RAILWAY PLANNING AND DELIVERY SYSTEMS

In the railway sector, train scheduling has been a serious problem. Numerous methods and tools have been created in recent years to compute railway scheduling. In this research, we strive to schedule the trains so that they do not collide while traveling along the same path by presenting a set of heuristics for a constraint-based train scheduling tool. Train scheduling is formulated as a constraint optimization problem. By eliminating delays, we can shorten the passengers' trip time as well as improving the system. Additionally, it has been extremely difficult to plan delivery routes for postmen, salespeople, delivery men, or to plan the sequence of pick-ups for a school bus, etc. Solving such issues involves the highly regarded discrete mathematics discipline of graph theory. This issue calls for a circuit that travels via several different locations. Each location needs to be visited once. And the amount of time and fuel required should be kept minimum. In the realm of developing delivery routes, these issues are solved by employing graph theory and optimization.

Railway Planning

The Ministry of Railways, Government of India, essentially owns Indian Railways. A National Rail Plan (NRP) for India upto 2030 has been created. The goal is to build a railroad system that is "future ready" so that it can develop strategies based on both operational capabilities and commercial policy measures to enhance the railroads' modal share of freight. There is a need to improve rail capacity because it frequently turns out that there aren't enough trains to meet public demands. Occasionally, few trains carry just a small number of passengers. Therefore, careful train scheduling and planning are urgently needed to reduce loss, adhere to, and satisfy public demands.

Delivery System

Routes of the postmans, sales men, delivery guys, etc are planned using the graph theory.
They have to travel to each of the places once and return to the place where they started. However, the time taken and distance covered must be minimum to make it effective in terms of cost and time.
So, the person starts from one place, goes to several places, each of them once and returns to the original place. To complete this in minimum time and/or traveled distance, it could be said that the person should pass from one path just once.
This is a combination of Eulerian circuit and Hamiltonian circuit as each edge as well as vertice needs to be traveled only once. Such a solution would be an optimal solution. However, it may not be possible to find such a circuit every time. So, in that case, one can find a circuit with repetition of minimum number of edges.
Graph theory is used to solve such problems. We have tried to explain how graph theory works and how it is used to solve these problems.