Optimal Location of Welds on the Vehicle Wiring Harness: P-Median Based Exact and Heuristic Approaches

Nowadays vehicles are highly customizable products. Indeed, they can be equipped with a great number of options directly chosen by the customers. This situation provides several harness design problems to automotive companies, where by harness we mean the set of conducting wires (cables), positioned within the vehicle frame (chassis), which transmit information and electrical power to the options to make them operative. In this context we focus on an optimization problem arising in the construction and assembly phase of the harness within a vehicle. The options selected by customers have to be connected through a harness shaped in a tree structure within the vehicle chassis. In particular, the wiring has to connect subsets composed of two or more options. The total length of the connecting cables could be very large if a dedicated cable would be used for each couple of options in each subset. This length can be significantly reduced by realizing the connection through the usage of cable weldings. This work introduces for the first time the problem of the optimal placement of the weldings on the wiring harness tree of a vehicle, aimed at minimizing the total length and/or the cost of the cables, weighted by their gauge. The problem can be schematized as a p-median problem (PMP) on a tree in a continuous and discrete domain, with additional technological constraints related to the welding positions and mutual distance. This work proposes an integer linear programming model and a matheuristic aimed at finding exact and/or heuristic solutions for this constrained PMP. The efficiency and the effectiveness of the proposed methodologies have been proved through the solution of test instances built from real data provided by an automotive company.