Determination of efficient solutions for point-objective locational decision problems

This paper studies the point-objective problem of locating in ℝ² 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.