Cluster saving - Eine konstruktive Methode des Operations Research

Abstract

How fast can a project be realized, which resources are required, how to allocate them and which economizing potential lays in the project budget? How to set up a network without causing any capacity transgression, but simultaneously, the areas of the servers are almost fully occupied? What are the least costs for a day delivery of products to our customers and what does moderate costs scheduling of delivery look like? Which beam-cut does a aluminum-frame construction require? How does an optimized scheduling of parallel processes look like in a multiprocessor system? Which jobs must be carried out on which engine? Which routes shall freight engines fly and how should take-offs and landings be planned?

Numerous optimization tasks from different areas of technology and economics are based on a common problem structure. Its solution contains the partitioning of a set of objects under economic points of view. The goal of the investigation is to gain a high capacity utilization rate of the corresponding system. In many cases the quality of a partition depends on the measure in which a favorable sequence (permutation) of the elements within the Cluster can be reached. Although application-specific restrictions can delimit the number of the feasible solutions, the combinatorial latitude generally remains enormously large so that heuristic procedures to the solution of these hard problems must be applied.

In this paper, a general class of combinatorial problems is defined first and then characteristic steps of a corresponding solution method based on the principle of the savings-method of CLARKE and WRIGHT are presented. Last the discussed approach is illustrated by means of the solution of a constrained Pickup and Delivery Problem in the area of people logistics.