Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

Determination of efficient solutions for point-objective locational decision problems

In this paper we study the point-objective problem of locating in ² a facility serving a finite number of customers to minimize the travel time, or the distance, to each customer.Travel times, or distances, are measured by going in the directions of some given vectors which means that, under some conditions, are evaluated by a norm function. An algorithm is proposed to find all the quasi-efficient points and all the efficient points (alternately or strictly), for any given set of travelling directions. Consequently, the problem of efficiency is addressed in a general framework.     

On the uniqueness of optimal solutions in continuous location theory

This paper deals with the uniqueness of an optimal solution in general continuous single facility minisum and minimax location problems. We define the concept of an S-norm and obtain general conditions which guarantee the existence of a unique optimal location. Some consequences for the uniqueness of optimal locations in multi-facility location problems are discussed.