Some new bounds for the travelling salesman problem

The Clarke and Wright heuristic for the travelling salesman problem (TSP) has been used for several decades as a tool for finding good solutions for TSP and other vehicle routing problems (VRP). In this paper we offer a simple, but fundamental relationship between the cost of a Hamiltonian cycle measured in the original cost matrix and the cost of the same cycle measured in a saving matrix. This relationship leads to a new and simple lower bound for TSP that some times is better than more traditional bounds based on so-called 1-trees. We also offer some upper bounds for the optimal solution of TSP. Some examples are given in order to illustrate the new bounds and compare these with the classical ones

The role of supply vessels in offshore logistics

Oil companies are gradually becoming more focused on optimizing their upstream logistics. However, little research regarding upstream logistics has been published. We argue that more research would be beneficial and that more attention must be given to one of the largest cost elements in the upstream chain – the supply vessels. We explore the supply vessel as a means of transport and carry out a logistics analysis based on their use on the Norwegian continental shelf. Carrying capacity, sailing, loading and unloading capabilities are established as the main features of a supply vessel. Thereafter we discuss relevant logistical trade-offs within and among these features, and also in relation to the environment the vessels operate in. This elaboration clearly shows the complexity involved when searching for the ‘optimal’ supply vessel. The analysis also indicates the design and logistics system features that should be challenged in the future. We believe that the findings in this article will be of considerable value for both practitioners and academic