Fuzzy cost-profit tradeoff model for locating a vehicle inspection station considering regional constraints

Facility location allocation （FLA） is one of the important issues in the logistics and transportation fields. In practice, since customer demands, allocations, and even locations of customers and facilities are usually changing, the FLA problem features uncertainty. To account for this uncertainty, some researchers have addressed the fuzzy profit and cost issues of FLA. However, a decision-maker needs to reach a specific profit, minimizing the cost to target customers. To handle this issue it is essential to propose an effective fuzzy cost-profit tradeoff approach of FLA. Moreover, some regional constraints can greatly influence FLA. By taking a vehicle inspection station as a typical automotive service enterprise example, and combined with the credibility measure of fuzzy set theory, this work presents new fuzzy cost-profit tradeoff FLA models with regional constraints. A hybrid algorithm integrating fuzzy simulation and genetic algorithms （GA） is proposed to solve the proposed models. Some numerical examples are given to illustrate the proposed models and the effectiveness of the proposed algorithm.