Dynamic programming algorithm for the vehicle routing problem with time windows and EC social legislation

In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a dynamic programming approach for the vehicle routing problem with time windows including the EC social legislation on drivers' driving and working hours. Our algorithm includes all optional rules in these legislations, which are generally ignored in the literature. To include the legislation in the dynamic programming algorithm we propose a break scheduling method that does not increase the time-complexity of the algorithm. This is a remarkable eect that generally does not hold for local search methods, which have proved to be very successful in solving less restricted vehicle routing problems. Computational results show that our method finds solutions to benchmark instances with 18% less vehicles and 5% less travel distance than state of the art approaches. Furthermore, they show that including all optional rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5%\ud regarding the travel distance. Therefore, the optional rules should be exploited in practice

A matheuristic approach for the Pollution-Routing Problem

This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by [Bektas and Laporte (2011), Transport. Res. B-Meth. 45 (8), 1232-1250]. The objective is to minimize operational and environmental costs while respecting capacity constraints and service time windows. Costs are based on driver wages and fuel consumption, which depends on many factors, such as travel distance and vehicle load. The vehicle speeds are considered as decision variables. They complement routing decisions, impacting the total cost, the travel time between locations, and thus the set of feasible routes. We propose a method which combines a local search-based metaheuristic with an integer programming approach over a set covering formulation and a recursive speed-optimization algorithm. This hybridization enables to integrate more tightly route and speed decisions. Moreover, two other "green" VRP variants, the Fuel Consumption VRP (FCVRP) and the Energy Minimizing VRP (EMVRP), are addressed. The proposed method compares very favorably with previous algorithms from the literature and many new improved solutions are reported.Comment: Working Paper -- UFPB, 26 page

Mixed Integer Programming Model for open Vehicle Routing Problem with Fleet and driver Scheduling Considering Delivery and Pick-Up Simultaneously

Vehicle Routing Problem (VRP) is a key element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve a set of customers It is required that these vehicles return to the depot after serving customers’ demand. This paper investigates a variant of VRP, in which the vehicles do not need to return to the depot, called open vehicle routing problem (OVRP). The problem incorporates time windows, fleet and driver scheduling, pick-up and delivery in the planning horizon. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling of fleet and driver and routing policies of the vehicles. The objective is to minimize the sum of the costs of all routes over the planning horizon. We model the problem as a linear mixed integer program. We develop a combination of heuristics and exact method for solving the model

Workforce management in periodic delivery operations

Service quality and driver efficiency in the delivery industry may be enhanced by increasing the regularity with which a driver visits the same set of customers. However, effectively managing a workforce of drivers may increase travel distance, a traditional metric of the vehicle routing problem (VRP). This paper evaluates the effect that workforce management has on routing costs, providing insight for managerial decision making. The analysis is presented in the context of the period vehicle routing problem (PVRP), an extension of the VRP with vehicle routes constructed to service customers according to preset visit frequencies over an established period of time. We develop models to apply workforce management principles. We show that multi-objective PVRP models can achieve a balance between workforce management and travel distance goals, through a computational study with standard PVRP test cases and real-world delivery data. With the proper parameters in place, workforce management principles may be successfully applied without sacrificing other operational objectives

Fully automated urban traffic system

The replacement of the driver with an automatic system which could perform the functions of guiding and routing a vehicle with a human's capability of responding to changing traffic demands was discussed. The problem was divided into four technological areas; guidance, routing, computing, and communications. It was determined that the latter three areas being developed independent of any need for fully automated urban traffic. A guidance system that would meet system requirements was not being developed but was technically feasible

Optimizing departure times in vehicle routes

Most solution methods for the vehicle routing problem with time\ud windows (VRPTW) develop routes from the earliest feasible departure time. However, in practice, temporal traffic congestions make\ud that such solutions are not optimal with respect to minimizing the\ud total duty time. Furthermore, VRPTW solutions do not account for\ud complex driving hours regulations, which severely restrict the daily\ud travel time available for a truck driver. To deal with these problems,\ud we consider the vehicle departure time optimization (VDO) problem\ud as a post-processing step of solving a VRPTW. We propose an ILP-formulation that minimizes the total duty time. The obtained solutions are feasible with respect to driving hours regulations and they\ud account for temporal traffic congestions by modeling time-dependent\ud travel times. For the latter, we assume a piecewise constant speed\ud function. Computational experiments show that problem instances\ud of realistic sizes can be solved to optimality within practical computation times. Furthermore, duty time reductions of 8 percent can\ud be achieved. Finally, the results show that ignoring time-dependent\ud travel times and driving hours regulations during the development of\ud vehicle routes leads to many infeasible vehicle routes. Therefore, vehicle routing methods should account for these real-life restrictions

Sustainable vehicle routing based on firefly algorithm and TOPSIS methodology

In a sustainable management of logistics, transportation plays a crucial role. Traditionally, the main purpose was to solve the Vehicle Routing Problem minimizing the cost associated with the travelled distances. Nowadays, the economic profit cannot be the only driver for achieving sustainability and environmental issues have to be also considered. In this paper, to satisfy the intricate limits involved in real vehicle routing problem, the study has been structured considering different types of vehicles in terms of maximum capacity, velocity and emissions, asymmetric paths, vehicle-client constraints and delivery time windows. The firefly algorithm has been implemented to solve the vehicle routing problem and the TOPSIS technique has been applied to integrate economic and environmental factors. Finally, to prove the effectiveness of the proposed approach, a numerical example has been proposed using data provided by a logistic company located in Sicily

Constrained Local Search for Last-Mile Routing

Last-mile routing refers to the final step in a supply chain, delivering packages from a depot station to the homes of customers. At the level of a single van driver, the task is a traveling salesman problem. But the choice of route may be constrained by warehouse sorting operations, van-loading processes, driver preferences, and other considerations, rather than a straightforward minimization of tour length. We propose a simple and efficient penalty-based local-search algorithm for route optimization in the presence of such constraints, adopting a technique developed by Helsgaun to extend the LKH traveling salesman problem code to general vehicle-routing models. We apply his technique to handle combinations of constraints obtained from an analysis of historical routing data, enforcing properties that are desired in high-quality solutions. Our code is available under the open-source MIT license. An earlier version of the code received the $100,000 top prize in the Amazon Last Mile Routing Research Challenge organized in 2021

Demand robust counterpart open capacitated vehicle routing problem time windows and deadline model of garbage transportation with LINGO 13.0

Demand robust counterpart-open capacitated vehicle routing problem with time windows and deadline (DRC-OCVRPtw,d) model formed and explained in this paper, is the model used to find the minimum distance and the time needed for vehicles to transport garbage in Sukarami Sub-District, Palembang that consists of the time it takes for the vehicle to pass through the route. Time needed to transport garbage to the vehicle is called time windows. Combination of the thoses times is called deadline. The farther the distance passed by vehicle and the more garbage transported, the longer the deadline is needed. This DRC-OCVRPtw,d model is completed by LINGO 13.0 to obtain the optimal route and time deadline for Sukarami Sub-District. The model shows that the improved model of open vehicle routing problem involving the robustness, time windows and deadline can achieve the optimal routes that enable driver to save operational time in picking up the garbage compared to similar problem not involving no-time windows and deadline stated in previous research