Critical Path Concept for Multi-Tool Cutting Processes Optimization

Abstract

in a cutting process an ordered set of pairs (an elementary cutting operation on an elementary machined surface, datum surfaces set) can be presented as a directed cycle free graph denoted as a KL-graph. Some partitions of the KL-graph lead to an assignment of machining stations to the partition classes of the elementary operations set. Problems similar to the (assembly) line balancing appear when some optimization tasks are formulated. Such tasks differ from the classical balancing problems because times of elementary operations are not constant but they are the functions of the cutting parameters. Since the tools actions may be mapped by a network (PERT methods) balancing and coordination constraints can be formulated as the conditions defining the critical path placement.