On vertex adjacencies in the polytope of pyramidal tours with step-backs

We consider the traveling salesperson problem in a directed graph. The pyramidal tours with step-backs are a special class of Hamiltonian cycles for which the traveling salesperson problem is solved by dynamic programming in polynomial time. The polytope of pyramidal tours with step-backs $PSB (n)$ is defined as the convex hull of the characteristic vectors of all possible pyramidal tours with step-backs in a complete directed graph. The skeleton of $PSB (n)$ is the graph whose vertex set is the vertex set of $PSB (n)$ and the edge set is the set of geometric edges or one-dimensional faces of $PSB (n)$. The main result of the paper is a necessary and sufficient condition for vertex adjacencies in the skeleton of the polytope $PSB (n)$ that can be verified in polynomial time.Comment: in Englis

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

The Traveling Salesman Problem

This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances

Shop scheduling with availability constraints

Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem. Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005