Hybrid approaches to optimize mixed-model assembly lines in low-volume manufacturing

In this paper, a production planning problem for mixed-model assembly lines in low-volume manufacturing as can be found in aircraft manufacturing is considered. This type of manufacturing is labor-intensive. Low-volume production of huge-sized jobs, i.e. airplanes, is typical. Balancing labor costs and inventory holding costs assuming a given job sequence is the purpose of this paper. Therefore, worker assignments to each station and start times and processing times for each job on each station are determined. Two different mathematical models are proposed. The first formulation is a time-indexed linear formulation that allows for a flexible allocation of workers to periods and stations while the second one has a non-linear objective function and allows only for a fixed assignment of workers to stations. It is proven that the second formulation leads to a linear program with continuous decision variables if the values of the decision variables that determine the number of workers assigned to a station are given, while the first formulation contains even in this situation binary decision variables. Heuristics that hybridize the mathematical formulations with variable neighborhood search techniques are proposed. Computational experiments on randomly generated problem instances and on real-world instances demonstrate the high performance of the heuristics.