for the master and the pricing problem that can be generalized to other branch-and-price schemes. Computational results show that the proposed approach outperforms commercial solvers. Furthermore, the developed algorithm allows for a comparative analysis between the hierarchical and the integrated solution approach that confirms the added value of integration in terms of cost reduction and efficient use of resources. To the best of our knowledge, this is the first exact branch-and-price algorithm for both the berth allocation problem and the berth allocation problem with quay crane assignment

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