This example considers the problem of selecting distribution centers along with their associated customer zones. The mathematical model uses a simple mixed-integer linear programming formulation and can be easily solved by using a standard solver for small and medium datasets.
However, when working this type of problem with a larger datasets, you may consider re-examining your approach to the problem. One option is to decompose the problem into several smaller subproblems that are solved sequentially rather than simultaneously. One such approach, namely Benders' decomposition, is illustrated in this example.
Geoffrion, A.M., and G.W. Graves, Multi-commodity distribution system design by Benders decomposition, Management Science 20, 822-844 (1974).
Distribution System Design, Integer Program, Mathematical Reformulation, Mathematical Derivation, Customized Algorithm, Benders decomposition, Auxiliary Model, Constraint Generation.
A zip file with this example can be downloaded here.