The paper [1] has three main contributions: • Modeling VRP (Vehicle Routing Problem) into the minimum cost Ktree problem. • Dualizing the side constraints to obtain a Lagrangian problem which provides lower-bounds in B&B. • Performing the algorithm on real problems. 1. Problem Definition and Lagrangian Relaxation The vehicle routing problem has the following parameters: • K = the number of vehi...

In this study, a two phase hybrid heuristic approach was proposed to solve the multi-depot multi-vehicle inventory routing problem (MDMVIRP). Inventory routing problem (IRP) is one of the major issues in the supply chain networks that arise in the context of vendor managed systems (VMI) The MDMVIRP combines inventory management and routing decision. We are given on input a fleet of homogeneous ...

This paper aims to compare a two-echelon and a single-echelon distribution system. A mathematical model for the Single-Echelon Capacitated Vehicle Routing Problem (SE-CVRP) is proposed. This SE-CVRP is the counterpart of Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) introduced in the authors’ previous work. The proposed mathematical model is Mixed-Integer Non-Linear Programming (MIN...

In this paper, we present a methodology for solving a multi-product, multi-depot periodic vehicle routing problem. The problem focuses on allocating products and assigning appropriate delivery days to a set of customers, and designing a set of delivery routes for every day of the planning period. A tabu-search based heuristic is proposed to find the best allocation and routing plan that would g...

Municipal waste management has become a challenging issue with the rise in urban populations and changes people’s habits, particularly developing countries. Moreover, government policy plays an important role associated municipal management. Thus, this research proposes regional location routing problem (RLRP) model multi-depot (MRLRP) model, which are extensions of (LRP), to provide better col...

Given a fleet of vehicles assigned to a single depot, the vehicle routing problem with time windows (vrptw) consists of determining a set of feasible routes to deliver goods to a set of customers while minimizing, first, the number of vehicles used and, second, total mileage. Each customer must be visited exactly once by a vehicle within a prescribed time interval. A route starts from the depot...

This paper considers stochastic load-constrained vehicle routing systems in which a fleet of homogeneous vehicles is dispatched from a central depot to serve the demands of surrounding customers. Customer locations and load sizes are known only in distribution before operations. Variants of this problem are often treated with very simple uncoordinated operating schemes, which are mathematically...

We consider distribution systems with a depot and many geographically dispersed retailers each of which faces external demands occurring at constant, deterministic but retailer specific rates. All stock enters the system through the depot from where it is distributed to the retailers by a fleet of capacitated vehicles combining deliveries into efficient routes. Inventories are kept at the retai...

Multi-depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This paper describes new inequalities, namely multicut constraints (MCC), that enforce this requirement in mathematical progra...

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assu...