New Lower Bounds for the Vehicle Routing Problem with Simultaneous Pickup and Delivery
نویسندگان
چکیده
This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell’Amico, Righini and Salani. The three formulations were tested within a branch-and-cut scheme and their practical performance was measured in well-known benchmark problems. The undirected two-commodity flow formulation obtained consistently better results. We also ran the three formulations in a particular case of the VRPSPD, namely the Vehicle Routing Problem with Mixed Pickup and Delivery (VRPMPD). Several optimal solutions to open problems with up to 100 customers and new improved lower bounds for instances with up to 200 customers were found.
منابع مشابه
The fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery: Formulation and a heuristic algorithm
In this paper, the fuzzy multi-depot vehicle routing problem with simultaneous pickup and delivery (FMDVRP-SPD) is investigated. The FMDVRP-SPD is the problem of allocating customers to several depots, so that the optimal set of routes is determined simultaneously to serve the pickup and the delivery demands of each customer within scattered depots. In the problem, both pickup and delivery dema...
متن کاملSolving the Vehicle Routing Problem with Simultaneous Pickup and Delivery by an Effective Ant Colony Optimization
One of the most important extensions of the capacitated vehicle routing problem (CVRP) is the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) where customers require simultaneous delivery and pick-up service. In this paper, we propose an effective ant colony optimization (EACO) which includes insert, swap and 2-Opt moves for solving VRPSPD that is different with common an...
متن کاملAn Improved Modified Tabu Search Algorithm to Solve the Vehicle Routing Problem with Simultaneous Pickup and Delivery
The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. The objective is to minimize the distance traveled. The VRPSPD is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of VR...
متن کاملThe Bi-Objective Location-Routing Problem based on Simultaneous Pickup and Delivery with Soft Time Window
The location-routing problem is the most significant and yet new research field in location problems that considers simultaneously vehicle routing problem features with original one for achieving high-quality integrated distribution systems in beside of the global optimum. Simultaneous pickup and delivery based on time windows are the two main characteristics of logistic management that have be...
متن کاملAn Improved Modified Tabu Search Algorithm to Solve the Vehicle Routing Problem with Simultaneous Pickup and Delivery
The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. The objective is to minimize the distance traveled. The VRPSPD is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of VR...
متن کاملAn Improved Particle Swarm Optimization for a Class of Capacitated Vehicle Routing Problems
Vehicle Routing Problem (VRP) is addressed to a class of problems for determining a set of vehicle routes, in which each vehicle departs from a given depot, serves a given set of customers, and returns back to the same depot. On the other hand, simultaneous delivery and pickup problems have drawn much attention in the past few years due to its high usage in real world cases. This study, therefo...
متن کامل