Cyclic Routing on Networks

Abstract

Every year, a team of executives in the corporate office of GTC visits each of the five regional offices to inspect the work at those offices. This trip is a round trip in which the officers visit each of the region offices exactly once before returning to the corporate office. The regional offices are located in cities connected to each other by air. The cost of flying between each pair of cities is given in Table 6.1. C denotes the city in which the corporate office is located, and R1 through R5 denote the cities in which the regional offices are located.

The total cost of air travel would obviously depend on the route that the team of executives takes. For instance, if they travel from C to R1 to R2 to R3 to R4 to R5 and back to C, then the cost per executive would be Є4200. On the other hand, if they travel from C to R3 to R5 to R2 to R4 to R1 and back to C, then the cost per executive reduces to Є3250. The financial department at GTC wants to find out how to route the travel of executives so that the total travel costs are minimized.