To develop the decision support system for courier dispatching, the problem is defined as finding the Hamiltonian circuit  with the minimum time, minimum distance and type of route travelled.
To determine the Hamiltonian circuit it self is a NP-complete problem and when shortest distance and minimum time is added with the Hamiltonian Cycle, it becomes a very hard optimization problem in the field of operations research.
Given a connected, undirected graph G with n nodes, a least cost Hamiltonian circuit H is a sub graph of a G that connects all of G's nodes and contains one cycle .
This is called a Hamiltonian circuit
after the Irish mathematician Sir William Rowan Hamilton, and sometimes, is referred to as the "traveling salesman's problem".
A closed Hamiltonian path is called a Hamiltonian cycle or Hamiltonian circuit, which we shall abbreviate as HC.
Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J.
Today this is called finding a Hamiltonian circuit.
Other informative Gardner articles about Hamiltonian circuits include "Graph Theory: (Chapter 10 in [G71]), "'Knights of the Square Table" (Chapter 14 in [G77], and "'Uncrossed Knight's Tours (p.
Subi, Nearly tight bounds on the number of Hamiltonian circuits
of the hypercube and generalizations, Inf.
Chapter 9: Multiplications, Divisions And Hamiltonian Circuits
5] Feder, Tomas and Subi, Carlos, Nearly Tight Bounds on the Number of Hamiltonian Circuits
of the Hypercube and Generalizations.
and path coverings of vertices in graphs.