Optimizing the Location of a Production Firm

A facility needs to be located in the plane to sell goods to a set of demand points. The cost for producing an item and the actual transportation cost per unit distance are given. The planner needs to determine the best location for the facility, the price charged at the source (mill price) and the transportation rate per unit distance to be charged to customers. Demand by customers is elastic and assumed declining linearly with the total charge. For each customer two parameters are given: the demand at charge zero and the decline of demand per unit charge. The objective is to find a location for the facility in the plane, the mill price charged to customers and the unit transportation rate charged to customers such that the company’s profit is maximized. The problem is formulated and an algorithm that finds the optimal solution is designed and tested on randomly generated problems.

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