What is Vehicle Routing Problems with Time Windows?
Vehicle routing problem with time windows (VRPTW) can be defined as choosing routes for limited number of vehicles to serve a group of customers in the time windows. Each vehicle has a limited capacity. It starts from the depot and terminates at the depot. Each customer should be served exactly once.
How do you fix a car routing problem?
Setting up the problem
- Minimize the global transportation cost based on the global distance travelled as well as the fixed costs associated with the used vehicles and drivers.
- Minimize the number of vehicles needed to serve all customers.
- Least variation in travel time and vehicle load.
What is open vehicle routing problem?
In the open vehicle routing problem (OVRP), a vehicle does not return to the depot after servicing the last customer on a route. Contractors who are not employees of the delivery company use their own vehicles and do not return to the depot.
What is multi depot vehicle routing problem?
The multi-depot vehicle routing problem (MDVRP) arises as a generalisation of the vehicle routing problem (VRP), where vehicles depart from and return to one of multiple depot locations. Therefore, besides the definition of the vehicles’ routes, it is also necessary to decide from which depot the customers are visited.
What is dynamic vehicle routing problem?
The Dynamic Vehicle Routing Problem (DVRP) is one of the important variants of VRP. Its aim consists in designing the optimal set of routes for a fleet of vehicles in order to serve a given set of customers while new customer orders arrive during the performance of the planned earlier work day.
Is vehicle routing problem NP-hard?
In mathematical terms, the VRP is classified as an NP-hard problem, meaning that the required solution time increases exorbitantly with size. The number of possible solutions to the VRP is of the order of n!, where n is the number of nodes (locations the vehicle must reach) in the network.
What are NP-hard problems?
A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.
What is NP problem in DAA?
Definition of NP class Problem: – The set of all decision-based problems came into the division of NP Problems who can’t be solved or produced an output within polynomial time but verified in the polynomial time. NP class contains P class as a subset. NP problems being hard to solve.
How do you know if a problem is NP-hard?
The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.
What is P and NP in DAA?
P: is the set of decision problems that are solvable in polynomial time. NP: is the set of decision problems that can be verified in polynomial time.
How do you know if it is a NP problem?
A decision problem is in NP if there exists a polynomial time verification algorithm C(I,S) that takes both an input and a proposed solution, and verified whether the solution is ok, and satisfies the following properties: polynomial in the length of the input.
How do you solve NP problems?
Solving NP-complete problems
- Approximation: Instead of searching for an optimal solution, search for a solution that is at most a factor from an optimal one.
- Randomization: Use randomness to get a faster average running time, and allow the algorithm to fail with some small probability.