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Encountering numerous vehicles on the roads can pose several risks, including a higher probability of accidents. To address these issues, a thorough examination of cars can significantly reduce these dangers. Technical inspection centers play a crucial role in this process and should be easily accessible. To provide the most customer service coverage at the lowest cost of transportation for technical inspection centers, facility location optimization is proposed in this paper. Specifically, we investigate the location of technical inspection centers (TICs) as a maximum coverage problem while minimizing the cost of TIC locations' construction and customers' transportation. To deal with this problem, we propose a robust programming considering our numeric data's uncertainty. Our research contributes to facility location optimization by providing a novel insight into solving the problem using a hybrid mathematical model. It presents a two-objective linear optimization model with binary variables to address this optimization problem. We used the Augmented Epsilon Constraint (AEC) method via the CPLEX solver and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) method for large-scale problems to solve the model. A case study was conducted to test the numerical analysis methodology and several practical problems of varying scales. The final results demonstrate the effectiveness of the proposed approach in meeting the optimality and feasibility robustness criteria. Identifying optimal TIC locations regarding the paper's main objective proves the advantage of using the mentioned innovative methodology.
Arabahmadi et al. (2023) studied this question.