Abstract The issue of carbon emission reduction has attracted extensive attention in academic circles, but there are few studies on the Pareto frontier analysis multi-depot green vehicle routing problem with multi-objective. In order to effectively balance economic and environmental effects, this paper constructs a bi-objective optimization model for open problems time windows, which takes oper...

The Capacitated Vehicle Routing problem is a generalization of the Traveling Salesman problem in which a set of clients must be visited by a collection of capacitated tours. Each tour can visit at most Q clients and must start and end at a specified depot. We present the first approximation scheme for Capacitated Vehicle Routing for non-Euclidean metrics. Specifically we give a quasi-polynomial...

Multi-echelon distribution systems are quite common in supply-chain and logistic management. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. In the literature, most studies address issues related to the movement of flows throughout the system from the origins to their final destinations....

This paper introduces the fleet size and mix location-routing problem with time windows (FSMLRPTW) which extends the location-routing problem by considering a heterogeneous fleet and time windows. The main objective is to minimize the sum of vehicle fixed cost, depot cost and routing cost. We present mixed integer programming formulations, a family of valid inequalities and we develop a powerfu...

-This article describes a tabu search algorithm for the multi-depot vehicle routing problem with capacity and route length restrictions. The algorithm is tested on a set of 23 benchmark instances. It is shown to outperform existing heuristics. 1. I N T R O D U C T I O N The purpose of this article is to describe a new heuristic algorithm for the Mult i -Depot Vehicle Routing Problem (MDVRP) def...

The effective distribution of relief plays a critical role for rescue operations in post disaster. This paper constructs a multi-objective location-routing model for relief distribution problem. Nondominated sorting differential evolution algorithm is introduced to solve the model. Case studies expound the application of the model and algorithm in practice.

We address the Open Vehicle Routing Problem (OVRP), a variant of the ‘‘classical’’ (capacitated and distance constrained) Vehicle Routing Problem (VRP) in which the vehicles are not required to return to the depot after completing their service. We present a heuristic improvement procedure for OVRP based on Integer Linear Programming (ILP) techniques. Given an initial feasible solution to be po...

The location-routing problem (LRP), which integrates location and routing decisions, has been an attraction to both researchers and practitioners. LRP as an important business problem has its own inherent uncertainty; especially, considering phenomena such as traffic congestion and weather conditions and their impact on transportation costs, routing in LRP is subject to uncertainty. In this pap...

The NP-hard Vehicle Routing Problem (VRP) is defined on an undirected network G = (V,E) with a node set V = {0, 1, . . . , n} and an edge set E. Node 0 is a depot with identical vehicles of capacity Q. Each client node i > 0 has a non-negative demand qi and each edge [i, j] has a non-negative cost cij = cji. The VRP consists of determining a set of vehicle trips of minimum total cost, such that...

The Vehicle Routing Problem with Time Windows (VRPTW) is currently the focus of very intensive research, and is used to model many realistic applications. The overall objective is to serve a set of customers at minimum cost with a fleet of vehicles of finite capacity housed at a central depot. The route of each vehicle starts and ends at the depot. Also, each customer has a known demand (i.e. s...