Optimizing Vehicle Repairs Scheduling Using Mixed Integer Linear Programming: A Case Study in the Portuguese Automobile Sector

This study investigates the scheduling of mechanical repairs performed at a Portuguese firm in the automobile sector. The aim is to reduce the amount of time that vehicles spend inactive between interventions by developing a mathematical model that takes into account the available resources and mechanics, the necessary interventions, and the time required for each repair. To accomplish this, a mixed-integer linear programming (MILP) model was employed, incorporating various variables to schedule interventions, allocate resources, and determine start times for each vehicle. The problem was formulated using the AMPL modeling language, and real-world instances of the problem, derived from data provided by the company, were solved using the Gurobi solver. Results show that the developed model significantly improves the scheduling of the vehicles’ repairs at the firm, leading to a reduction of 67% on average in the downtime of the vehicles and allowing an automatic correct schedule of the mechanical interventions. Moreover, the comparison of the scheduling obtained from the developed model and the firm’s procedure shows that interventions on vehicles arriving at the repair shop are mostly repaired on the day of entry, allowing for quicker delivery to the customer.