Solve Small-Scale Vehicle Routing Problem

[Vehicle Routing Problem (VRP)](https://en.wikipedia.org/wiki/Vehicle_routing_problem#:~:text=The vehicle routing problem (VRP,given set of customers%3F".&text=The objective of the VRP is to minimize the total route cost.) is a combinatorial problem that determines the optimal path for vehicles to deliver goods from source to destination minimizing cost. Thus, it is formulated as a Mixed Integer Non-Linear Programming (MINLP) problem with a minimizing Objective function.

VRP generalizes the [Travelling Salesman Problem (TSP)](https://en.wikipedia.org/wiki/Travelling_salesman_problem#:~:text=The travelling salesman problem (also,returns to the origin city%3F").

Problem Description: Consider a network with N=6 nodes with _E=10 _edges connection these nodes as shown below. The goal is to find the path with the lowest cost connecting nodes _A _and _F _without making any sub-tours.

Routing Network Diagram

Solution: There are 16 possible paths that connect node A and in the above diagram, which are A-B-C-F, A-B-C-E-F, A-B-C-D-E-F, A-B-D-C-F, A-B-D-C-E-F

A-B-D-E-F, A-C-F, A-C-E-F, A-C-D-E-F, A-C-B-D-E-F, A-D-B-C-F, A-D-B-C-E-F, A-D-C-F, A-D-C-E-F, A-D-E-C-F, and A-D-E-F. The optimal path is A-D-E-F with total cost = 4.

#vehicle-routing-problem #prescriptive-analytics #mathematical-modeling #gam #operations-research #data analytic

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