Silvia Schwarze

A mathematical formulation and complexity considerations for the blocks relocation problem

The blocks relocation problem (BRP) may be defined as follows: given a set of homogeneous blocks stored in a two-dimensional stock, which relocations are necessary to retrieve the blocks from the stock in a predefined order while minimizing the number of those relocations? In this paper, we first prove NP-hardness of the BRP as well as a special case, closing open research questions. Moreover, we propose different solution approaches. First, a mathematical model is presented that provides optimal solutions to the general BRP in cases where instances are small. To overcome such limitation, some realistic assumption taken from the literature is introduced, leading to the definition of a binary linear programming model. In terms of computational time, this approach is reasonably fast to be used to solve medium-sized instances. In addition, we propose a simple heuristic based upon a set of relocation rules. This heuristic is used to generate “good” quality solutions for larger instances in very short computational time, and, consequently, is proposed for tackling problem instances where solutions are required (almost) immediately. Solution quality of the heuristic is measured against optimal solutions obtained using a state-of-the-art commercial solver and both of them are compared with reference results from literature.

Container Rehandling at Maritime Container Terminals

In this paper, we review recent contributions dealing with the rehandling of containers at maritime container terminals. The problems studied in the paper refer to a post-stacking situation, i.e. problems arising after the stacking area has already been arranged. In order to increase efficiency of loading/unloading operations, once updated information about the state of the containers as well as of the vessels becomes available, it is possible to reshuffle the container yard, or a portion of it, in such a way that future loading operations are carried out with maximal efficiency. The increase in efficiency of loading/unloading operations has a bearing on the berthing time of the vessels, which, in turn, is a widely accepted indicator of port efficiency. Three types of post-stacking problems have been identified, namely (i) the remarshalling problem, (ii) the premarshalling problem, and (iii) the relocation problem. With respect to each of these problems, a thorough explanation of the problem itself, its relevance and its connections with other container handling issues are offered. In addition, algorithmic approaches to tackle such problems are summarized.

Improved load balancing and resource utilization for the Skill Vehicle Routing Problem

The Skill Vehicle Routing Problem (Skill VRP) considers vehicle routing under the assumption of skill requirements given on demand nodes. These requirements have to be met by the serving vehicles. No further constraints, like capacity or cost restrictions, are imposed. Skill VRP solutions may show a tendency to have a bad load balancing and resource utilization. In a majority of solutions only a subset of vehicles is active. Moreover, a considerable share of demand nodes is served by vehicles that have a skill higher than necessary. A reason for that solution behavior lies in the model itself. As no resource restrictions are imposed, the Skill VRP tends to produce TSP-like solutions. To obtain better balanced solutions, we introduce two new approaches. First we propose a minmax model that aims at minimizing the maximal vehicle tour length. Second we suggest a two-step method combining the minmax approach with a distance constrained model. Our experiments illustrate that these approaches lead to improvements in load balancing and resource utilization, but, with different impact on routing costs.

An improved mathematical formulation for the blocks relocation problem

This paper deals with the blocks relocation problem (also called container relocation problem). First, it corrects the binary linear programming model BRP-II presented in Caserta et al. (2012). Second, it improves the initial model formulation by removing superfluous variables, tightening some constraints, introducing a new upper bound and applying a pre-processing step to fix several variables. Computational results show the efficiency of the improved model for small and medium sized instances.

An Analysis of Digital Transformation in the History and Future of Modern Ports

Digital transformation is of utmost importance in the business world with major impacts on any of its sectors. Here we consider ports and logistics within maritime shipping to exemplify those developments. That is, as actors in world-wide supply chains, seaports are particularly affected by technological change. Due to the high requirements in the logistics sector, e.g., regarding costs, efficiency, security, and sustainability, digital innovation is essential to stay competitive. Past developments show how digital innovation can shape the modernization of ports. In order to understand future challenges in this area, it is inevitable to review the outcomes of past developments and their impact on port operations. In this paper, we provide an extensive analysis of digital transformations in seaports. We identify three generations and analyze the stages of respective digital transformations using a well-known model from literature. Based on the observations, we identify important aspects and challenges.

A Bicriteria Skill Vehicle Routing Problem with Time Windows and an Application to Pushback Operations at Airports

In the Skill Vehicle Routing Problem (Skill VRP), each vehicle is assigned a skill, representing its qualification. A vehicle is able to serve a node if its skill is sufficiently large regarding the skill requirement of the node. In this paper, we move the focus of the cost-oriented Skill VRP to time-related aspects. To that end, we add time window restrictions and, secondly, design an alternative, time-oriented, objective function. This problem extension is motivated by an application in the airport ground control where time issues play a major role. We present a mathematical model and carry out an extensive numerical study that includes load-balancing aspects as well as a multi-objective analysis.

Interaction of maritime shipping and hinterland traffic using a two-level hierarchical transport network

A transport scenario based on a two-level network is developed in order to model operations in maritime transport. To enhance competitiveness and sustainability of shipping companies, the interaction between maritime shipping and hinterland traffic is considered in the novel two-level hierarchical transport network. Demand occurs on the second level, the hinterland, whereas the first level, the sea transport, acts as a pure distribution network. The two-level hierarchical transport model allows regulating the degree of interaction a liner operator has regarding the hinterland traffic. Moreover, access of vehicles to nodes or edges is given subject to feasibility constraints, relating to the size of a vehicle. In this work, the relation to existing routing models, such as the travelling salesman problem, the vehicle routing problem, or the travelling purchaser problem, is illustrated. Moreover, through the definition of a proper set of assumptions, it is possible to reduce the considered two-level hierarchical transport network to different standard routing models. These new insights allow the application of existing solution methods. Numerical experiments are conducted for a particular case and illustrate the influence of node costs on the distribution of workload to the vehicles.

Pricing strategies for the site-dependent vehicle routing problem

The vehicle pricing game (VPG) which addresses the vehicles’ viewpoints within a vehicle routing problem (VRP) is introduced. Each vehicle acts as a player who demands a price per kilometer. That is, vehicles represent decentralized actors in transport systems, e.g., carriers under subcontracts. Based on these prices, a VRP is solved and profits are generated. Which price should a vehicle choose to maximize its own profit, considering the competition among vehicles? To answer this question, site dependencies leading to inhomogeneous vehicles are included. More detailed, skill-levels, e.g., relating to the size of a vehicle, are used to indicate a vehicle’s ability to carry out particular services. Moreover, penalty options are added. The VPG serves as an element of a vertical collaboration in a transport scenario and thus provides decision support for cooperative models. Theoretical results for the VPG are provided for a particular case of a two-player ring network game, for which the full set of equilibria is described and their uniqueness is discussed. It is shown that the uniqueness of the higher-skilled vehicle’s payoff is guaranteed even for multiple equilibria. The competition ratio is defined; it restricts a vehicle’s price to keep its competitiveness. Moreover, the acceptance ratio gives a lower bound on prices such that a loss of market share is still accepted. Experimental results are provided for general networks including the analysis of penalty options. It is demonstrated that strict site dependencies by tendency lead to monopolistic structures. In addition, particular penalty types show a positive effect regarding load imbalances caused by universally skilled vehicles.

Scientometric analysis of container terminals and ports literature and interaction with publications on distribution networks

Ports and container terminals have been modernized and expanded world-wide in recent years. In particular under the aspect of recent developments based on the financial crisis and resulting intensified competition in global markets, modern techniques for structuring and operating of harbors and container handling are required. These needs are reflected in the increased research activity in the field of container terminals and ports. We apply scientometric means to study trends and developments within this area. Moreover, we investigate the interplay with supply chain management in distribution networks tovisualize collaboration structures and interdependencies.

The path player game

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow shall be routed along their paths. The competitive nature of the game is due to the following two aspects: First, a capacity bound on the overall network flow links the decisions of the players. Second, edges may be shared by several players which might have conflicting goals. In this paper, we prove the existence of feasible and pure-strategy equilibria in path player games, which is a nontrivial task due to noncontinuity of payoff functions and the infinite, mutually dependent strategy sets. We analyze different instances of path player games in more detail and present characterizations of equilibria for these cases.