A simheuristic for routing electric vehicles with limited driving ranges and stochastic travel times

Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.Peer Reviewe

Three-Dimensional Capacitated Vehicle Routing Problems with Loading Constraints

City logistics planning involves organizing the movement of goods in urban areas carried out by logistics operators. The loading and routing of goods are critical components of these operations. Efficient utilization of vehicle space and limiting number of empty vehicle movements can strongly impact the nuisances created by goods delivery vehicles in urban areas. We consider an integrated problem of routing and loading known as the three-dimensional loading capacitated vehicle routing problem (3L-CVRP). 3L-CVRP consists of finding feasible routes with the minimum total travel cost while satisfying customers’ demands expressed in terms of cuboid and weighted items. Practical constraints related to connectivity, stability, fragility, and LIFO are considered as parts of the problem. We address the problem in two stages. Firstly, we address the three-dimensional (3D) loading problem followed by 3L-CVRP. The main objective of a 3D loading problem without routing aspect is finding the best way of packing 3D items into vehicles or containers to increase the loading factor with the purpose of minimizing empty vehicle movements. We present the general linear programming model to the pure three-dimensional vehicle loading problem and solve it by CPLEX. To deal with large-sized instances, Column Generation (CG) technique is applied. The designed method in this work outperforms the best existing techniques in the literature.   The 3DVLP with allocation and capacity constraints, called 3DVLP-AC, is also considered. For the 3DVLP-AC, CPLEX could handle moderate-sized instances with up to 40 customers. To deal with large-sized instances, a Tabu Search (TS) heuristic algorithm is developed. There are no solution methods or lower bounds (LBs) for the 3DVLP-AC existent in the literature by which to evaluate the TS results. Therefore, we evaluate our TS with the CPLEX results for small instances. 3L-CVRP is addressed by using CG technique. To generate new columns, the pricing problem that is part of CG is solved by using two approaches: 1-by means of shortest path problem with resource constraints (ESPPRC) and loading problem, and 2-a heuristic pricing method (HP). CG using HP with a simple scheme can attain solutions competitive with the efficient TS algorithms described in the literature

MATLAB tool for loading of boxes in 3L-CVRP problem

The Three-Dimensional Capacitated Vehicle Routing Problem, or 3L-CVRP, is one NP-Hard Problem in the logistics field. In the 3L-CVRP the length, width and height dimensions of items and vehicle are considered. Hence, each item must be sequentially loaded to avoid overlaps between items of different customers, fragile items must not support no fragile items. Items can be rotated in x-y axes. In this work, a MATLAB program for plotting the solutions obtained for 3L-CVRP is proposed as a technique to verify errors such as overlaps, intersections, not enough supporting area and the invalid combination of items

Three-axes rotation algorithm for the relaxed 3L-CVRP

The purpose of this work is to present a developed three-axes rotation algorithm to improve the solving methodology for the relaxed 3L-CVRP (Three-Dimensional Capacitated Vehicle Routing Problem). Although there are reported works on solving approaches for the relaxed 3L-CVRP that consider product rotation to optimize load capacity, rotation on the three axes has not been thoroughly studied. In this aspect, the present work explicitly explores the three-axes rotation and its impact on load capacity optimization. In order to improve the relaxed 3L-CVRP problem, a two-phase solution was developed. The first phase consists of finding the solution for the CVRP problem, using a demand previously obtained with a heuristic developed to convert the 3L-CVRP demand into CVRP demand. The second phase is to obtain the loading of the vehicle using a heuristic developed to load the items using rules to obtain the rotation of the items. The proposed approach was able to improve the load assignment in 48.1% of well-known 3L-CVRP instances when compared to similar approaches on the relaxed 3L-CVRP. The outcomes of this research can be applied to transportation problems where package rotation on the z-axis is an option, and there are not fragile items to load in the vehicles

Low Carbon Logistics Optimization for Multi-depot CVRP with Backhauls - Model and Solution

CVRP (Capacitated Vehicle Routing Problems) is the integrated optimization of VRP and Bin Packing Problem (BPP), which has far-reaching practical significance, because only by taking both loading and routing into consideration can we make sure the delivery route is the most economic and the items are completely and reasonably loaded into the vehicles. In this paper, the CVRP with backhauls from multiple depots is addressed from the low carbon perspective. The problem calls for the minimization of the carbon emissions of a fleet of vehicles needed for the delivery of the items demanded by the clients. The overall problem, denoted as 2L-MDCVRPB, is NP-hard and it is very difficult to get a good performance solution in practice. We propose a quantum-behaved particle swarm optimization (QPSO) and exploration heuristic local search algorithm (EHLSA) in order to solve this model. In addition, three groups of computational experiments based on well-known benchmark instances are carried out to test the efficiency and effectiveness of the proposed model and algorithm, thereby demonstrating that the proposed method takes a short computing time to generate high quality solutions. For some instances, our algorithm can obtain new better solutions

Multi-objective vehicle routing and loading with time window constraints:a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set