Three Variants of a Discrete Median Problem Including a Train Network

Abstract

In this paper, we treat a problem for locating facilities within a train network. Concretely, given the number of facilities, a train network, and a distribution of facility users in an area, the problem objective is to minimize the sum of journey times to the nearest facilities for all users, where each facility is located on a station. The problem is referred to as a discrete median problem including a train network. We first introduce three models for accessing a facility. We then formulate the problem under each model, the first of which reduces to a p-median problem, whilst the remaining two are formulated as two geographical optimization problems. For each problem, we also implement a simple solution method using a standard local search,and show some computational results.