| n this work, we are interested in the Traveling Salesman problem (TSP) in two and three dimensions and its application to some optimization problems arising in the operations of a numerical control machine such as a punch press. We begin by describing our problem in chapter 1, then we introduce its sub-problem which is the average distance between two points. In chapter 2, we give the definition, the applications and some exact and approximatif methods used to resolve the TSP problem in the literature.;In chapter 3, the expected distance between two random points in a rectangle (square) or in a rectangular parallelepiped (cube) is computed under three different metrics: the Manhattan metric, the Euclidean metric, and the Chebychev metric.;In chapter 4, optimal strip strategies are developed for a variety of two-dimensional and three-dimensional sequencing problems arising in flexible manufacturing. These strategies are appropriate for CNC drilling operations, NC punching operations, and circuit board population, for example. Seven different metrics are considered.;In chapter 5, we will suppose that at least one of the one-dimensional variable X,Y or Z is uniformally discrete and we will retrieve asymptotically some chapter 4 and 5 results.;The purpose of chapter 6 is to formulate and solve an optimization problem arising in the operations of a numerical control machine such as a punch press. Holes of n different types must be punched by a press on a linear object such as a metallic bar. Each type of hole requires a different tool and tools are mounted on a fixed rotating carousel. Holes are punched in several passes on the bar, using each time a contiguous subset of tools. The problem is to determine a partition of the tools into subsets that will minimize expected completion time. The problem is first formulated as a shortest path on an acyclic graph. It is shown how this problem can be solved in... |
