A multi-objective open shop model for optimizing scheduling in automotive repair shops

Warranty and after-sales services have become increasingly critical due to their significant cost implications for both manufacturers and consumers. Efficient scheduling in automobile repair shops plays a key role in enhancing customer satisfaction while minimizing operational inefficiencies. This study addresses the daily repair scheduling problem by formulating it as a bi-objective open shop scheduling model. The objectives are to minimize (i) both the total flow time of cars and (ii) the idle and overtime costs of repair stations. We first develop a deterministic Mixed-Integer Linear Programming (MILP) model to determine the assignment and sequencing of repair procedures across specialized stations under eligibility and capacity constraints. To solve larger instances where the MILP becomes computationally expensive, we propose a modified Non-dominated Sorting Genetic Algorithm II (NSGA-II) that uses a station-sequence chromosome, feasibility-aware decoding with conflict-repair (time-shifting) to eliminate inter-station overlaps for each car, and problem-specific crossover/mutation operators. The approach is validated on synthesized test instances and a real-world case study from a major automotive repair center in Iran. Results show that, relative to the manual schedule, the proposed method can reduce total flow time by approximately 42% and idle/overtime costs by 47%, demonstrating the value of optimization-based scheduling for automotive after-sales service operations.