Consider a version of the warehouse-location problem, where a manager must decide which of N warehouses to open for meeting the demands of M customers for a good with minimum costs. The decisions to be made are which warehouses to operate and how much to ship from any warehouse to any customer.

The relevant parameters are:

fj=Fixed operating cost for warehouse i, if opened fj=Fixed operating cost for warehouse i, if opened

cij=per unit transportation cost for shipping from warehouse i to customer jcij=per unit transportation cost for shipping from warehouse i to customer j

Dj=Demand at customer jDj=Demand at customer j

1. Formulate the problem as a mixed integer programming model.

2. Assume that each customer has to be served from a single warehouse; i.e., no splitting of orders is allowed. How should the warehousing model be modified?

3. Indicate how the model would be modified if there were three distribution stages (facilities->warehouses->customers).