Bi-Level Programming for Competitive Facility Location in the Nigerian Retail Banking Sector

Branch location decisions in Nigeria's competitive retail banking sector involve strategic interaction between rival banks, as the value of a branch location depends not only on its proximity to customers but also on the locations chosen by competing institutions. This study develops a bi-level programming model for competitive branch location decisions in the retail banking sector across Ibadan metropolis, Oyo State, South West Nigeria. The bi-level model captures the leader-follower dynamic in which a bank entering the market (leader) locates branches anticipating that an incumbent competitor (follower) will respond optimally to the entrant's choices. Customer demand is modelled using a probabilistic choice model that allocates banking patronage among branches based on proximity, service quality, and loyalty parameters estimated from a survey of 380 retail banking customers. The inner optimization problem is the follower's branch network response, while the outer problem maximizes the leader's captured demand share. A descent search heuristic is applied to solve the computationally challenging bi-level formulation. Results from the empirical case indicate that the bi-level optimal location plan for the entrant captures 23 percent greater market share than a naively optimal solution that ignores competitive response, demonstrating the strategic value of modelling competitive dynamics explicitly. Recommendations include embedding bi-level location analysis in new market entry planning for retail banks and other competitive service sectors in Nigerian cities. Keywords: bi-level programming, competitive facility location, retail banking, Ibadan, market share