Bjørn Nygreen

Learn More
Here, we describe a real planning problem in the tramp shipping industry. A tramp shipping company may have a certain amount of contract cargoes that it is committed to carry, and tries to maximize the profit from optional cargoes. For real long-term contracts, the sizes of the cargoes are flexible. However, in previous research within tramp ship routing,(More)
This paper considers the problem of grouping Parliamentary constituencies for Wales together into European constituencies in such a way that the resulting European constituencies have as equal electorates as possible. Three different solution methods are compared. These methods are integer programming, set partitioning and implicit enumeration. Computat(More)
We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by an interval instead of a fixed value. We show that the introduction of flexible cargo sizes to the column generation framework is not(More)
We present a multi-start local search heuristic for a typical ship scheduling problem. A large number of initial solutions are generated by an insertion heuristic with random elements. The best initial solutions are improved by a local search heuristic that is split into a quick and an extended version. The quick local search is used to improve a given(More)
The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We(More)
Cloud services with a multi-tiered architecture are often difficult to evaluate in terms of performance and dependability. The tiered architecture complicates the resource capacity decisions of the service provider, and makes it more demanding to maintain a good balance between capacity and quality of service. In this work we present an approximation of the(More)
The split pickup split delivery crude oil tanker routing and scheduling problem is a difficult combinatorial optimization problem, both theoretically and practically. However, because of the large expenses in crude oil shipping it is attractive to make use of optimization that exploits as many degrees of freedom as possible to save transportation cost. We(More)