problem becomes that of minimizing the sum (H) of the radial distances from a single junction to each city. This is equal to
where d(ij) is the network distance between any pair of centres,i and J. Figure 3.5 shows two possible outcomes. If the triangle formed by three centres has no angle greater than or equal to 120°, then the optimum location for the junction is that point where the radial routes to each centre form three angles of 120° (Figure 3.5A) if the triangle contains an angle greater than 120° the optimal location for the junction is at that vertex Figure 3.5B)
Figure 3.5 Figure Location of routes within a three city system.