A robust optimization approach to multi-period competitive location problem for bank branches considering first-mover advantage

Abstract

This paper proposes a robust, dynamic, multi-objective optimization approach to the capacity-location problem for bank branches in a competitive environment named Multi-Period Competitive Location (MPCLP) Problem. The objective functions include, maximizing total profit and maximizing minimum distance between active branches. The decision variables include branch merger and acquisition (M&A), branch establishment and determination of branch capacities at each period. Market share is calculated using a modified Huff gravity function that considers distance and design (capacity) of the branch, as well as the effect of first-mover advantage. In other words, in this model, branches established sooner have comparative advantage over new comers. The resultant bi-objective model is transformed into a single objective nonlinear mixed integer programming problem using Epsilon Constraint technique. To deal with uncertainty in demand, a scenario-based robust optimization approach is applied. Given the NP-hard nature of the proposed model, we apply a hybrid Genetic Algorithm-Variable Neighbourhood Search (GA-VNS) algorithm to deal with large-scale problems. We demonstrate the performance of our proposed algorithm on a real case study in northern Tehran and validate the results against those obtained from exact algorithms in small-sized problems, as well as single genetic and variable neighbourhood search algorithms in large-scale problems. Our results show that our algorithm's performance in small-scale problems is comparable to that provided by exact algorithms, while also outperforming both genetic algorithm and variable neighbourhood search in most large-scale problems.