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

The Vehicle Routing Problem with Discrete Split Delivery and Time Windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles capacity and customer time windows. The delivery request of a customer consists of several discrete items which cannot be split further. The problem belongs to the class of split delivery problems since each customers demand can be split in orders, i.e. feasible combinations of items, and each customer can be visited by more than one vehicle. In this work, we model the DSDVRPTW as a mixed integer linear program, assuming that all feasible orders are known in advance and that each vehicle can serve at most one order per customer. Remarkably, service time at customers location depends on the serviced combination of items, which is a modeling feature rarely found in literature. We present a branch-and-price algorithm, analyzing the implications of the classical Dantzig-Wolfe reformulation. Preliminary computational results on instances based on Solomons data set are discussed

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

An exact algorithm for the discrete split delivery vehicle routing problem with time windows

The Split Delivery Vehicle Routing Problem (SDVRP) is a variant version of the classical VRP in which each customer can be visited by more than one vehicle which serves a fraction of its demand. The Discrete SDVRP is another variant in which the delivery request of a customer consists of several items which cannot be split further. In this work we consider the DSDVRP with time windows where the service of items' combinations imply a corresponding service time. We present a branch-and-price algorithm and discuss preliminary computational results

Branch and Price for the Vehicle Routing Problem with Discrete Split Deliveries and Time Windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles capacity and customer time windows. The delivery request of a customer is discrete since it consists of several items that cannot be split further. The problem belongs to the class of split delivery problems since each customers demand can be split in orders, i.e. feasible combinations of items, and each customer can be visited by more than one vehicle. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance and that each vehicle can serve at most one order per customer. Remarkably, service time at customers location depends on the serviced combination of items, which is a modeling feature rarely found in literature. We present a mixed integer program for the DSDVRPTW based on arc-flow formulation, we reformulate it via Dantzig-Wolfe and we apply column generation. We propose a branch-and-price algorithm, implemented using state-of-the-art techniques for the pricing and the master problem. Computational results on instances based on Solomons data set are presented and discussed

Optimization of operations in container terminals: hierarchical vs integrated approaches

Over the last years, international sea freight container transportation has grown dramatically and container terminals play nowadays a key role within the global shipping network. Terminal's operations have received increasing interest in the scientific literature and operations research techniques are more and more used to improve efficiency and productivity. In this work we provide an overview of container terminal's operations and associated decision problems. We review state-of-the-art optimization approaches in terminal's management and we discuss what are in our opinion the current research trends. In particular, we focus on the following streams: the integrated optimization of interdependent decision problems, the analysis of issues related to traffic congestion in the yard and the tactical planning of operations. The discussion is based on the Tactical Berth Allocation Problem (TBAP), an integrated decision problem that deals with the simultaneous optimization of berth allocation and quay crane assignment. Yard housekeeping costs are also taken into account in the objective function. We use the TBAP as a case study to illustrate the benefits of an integrated optimization approach. A comparative analysis with the traditional hierarchical solution approach is provided. Computational results based on real-world data provided by the MCT (port of Gioia Tauro, Italy) show that the additional computational effort required by the integrated optimization approach allows for more efficient solutions

Optimization at Container Terminals: Status, Trends and Perspectives (revised version)

International sea-freight container transportation has grown dramatically over the last years and container terminals represent nowadays a key actor in the global shipping network. Terminal managers have to face with an increasing competitiveness among terminals, which require more and more efficiency in container operations both along the quayside and within the yard: the objective is usually to minimize ships turnaround time, one of the main indicators of the terminal performance for the shipping companies. Moreover, the minimization of operational costs directly entails the achievement of competitive terminal fares, thus increasing the attractiveness for new customers. Operations research methods and techniques are therefore worth being used in optimizing terminal operations. In this work, we firstly give an overview of decision problems which arise in the management of a container terminal (e.g. berth allocation, quay crane scheduling, storage policies and strategies, transfer operations, ship stowage planning) and provide a review of recent papers in the OR literature. Then, starting from a collaboration with some of the busiest ports in Europe, we identify some critical issues: in particular, we discuss the impact that gate and transshipment operations have on the yard. We also focus on competition and cooperation issues among port market players and decision makers. Finally, we conclude by suggesting possible research tracks and open issues

Optimization of Container Terminal Operations

Over the last years, international sea-freight container transportation has grown dramatically and container terminals play nowadays a key-role in the global shipping network. The increased competitiveness among terminals requires more and more efficiency in container operations, both along the quayside and within the yard, in order to minimize ships turnaround time. Operations research methods and techniques are therefore worth being used in optimizing terminal operations. In this work, we first give an overview of decision problems which arise in the management of a container terminal (e.g. berth allocation, crane scheduling, storage policies and strategies, transfer operations) and we briefly describe models and methods presented in the literature. Then, starting from a collaboration with some of the busiest ports in Europe, we have identified some critical issues which will be illustrated: in particular, we focus on the impact that gate operations and transshipment operations have on the yard and we propose a new approach to the yard management which takes into account these interactions. We conclude with suggestions of possible research tracks and open issues