CHB, Inc., is a bank holding company that is evaluating the potential for expanding into a 13-county region in the southwestern part of the state. State law permits establishing branches in any county that is adjacent to a county in which a PPB (principal place of business) is located. The following map shows the 13-county region with the population of each county indicated.
a. Assume that only one PPB can be established in the region. Where should it be lo- cated to maximize the population served? (Hint: Review the Ohio Trust formulation in Section 7.3. Consider minimizing the population not served, and introduce variable yi = 1 if it is not possible to establish a branch in county i, and yi = 0 otherwise.)
b. Suppose that two PPBs can be established in the region. Where should they be located to maximize the population served?
c. Management learned that a bank located in county 5 is considering selling. If CHB purchases this bank, the requisite PPB will be established in county 5, and a base for beginning expansion in the region will also be established. What advice would you give the management of CHB?
Text Book: An Introduction to Management Science: Quantitative Approaches to Decision. By David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm, James Cochran.