In the banking industry, banks often serve customers through successive stages of banking facilities

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1. Problem description

In the banking industry, banks often serve customers through successive stages of banking facilities (Min and Melachrinoudis, 2001). For instance, automatic teller machines (ATMs) can only provide basic banking services that allow customers to deposit funds, receive cash, and obtain statements of their current account balance. Besides the basic banking services, bank branches can provide a variety of advanced banking services such as maintaining a safety deposit box, applying for residential loans, and purchasing government bonds.

Bank Z is planning to establish a banking system in a new region. Let I denote the set of market areas within the region. Bank Z has predicted the demands in each market area i I. Let hBSC and hADV denote the predicted demands for basic banking services and advanced banking services in market area i Є I, respectively.

Bank Z has also identified a number of candidate sites for banking facilities. Let JATM denote the set of candidate sites for ATM facilities and JBR denote the set of candidate sites for bank branches. Let fATM denote the cost to build an ATM facility at candidate site jE JATM and FBR denote the cost to build a bank branch at candidate site jЄ JBR. The total cost on building banking facilities (including both ATM facilities and bank branches) cannot exceed a budget B.

Define a graph G = (N, A), where N = IU JATM U JBR is the node set, and A = {(i,j) i, j N,ij} is the arc set connecting the nodes in N. Each arc (i,j) € A is associated with a nonnegative travel distance dij. The objective of Bank Z is to minimize the total demand-weighted travel distance between the market areas and banking facilities.

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