Optimization of Discrete Manufacturing Processes — Branch and Bound Method

Abstract

There are three kinds of papers connected with the branch and bound method (B&B). The very general ones (artifical intelligence level), the papers presenting algorithms for fixed problems and the papers considering the method applied to some class of problems (e.g. the discrete programming. The papers dealing with B&B applied to optimization of control of discrete manufacturing processes are usually of the second kind. This paper is aimed at generalization and formal discussion of given there algorithms, thus it belongs to the last group. It uses the mathematical model of the vast class of discrete manufacturing processes, proposed in the earlier author’s papers. Basing on the introduced there formalism, a new classification of fundamental conception of algorithms is presented, different types of lower bounds are defined and domination rules for lower bounds are determinated. The paper refers to algorithms that do not use the discrete programming model.