Vehicle routing problem is a classical application case of Operation research.
I need to implement the same in electric vehicle routing problem with different constraints.
I want to understand mathematics behind this. The journals available discuss different applications without much talking of mathematics.
Any book/ basic research paper/ PhD/ m.tech thesis will do the needful.
Thanks in advance.
You can check the following books on Operations research:
1. Operations Research by Hamdy Taha
2. Linear Programming and Network flows by Bazaara
3. Mathematical Programming by Kambo
4. Nonlinear Programming by Bazaara, Sherali and Shetty.
2. Operations Research book by Gupta and Hira
please read this article:
https://www.semanticscholar.org/paper/Modeling-and-Analysis-of-Bus-Scheduling-Systems-of-Berhan-Mengistu/307376f412c5f36805cae91e4b99f1a7762afa60#citing-papers
Hi,
You may find this presentation useful:
https://www.slideshare.net/ArianRazmiFarooji/multi-depot-timedependent-vehicle-routing-problem-with-heterogeneous-fleet
VRP is generalisation of another classical Operation Research (OR) problem, called Travelling Salesman Problem or TSP in short. TSP is defined as follows:
There is a list of cities and distances between them are known. What will be the shortest path, entering and exiting from each city exactly once, and at the end returning to city, where we started from.
VRP generalises TSP, in that sense there is a vehicle with known capacity which needs to start from "depot", visit certain cities (with known distance) and when its capacity limit is met or at the end of service time returns to the depot.
There is a vast literature on exact and heuristic approaches to vehicle routing problems. (You are looking at several thousands journal articles!)
If you are interested in exact approaches, then you need to be familiar with the following:
(i) The basics of integer programming, including the branch-and-bound method and cutting-plane methods.
(ii) The basics of computational complexity, including the concept of polynomial-time algorithms, pseudo-polynomial-time algorithms and NP-completeness.
(iii) Elementary graph theory (nodes, edges, arcs, and so on).
It also helps to know a bit about:
(iv) Dynamic programming.
(v) Lagrangian relaxation.
(vi) The branch-and-cut method, which combines branch-and-bound with strong cutting planes from polyhedral studies.
(vii) The branch-and-price method, which combines branch-and-bound with Dantzig-Wolfe decomposition and dynamic programming.
A good place to start is the book "The Vehicle Routing Problem", edited by Toth and Vigo. There is also "The Vehicle Routing Problem: Latest Advances and New Challenges", edited by Golden et al.
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