Anastassios N. Perakis

Fleet deployment optimization for liner shipping Part 1. Background, problem formulation and solution approaches

The background and the literature in liner fleet scheduling is reviewed and the objectives and assumptions of our approach are explained. We develop a detailed and realistic model for the estimation of the operating costs of liner ships on various routes, and present a linear programming formulation for the liner fleet deployment problem. Independent approaches for fixing both the service frequencies in the different routes and the speeds of the ships, are presented.

Optimal liner fleet routeing strategies

The objective of this paper is to suggest practical optimization models for routing strategies for liner fleets. Many useful routing and scheduling problems have been studied in the transportation literature. As for ship scheduling or routing problems, relatively less effort has been devoted, in spite of the fact that sea transportation involves large capital and operating costs. This paper suggests two optimization models that can be useful to liner shipping companies. One is a linear programming model of profit maximization, which provides an optimal routing mix for each ship available and optimal service frequencies for each candidate route. The other model is a mixed integer programming model with binary variables which not only provides optimal routing mixes and service frequencies but also best capital investment alternatives to expand fleet capacity. This model is a cost minimization model.

Fleet deployment optimization for liner shipping part 2. Implementation and results

We use linear programming (LP) for solving the problem of the optimal deployment of an existing fleet of multipurpose or fully containerized ships, among a given set of routes, including information for lay-up time, if any, and type and number of extra ships to charter, based on a detailed and realistic model for the calculation of the operating costs of all the ship types in every route and on a suitable LP formulation developed in earlier work of the authors. The optimization model is also applicable to the problem of finding the best fleet compostion and deployment, in a given set of trade routes, which may be the case when a shipping company is considering new or modified services, or a renewal of the existing fleet. In addition, two promising mixed linear-integer programming formulations are suggested.

A survey of short sea shipping and its prospects in the USA

The continuing growth of international container trade has created capacity problems at major US ports, and the truck-based freight transportation has caused a deterioration of traffic congestion on important US transportation corridors. Using inland and coastal waterways, short sea shipping (SSS) can provide an improvement to these problems. Furthermore, SSS offers many additional benefits for the environment, the economy and society as a whole. Both the US Department of Transportation and the European Commission actively support SSS as an alternative, environmentally friendly mode of transportation. However, there are obstacles, administrative barriers and challenges that should be addressed. Several successful operations on both sides of the Atlantic make a strong case in favour of SSS. SSS can develop customized and technologically advanced solutions that will further integrate it into the intermodal transportation chain and will improve its image among shippers as a mode that can provide reliable door-to-door transportation. This paper reviews several studies on the subject and discusses the latest developments on SSS in the US and in Europe. It also addresses the major issues and the benefits of SSS and examines the prospects for potential short sea operations in the US. Finally, it proposes research opportunities for a multimodal transportation system that will include a short sea component.

Deterministic minimal time vessel routing

We develop general methodologies for the minimal time routing problem of a vessel moving in stationary or time dependent environments, respectively. Local optimality considerations, combined with global boundary conditions, result in piecewise continuous optimal policies. In the stationary case, the velocity of the traveling vessel within each subregion depends only on the direction of motion. Variational calculus is used to derive the geometry of piecewise linear extremals. For the time dependent problem, the speed of the vessel within each subregion is assumed to be a known function of time and the direction of motion. Optimal control theory is used to reveal the nature of piecewise continuous optimal policies.

An operational tanker scheduling optimization system: Background, current practice and model formulation

We describe the operational tanker scheduling problem in detail, as it relates to Chevron Shipping Company. We review the literature and current Chevron practice. We develop a model for the schedul...

Minimal Time Vessel Routing in a Time-Dependent Environment

We examine the two-dimensional minimal time routing problem for a vessel traveling from an origin to several ordered destination points. The sailing space is characterized by time-dependent routing properties. The controls are the power setting and the heading. For the vessel performance model, we prove that the optimal power setting always takes its upper permissible value. Moreover, appropriate first variation considerations result in local optimality conditions which, combined with global boundary conditions, form the framework of our “broken extremal” approach. The algorithmic implementation of the methodologies developed is also discussed. In particular, we emphasize that if the departure time from the origin location is known, the problem becomes much easier than the one with unspecified departure time. Elliptical bounds for the optimal state evolution are derived, significantly reducing the dimensionality of the problem. Finally, we present numerical examples based on the above methodologies.

Fleet deployment optimization models.Part 2

The fleet deployment problem for the one origin,one destination fixed-price contract requiring the transport of a given total amount of cargo within a given period is formulated and solved for the case that one or more cost components are given staircase functions of time. A computer program has been developed to implement the solution of this problem. The fleet deployment problem with one or more costs being random variables with known probability density functions is also formulated. Analytical expressions for hte basic probabilistic quantities, i.e the probability density function,the mean and the variance of the total operating cost, are presented. Finally, sample results are presented and discussed and some extensions for further research are suggested.

An improved formulation for bulk cargo ship scheduling with a single loading port

This paper presents an improved, significantly more efficient formulation of an existing model for bulk cargo or semi-bulk cargo ship scheduling problems with a single loading port. The original model, published by Ronen in 1986, was formulated as a non-linear, mixed integer program. In this work, the authors were able to re-formulate it into a linear one, by eliminating all the non-linearities of the original model. In addition, this model has far fewer integer variables than the original one. A numerical example has been given to illustrate the elimination of non-linearities and how 40 integer variables, in the original model, are reduced to just eight. This example also shows that this model is better at finding exact optimal solutions than the original one. It is also worth observing that the resulting model is a generalization of the ‘capacitated facility location problem’.

An operational tanker scheduling optimization system: model implementation, results and possible extensions

In a previous article by the same authors, we described the operational, short term tanker scheduling problem, focusing on the Chevron Shipping Company case study. We developed a model for the scheduling situation and described an integer programming formulation for schedule optimization. In this paper, we describe the scheduling system implementation on the University of Michigan IBM 3090–600E computer. The system generates feasible schedules for each vessel and then uses integer programming to attempt to solve for the optimal overall schedule. Use of the system and the potential for cost savings is demonstrated with a realistic scheduling situation based on Chevron Shipping Company information.