We use a branch-and-cut search to solve the Whizzkids’96 vehicle routing problem, demonstrating that the winning solution in the 1996 competition is in fact optimal. Our algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, Chvátal, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located a...

The Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem that can be described as follows: given a fleet of vehicles with uniform capacity, a common depot, and several costumer demands; find the set of routes with overall minimum route cost which service all the demands. The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling sales...

The multiple traveling salesmen problem (MTSP) is an extension of the traveling salesman problem with many production and scheduling applications. The TSP has been well studied including methods of solving the problem with genetic algorithms. The MTSP has also been studied and solved with GAs in the form of the vehicle-scheduling problem. This work presents a new modeling methodology for settin...

multiple traveling salesman problem (mtsp) is one of the most popular operation research problem and is known as combinatorial optimization problems. mtsp is an extension version of the famous and widely used problem named traveling salesman problem (tsp). because of its benefices in various domains, many researchers have tried to solve that, and many methods have proposed so far. mtsp is a np-...

We address the one-to-one multi-commodity pickup and delivery traveling salesman problem (m-PDTSP) which is a generalization of the TSP and arises in several transportation and logistics applications. The objective is to find a minimum-cost directed Hamiltonian path which starts and ends at given depot nodes and such that the demand of each given commodity is transported from the associated sou...

A Steady State Genetic Algorithm (GA) is proposed for the Traveling Salesman Problem with Pickup and Delivery (TSPPD). TSPPD is an extension of the well known Traveling Salesman Problem (TSP). TSPPD is a graph and grouping optimization problem.In this thesis, TSPPD is differentiated by a group of cities as customers, each of them supplying (picking customer) or demanding (delivery customer) a g...

the inventory routing problem (irp) arises in the context of vendor-managed systems. this problem addresses jointly solving an inventory management problem and a vehicle routing problem. in this paper, we consider a multi-depot multi-vehicle inventory routing problem in which suppliers produce one type of product to be delivered to customers during a finite time horizon. we propose a two-phase ...

In this paper the problem of eeciently serving a sequence of requests that are presented in a metric space in an on-line fashion and then returning back to the departure point is considered. The problem, that is the on-line version of a variant of the Traveling Salesman Problem (namely the Vehicle Routing Problem with release times), and that for the sake of intuition we call On-Line Traveling ...

Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of (VRP) in which, besides the original constraint on vehicle capacity present Capacitated Problem (CVRP), other attributes that model diverse real-life system characteristics present. Among most common studied literature and route duration constraints. The influence these restrictions overall structure problem performance local sear...