The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

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

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

Optimal Planning of Container Terminal Operations

Due to globalization and international trade, moving goods using a mixture of transportation modes has become a norm; today, large vessels transport 95% of the international cargos. In the first part of this thesis, the emphasis is on the sea-land intermodal transport. The availability of different modes of transportation (rail/road/direct) in sea-land intermodal transport and container flows (import, export, transhipment) through the terminal are considered simultaneously within a given planning time horizon. We have also formulated this problem as an Integer Programming (IP) model and the objective is to minimise storage cost, loading and transportation cost from/to the customers. To further understand the computational complexity and performance of the model, we have randomly generated a large number of test instances for extensive experimentation of the algorithm. Since, CPLEX was unable to find the optimal solution for the large test problems; a heuristic algorithm has been devised based on the original IP model to find near „optimal‟ solutions with a relative error of less than 4%. Furthermore, we developed and implemented Lagrangian Relaxation (LR) of the IP formulation of the original problem. The bounds derived from LR were improved using sub-gradient optimisation and computational results are presented. In the second part of the thesis, we consider the combined problems of container assignment and yard crane (YC) deployment within the container terminal. A new IP formulation has been developed using a unified approach with the view to determining optimal container flows and YC requirements within a given planning time horizon. We designed a Branch and Cut (B&C) algorithm to solve the problem to optimality which was computationally evaluated. A novel heuristic approach based on the IP formulation was developed and implemented in C++. Detailed computational results are reported for both the exact and heuristic algorithms using a large number of randomly generated test problems. A practical application of the proposed model in the context of a real case-study is also presented. Finally, a simulation model of container terminal operations based on discrete-event simulation has been developed and implemented with the view of validating the above optimisation model and using it as a test bed for evaluating different operational scenarios

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

Containership Load Planning with Crane Operations

Since the start of the containerization revolution in 1950's, not only the TEU capacity of the vessels has been increasing constantly, but also the number of fully cellular container ships has expanded substantially. Because of the tense competition among ports in recent years, improving the operational efficiency of ports has become an important issue in containership operations. Arrangement of containers both within the container terminal and on the containership play an important role in determining the berthing time. The berthing time of a containership is mainly composed of the unloading and loading time of containers. Containers in a containership are stored in stacks, making a container directly accessible only if it is on the top of one stack. The task of determining a good container arrangement to minimize the number of re-handlings while maintaining the ship's stability over several ports is called stowage planning, which is an everyday problem solved by ship planners. The horizontal distribution of the containers over the bays affects crane utilization and overall ship berthing time. In order to increase the terminal productivity and reduce the turnaround time, the stowage planning must conform to the berth design. Given the configuration of berths and cranes at each visiting port, the stowage planning must take into account the utilization of quay cranes as well as the reduction of unnecessary shifts to minimize the total time at all ports over the voyage. This dissertation introduces an optimization model to solve the stowage planning problem with crane utilization considerations. The optimization model covers a wide range of operational and structural constraints for containership load planning. In order to solve real-size problems, a meta-heuristic approach based on genetic algorithms is designed and implemented which embeds a crane split approximation routine. The genetic encoding is ultra-compact and represents grouping, sorting and assignment strategies that might be applied to form the stowage pattern. The evaluation procedure accounts for technical specification of the cranes as well as the crane split. Numerical results show that timely solution for ultra large size containerships can be obtained under different scenarios

Sea Container Terminals

Due to a rapid growth in world trade and a huge increase in containerized goods, sea container terminals play a vital role in globe-spanning supply chains. Container terminals should be able to handle large ships, with large call sizes within the shortest time possible, and at competitive rates. In response, terminal operators, shipping liners, and port authorities are investing in new technologies to improve container handling infrastructure and operational efficiency. Container terminals face challenging research problems which have received much attention from the academic community. The focus of this paper is to highlight the recent developments in the container terminals, which can be categorized into three areas: (1) innovative container terminal technologies, (2) new OR directions and models for existing research areas, and (3) emerging areas in container terminal research. By choosing this focus, we complement existing reviews on container terminal operations

Two-stage column generation: a novel framework

Column generation has been intensively used in the last decades to compute good quality lower bounds for combinatorial problems reformulated through Dantzig-Wolfe decomposition. In this work we propose a novel framework to cope with problems in which the structure of the original formulation, namely the presence of a combinatorial number of decision variables, does not allow for straightforward reformulation. The basic idea is to start from a meaningful subset of original variables, apply the DW reformulation to the subset, solve the reformulation with column generation and perform the explicit pricing on original variables retracing back the reformulation and using complementary-slackness conditions. The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) is used as an illustration for the method, which provides a new exact approach to the problem. Preliminary computational experiments are reported. This is joint work with Matteo Salani