Lockbox Location

Problem: You need to locate postal lockboxes to minimise "float" while still serving all customers.

As a corporate cash manager or officer of a bank whose clients must deal with the problem of optimising collections from customers located at large distances from your home office, you must decide where to locate postal lockboxes so that customers' deposits can be credited with a minimum of expense caused by mail delay (or "float time") while minimising operating costs associated with the locations. In addition, each customer must be assigned to exactly one location.

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Your customers, located in Seattle, Los Angeles, Houston, Philadelphia, and Miami, whose deposits must be credited with a minimum of float time, may be assigned to potential lockbox locations in New York, Atlanta, Cincinnati, Denver, or St. Louis. 

It may also be more cost-efficient to assign them to the home office.

Each customer must be assigned to a postal lockbox so as to minimise the sum of float-time expense and monthly fixed operating costs.

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