A vehicle routing model with split delivery and stop nodes

In this work, a new variant of the Capacitated Vehicle Routing Problem (CVRP) is presented where the vehicles cannot perform any route leg longer than a given length L (although the routes can be longer). Thus, once a route leg length is close to L, the vehicle must go to a stop node to end the leg or return to the depot. We introduce this condition in a variation of the CVRP, the Split Delivery Vehicle Routing Problem, where multiple visits to a customer by different vehicles are allowed. We present two formulations for this problem which we call Split Delivery Vehicle Routing Problem with Stop Nodes: a vehicle flow formulation and a commodity flow formulation. Because of the complexity of this problem, a heuristic approach is developed. We compare its performance with and without the stop nodesSplit delivery vehicle routing problem, Stop node, Granular neighborhood, Tabu search

An efficient heuristic for the multi-vehicle one-to-one pickup and delivery problem with split loads

In this study, we consider the Multi-vehicle One-to-one Pickup and Delivery Problem with Split Loads (MPDPSL). This problem is a generalization of the one-to-one Pickup and Delivery Problem (PDP) where each load can be served by multiple vehicles as well as multiple stops by the same vehicle. In practice, split deliveries is a viable option in many settings where the load can be physically split, such as courier services of third party logistics operators. We propose an efficient heuristic that combines the strengths of Tabu Search and Simulated Annealing for the solution of MPDPSL. Results from experiments on two problems sets in the literature indicate that the heuristic is capable of producing good quality solutions in reasonable time. The experiments also demonstrate that up to 33\% savings can be obtained by allowing split loads; however, the magnitude of savings is dependent largely on the spatial distribution of the pickup and delivery points

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature

Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

Exploring Heuristics for the Vehicle Routing Problem with Split Deliveries and Time Windows

This dissertation investigates the Vehicle Routing Problem with Split Deliveries and Time Windows. This problem assumes a depot of homogeneous vehicles and set of customers with deterministic demands requiring delivery. Split deliveries allow multiple visits to a customer and time windows restrict the time during which a delivery can be made. Several construction and local search heuristics are tested to determine their relative usefulness in generating solutions for this problem. This research shows a particular subset of the local search operators is particularly influential on solution quality and run time. Conversely, the construction heuristics tested do not significantly impact either. Several problem features are also investigated to determine their impact. Of the features explored, the ratio of customer demand to vehicle ratio revealed a significant impact on solution quality and influence on the effectiveness of the heuristics tested. Finally, this research introduces an ant colony metaheuristic coupled with a local search heuristic embedded within a dynamic program seeking to solve a Military Inventory Routing Problem with multiple-customer routes, stochastic supply, and deterministic demand. Also proposed is a suite of test problems for the Military Inventory Routing Problem

Ant colony optimization and its application to the vehicle routing problem with pickups and deliveries

Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickup and Delivery (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of ACO approach and presents several implementations to various combinatorial optimization problems. Next, VRPPD is described and the related literature is reviewed, Then, an ACO approach for VRPPD is discussed. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature

A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

[EN] This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the vehicles are not required to return to the depot after completing a service. In this new problem, the demands of customers are fulfilled by a heterogeneous fixed fleet of vehicles having various capacities, fixed costs and variable costs. This problem is an important variant of the open vehicle routing problem (OVRP) and can cover more practical situations in transportation and logistics. Since this problem belongs to NP-hard Problems, An approach based on column generation (CG) is applied to solve the HFFOVRP. A tight integer programming model is presented and the linear programming relaxation of which is solved by the CG technique. Since there have been no existing benchmarks, this study generated 19 test problems and the results of the proposed CG algorithm is compared to the results of exact algorithm. 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