2-Median Problem on a Tree with Grey Parameters

Abstract

The purpose of this paper is to find solutions to the 1-median and 2-median problems on a tree network with grey parameters. Generally, the p-median problem asks for finding a set of p facilities on the vertices of a given tree such that the sum of weighted distances from vertices to the closest facility is minimized. First, the 1median problem with grey weight of vertices and edge lengths is considered, and by showing some properties for this problem, a linear time algorithm is proposed. Then an edge deletion method with time complexity is developed to find a solution to the 2-median problem with grey parameters. Moreover, some new concepts of networks with grey parameters are defined in this paper.

Prioritization of emergency assembly points in a campus using grey p-median linear programming model

“…While solving this problem for a general network is computationally classified as NP-hard, it is highly relevant in various fields. Practical implementations include the strategic positioning of essential services like police stations, distribution hubs, switchboards for telecommunication and financial institutions to serve populations efficiently (Fathali and Salookolaei, 2023; Kariv and Hakimi, 1979). So, the p-median linear programming method with grey parameters is adopted and used as an optimizer to assign the people to the most proper EAPs with grey capacity levels for each EAP area in this study.…”