Production line balancing by P-graphs

Abstract

Assembly industry plays a key role in Central and Eastern Europe. Large companies and their subcontractors manufacture automotive and electronic products from components, employing a significant number of human resources. Due to the growing labor shortage, it is critical that the production lines should be optimally loaded, i.e., the tasks have to be evenly distributed among the workstations according to their cycle times. In this article a novel formulation of the problem by process graphs or P-graphs is presented leading in an easy to follow visual definition of the potential task to employee allocations, as well as the options to generate a mathematical programming model algorithmically, to be solved by general purpose solvers or get the optimal and alternative N-best allocations by P-graph software. In addition to the theoretical presentation, the article shows the results achieved by applying the proposed methodology in a real-world environment in a computer assembly plant. The P-graph approach provides visual modeling by graphs in a graphical editor and helps understand the relations of decision variables while generating the corresponding mathematical model, which can be generalized for a class of problems and rebuilt according to actual data. As a result, the basis for rigorous mathematical optimization-based decision support can be built up according to graphical models easily understandable by end users as well.