Pricing and locating economic activities in a competitive environment, and maximize profit

What is it about?

We face the problem of (locating facilities and) finding optimal prices of a service or good offered to a discrete set of clients, under the assumption that each client will select a provider that minimizes price + transportation (or generic distance) cost. We examine this problem in the special case of clients and facilities scattered on a line, providing an efficient algorithm for the case of a single competitor facility, and proving - on the other hand - that the problem is hard when two competing facilities are involved.

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Why is it important?

This problem has a strong relationship to envy-free pricing and spatial competition in general.