Optimizing a new robust location-pricing problem in agricultural economy by customized bi-level algorithm

This study investigates the joint optimization of maintenance center location and pricing (MCLP) within the operational context of agricultural economies, focusing on agricultural machinery maintenance centers operated by manufacturing companies that provide maintenance services to customers at predetermined prices. We model the MCLP problem as a bi-level optimization model to capture its bi-level decision structure. In the upper level model, the company makes location and pricing decisions, while in the lower level model, customers decide whether to visit the maintenance center to seek services based on these decisions and their own budgets. In case of general uncertainty in maintenance demands, we adopt the globalized distributionally robust optimization method to model the maintenance problem. Under the company’s risk-averse criterion, upper level objectives are established using the Mean-Conditional Value at Risk standard, which addresses expected performance and potential tail losses under uncertainty. In order to improve computational efficiency, we design a new customized bi-level solving algorithm to solve our transformed bi-level model. Finally, we conduct a series of numerical experiments based on real case studies to validate the effectiveness of our proposed optimization method and algorithm. The experimental results indicate that modeling and characterizing uncertainty are crucial in shaping a company’s strategic decisions and customers’ response behaviors. In addition, the company’s risk preference has a multiplier effect on customer responses, emphasizing the necessity of disclosing risk attitudes within a bi-level decision-making framework.