Caro-Life is a financial services firm that specializes in selling life-, auto-, and home- insurance to residential consumers in the state of North Carolina The company is planning to expand and offer its services in South Carolina as well. The company wants to open a set of 10 offices throughout the state in such a way to ensure that all residents of the state can access at least 1 office in either their county of residence or an adjacent county. The set of counties adjacent to the county containing each office will be regarded as the sales territory for that office. (Note that a county is considered to be adjacent to itself.) Figure 7.21 (and the file Fig7-21xIsm that accompanies this book) shows a portion of an Excel spreadsheet with a matrix indicating county adjacencies throughout the state and the estimated population and geographic size (in square miles) for each potential sales territory. (Values of 1 in the matrix indicate counties that are adjacent to one another.)

Sales of insurance products in a given area tend to be highly correlated with the number of people living in the area As a result, agents assigned to the various offices want their sales territories to contain as many people as possible (to maximize sales potential). On the other hand, territories containing large amounts of people may also be comprised of a Large geographic area that may require lots of travel on the part of the agents. So the goal of having a territory with lots of People is sometimes in conflict with having a territory that is compact in size. It is important for Caro-Life to design its sales territories in as equitable a manner as possible (that is, where the territories are similar in terms of geographic size and sales potential).

Figure 7.21 Data for the Caro-Life sales territory planning problem

1. Assume Caro-Life wants to maximize the average sales potential of its 10 offices. Where should it locale offices, and what is the population and geographic area associated with each office?
2 Assume Caro-Life wants to minimize the average geographic area covered by each of its 10 offices. Where should it locate offices, and what is the population and geographic area associated with each office?
3. Determine the solution that minimizes the maximum percentage deviation from the optimal objective function values identified in parts a and b. According to this solution, where should Caro-Life locate its offices, and what is the population and geographic area associated with each office?
4. Suppose Caro-Life considers maximizing average sales potential of its territories to be twice as important as minimizing the average geographic size of its territories. Find the solution that minimizes the maximum weighted percentage deviations. According to this solution, where should Caro-Life locate its offices, and what is the population and geographic area associated with each office?
5. What other issues would you suggest Oro-Life take into account in modeling this decision problem?

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