Robust competitive facility location model with uncertain demand types.

In competitive settings, firms locate their facilities according to customers' behavior to maximize their market share. A common behavior is consuming from different motivations: one is for convenient demand, and the other is for quality demand. In this behavioral pattern, consumers patronize facilities within convenience for some demands, and patronize high quality facilities beyond convenience range for other demands. This behavior has never been included in competitive facility location problems. Given several other companies' facilities in the market offering similar products or services, we study how a new entrant company can locate facilities based on this customer behavior to maximize its market share. A two-level robust model for the new entrant company is proposed to locate its facilities by taking into account the uncertainty of the types of customers' demands. For medium size problems, we propose an equivalent mixed binary linear programming to obtain exact solutions. For large size problems, an exact algorithm (GCKP-A) for solving the inner-level model is given first by exploring the optimal solution. Then a heuristic algorithm is proposed by imbedding (GCKP-A) and 2-opt strategy into the framework of the improved ranking-based algorithm. The performance of the proposed heuristic algorithm is checked for different size problems. The sensitivity analysis of a quasi-real example shows that: (1) in most cases, the uncertainty between two types of demands does not affect the location scheme; (2) the convenience range, the quality range and the quality threshold play an important role in the market share of the new entrant company.