A Lagrangian-ACO matheuristic for car sequencing

In this study, we investigate a hybrid Lagrangian relaxation ant colony optimisation for optimisation version of the car sequencing problem. Several cars are required to be scheduled on an assembly line and each car requires a number of options such as sunroof and/or air conditioning. These cars are required to be sequenced such that sub-sequences of specific sizes may only include a limited number of any option. While this is usually a hard constraint, in this study we treat it as a soft constraint and further require the utilisation of options be modulated across the sequence leading to the optimisation problem. We investigate various Lagrangian heuristics, ant colony optimisation (ACO) and hybrids of these methods. The results show that the Lagrangian-ACO hybrid is the best performing method for up to 300 cars.