This bachelor thesis describes the Lagrange relaxation. An important step in this solving technique is the way of updating the Lagrange multipliers in it. Therefore two basic tech- niques, named as the subgradient method and the bundle method, and some betterment of these are introduced. The subgradient method uses line search with subgradients to reach the best multipliers. In comparison to that the bundle method uses an approxima- tion based on a collection of subgradients. The profits and disadvantages of these two methods and their betterments are discussed in this thesis. Additionally the Lagrange relaxation method is used to solve the optimal scheduling and routing in extramural health care. Therefore two variants of Lagrange relaxation are presented. One of them has been implemented with two different ways of updating the multipliers, the subgradient method and in comparison to that the bundle method. In this implementation the bundle method returned better results for specific parameters. The way of selecting these specific parameters is discussed in the end of this thesis.     «

This bachelor thesis describes the Lagrange relaxation. An important step in this solving technique is the way of updating the Lagrange multipliers in it. Therefore two basic tech- niques, named as the subgradient method and the bundle method, and some betterment of these are introduced. The subgradient method uses line search with subgradients to reach the best multipliers. In comparison to that the bundle method uses an approxima- tion based on a collection of subgradients. The profits an...     »