Exact and metaheuristic approaches for a real-world discrete lot-sizing and scheduling problem in the automotive industry

We address a production scheduling problem arising in the seat manufacturing auto industry, characterised by multiple racetracks and a wide variety of car models. The challenge is to determine the optimal sequence of molds to mount on each racetrack to maintain inventory levels within target ranges while minimising changeovers. To tackle this, we formulate a mixed-integer programming model evaluated using Gurobi. Additionally, we develop a Greedy Randomised Adaptive Search Procedure (GRASP) to provide a practical, non-commercial alternative. The GRASP incorporates two specialised local search procedures: the first achieves feasibility by reducing shortages, and the second aims to minimise changeovers. Computational experiments on 133 real-world instances demonstrate the merit of our approaches. The exact MIP solver proves optimality in under 30 seconds on average. Given the same 30-second budget, GRASP achieves a 2.42% average deviation, which is equivalent to fewer than a single additional changeover, finding 77% of global optima. Extending the runtime to the 5-minute company limit reduces deviation to 1.65%. Most importantly, compared to the historical manual baseline, this approach reduces tool changeovers by nearly 50%, resulting in estimated annual savings of $250,000 per plant.