Leader-follower competitive facility Location and Design problem in an uncertain environment

This paper aims at providing a new approach to optimize location and design (quality) decision for new facilities as a leader-follower competitive configuration under the condition that competitor’s reaction is unknown. A chain is considered as a leader in the first level and tends to open a new facility in a specific market where similar competitor facilities as follower already exist. In the second level, the follower decides on locating and designing some facilities through the market subject to the location and design of leader’s facilities to keep or capture more market share. The market share captured by each facility depends on its distance to customers and its quality based on probabilistic Huff-like model. In facts, the leader decides on location and quality of its own new facility based on the follower reaction strategies to maximize its profit. Since the number of the follower’s new facilities are unknown for the leader, "robust optimization" is used for modeling this problem. A case from two chain stores in the city of Tehran, Iran, is studied and the proposed model is implemented. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in uncertain competitive environments.