Connecting business centres and establishing central nodal centres considering distance, population and real GDP as weights using the Weiszfeld algorithm and concept of minimum cost spanning tree - an analysis

This paper proposes a model to find central nodal centres (CNCs) and connect different capitals of states and union territories (UTs) of India based on distance, population and real GDP. The centres are different for different criteria. To locate these centres, the geodetic data are collected for the 34 capital cities of states and union territories (UTs). Using Haversine formulae and the iterative Weiszfeld's algorithm, these centres are located. Both Prim's and Kruskal's algorithms are used to form the minimum spanning tree (MST). In the first case where only the distance is considered, the minimum connecting length of the MST is estimated to be 10,294 km. Finally, considering all the cities and assuming as a TSP; the optimum Eulerian network is framed. Brute force algorithm is used for this purpose. The total aerial distance to be covered is estimated for the network. To convert this to the road distance, the distance has to be multiplied by the wiggle factor. The approximate wiggle factor (road) is estimated considering these 34 cities and is equal to 1.273807. Finding the CNC and mapping the MST shall help in management decisions to find an optimum route and reduce transportation cost.