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.
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.
Start at any corner of the solid (Hamilton labeled each corner with the name of a large city), then by traveling along the edges make a complete 'trip around the world', visiting each vertex once and only once, and return to the starting corner." Today this is called finding a Hamiltonian circuit
. The 20 3-cycles of PELARGONIUMS are the "vertices" that must be visited in a circuit on our graph.
Martello, "Algorithm 595: An Enumerative Algorithm for Finding Hamiltonian Circuits
in a Directed Graph," ACM Transactions on Mathematical Software, vol.
Subi, Nearly tight bounds on the number of Hamiltonian circuits
of the hypercube and generalizations, Inf.
Ore, "Note on hamiltonian circuits
," The American Mathematical Monthly, vol.
 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.
A note on Hamiltonian circuits
. Discrete Mathematics, 2:111-113, 1972.