# In Section 9.1 of the text, we presented the following simplified version of the…

In Section 9.1 of the text, we presented the following simplified version of the warehouse-location problem:

a) The above model assumes only one product and two distribution stages (from warehouse to customer). Indicate how the model would be modified if there were three distribution stages (from plant to warehouse to customer) and L different products. [Hint. Define a new decision variable xijkl equal to the amount to be sent from plant i, through warehouse j, to customer k, of product `.]

b) Suppose there are maximum capacities for plants and size limits (both upper and lower bounds) for warehouses. What is the relevant model now?

c) 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? [Hint. Define a new variable zjk = fraction of demand of customer k satisfied from warehouse j.]

d) Assume that each warehouse i experiences economies of scale when shipping above a certain threshold quantity to an individual customer; i.e., the unit distribution cost is ci j whenever the amount shipped is between 0 and di j, and c 0 i j (lower than ci j) whenever the amount shipped exceeds di j . Formulate the warehouse location model under these conditions.

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