The Robotic Assembly Line Design (RALD) problem: Model and case studies with practical extensions

Spot welding assembly lines are widely present in the automotive manufacturing industry. The procedure of building the vehicle's body employs several robots equipped with spot welding tools. These robots and tools are a quite costly initial investment, requiring an efficient and conscious line design that meets product demands and minimises implementation expense at the same time. In this paper, the Robotic Assembly Line Design (RALD) problem is proposed and studied based on practical characteristics from an automotive company located in Brazil. A Mixed-Integer Liner Programming (MILP) formulation is developed allowing: (i) station paralleling, (ii) equipment selection, and (iii) multiples robots per workstation. The mathematical model aims at minimising the total cost at the desired production rate, which involves robots, tools and facilities. The proposed model considers dead time during a cycle, space constraints, task assignment restrictions, and parallelism possibilities. Dead time is an unproductive and fixed work-piece handling time included in the capacitated transporter robots' movement time. Computational experiments were performed in order to evidence the parameters' influence over the optimal line design solution. In addition, practical case studies were conducted with parameters collected from a real-world robotic welding assembly line located on the outskirts of Curitiba-PR (Brazil), reaching optimality. Compared to the strictly serial lines, the model led to great advantages by allowing parallel stations in the production system, making it possible to evaluate an expected trade-off between the production rate and the total cost; reductions of several hundred thousand dollars on the production layout cost can be achieved by the company, as indicated by the studied cases.