Bank-Branch Location and Sizing under Economies of Scale

The bank-branch restructuring problem seeks to locate bank-branches, maintaining or closing existing branches, in order to provide the service required by its clients, at minimum total cost. This problem has not been the subject of much study, nonetheless it is a common problem that banks are faced with from time to time. We address this nonlinear problem, since economies of scale exist, by formulating it as a mixed binary, integer linear model. The model obtained can be solved by a ready-available software, such as CPLEX. However, the dimensionality problem soon becomes the issue and thus, we also propose a heuristic to solve, approximately, this problem. We have developed a local search heuristic to solve the bank-branch location and sizing problem with concave cost functions. In order to do so, we have modelled this problem as a mixed integer and binary programming model. The heuristic is based on the solution to a related linear integer programming problem. This solution is subsequently improved by iteratively applying drop and swap operations. The computational experiments performed show the effectiveness and efficiency of the proposed heuristic.