Stochastic Cost-Profit Tradeoff Model for Locating an Automotive Service Enterprise

Facility location allocation (FLA) is considered as the problem of finding optimally a facility´s location with the maximum customer satisfaction, the maximum profit of investors of the facility, and the minimum transportation cost of its oriented-customers. In practice, some factors of the FLA problem, i.e., customer demands, allocations, even locations of customers and facilities, are usually changing, and thus the problem features with uncertainty. To account for this uncertainty, some researchers have addressed the stochastic profit and cost issues of FLA. However, a decision-maker hopes to obtain the specific profit of investors of building facility and meanwhile to minimize the cost of target customers. To handle this issue via a more practical manner, it is essential to address the cost-profit tradeoff issue of FLA. Moreover, some region constraints can greatly influence FLA. By taking the vehicle inspection station as a typical automotive service enterprise example, this work presents new stochastic cost-profit tradeoff FLA models with region constraints. A hybrid algorithm integrating stochastic 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.