History

Weber, at the beginning of the 20th century, generalized the problem by adding weights to facilities, which represents the amount of demand or population added to the points. If an installation was in a weighted medium, it satisfied the demand of the points with the minimum cost of transport, this problem came to be known as the multi-Weber problem.

In the 20th century, Cooper (1963, 1964) provided heuristic solutions for this problem.

Hakimi did not formulate the p-median as a whole linear programming problem. The P-median problem, introduced by Hakimi (1964), takes the demand between points by measuring the average that is the distance between the demand points and the facilities, when the average distance decreases the accessibility and efficiency of the facilities increases this measure. define as: determine the location of the P facilities so that the total distances between the demands and the facilities are minimized.

Later ReVelle and Swain (1970) were not familiar with the results of Hakimi assumed the node location of only what they call the central facilities. They formulated the P-median problem as a whole linear programming problem where the problem of central location facilities consists of designating m of n communities (m <n) as centers in such a way that the average distance or travel time per person is minimum. The average distance (or time) is equal to the sum of the products of the population and miles (or minutes) traveled divided by the sum of the populations.

"Taking into account the location of n points that contain known quantities of the demand, p these points are designated as facilities and assigned to each demand to an installation, in such a way that it is minimized in the total weighted distance between the demands and the facilities."