Solving Some Graph Problems in Composite 3D Printing Using Spreadsheet Modeling

Abstract

The use of composite materials in additive manufacturing has significant potential and prospects for development. However, the 3D printing of composite materials also has some challenges, such as tool path planning and optimization, material distribution and planning, optimization of printing parameters, and others. Graph theory may be suitable for solving some of them. Many practical problems can be modeled as problems of identifying subsets of graph vertices or edges with certain extremal properties. Such problems belong to the category of graph extremal problems. Some of these problems can be represented as integer linear programming problems, for which, in order to solve, modifications of simplex method can be used. These methods are supported by MS Excel Solver add-in, which suggests the possibility of solving these problems effectively with its help. The task of implementing procedures for solving such problems by means of standard engineering software seems to be possible. This paper aims to develop efficient spreadsheet models of some extremal problems for graphs of higher strength in order to prove the feasibility and to unify the procedures of solving such problems via the MS Excel Solver add-in. Several spreadsheet models based on the graph representation by its expanded incidence matrix, while specifying a vector of unknowns as the vector of binary variables associated with vertices or edges of the sought parts of the graph, have been developed and proven to be efficient for solving such problems by simplex method via the MS Excel Solver add-in.