A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption

The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all of the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu-search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.Comment: 18 page

Green logistic network design : intermodal transportation planning and vehicle routing problems.

Due to earth\u27s climate change and global warming, environmental consideration in the design of logistic systems is accelerating in recent years. In this research we aim to design an efficient and environmentally friendly logistical system to satisfy both government and carriers. In particular, we considered three problems in this dissertation: intermodal network design, deterministic green vehicle routing problem and stochastic green vehicle routing problem. The first problem aims to design an economic and efficient intermodal network including three transportation modes: railway, highway and inland waterway. The intent of this problem is to increase the utilization percentage of waterway system in the intermodal transportation network without increasing the cost to the consumer. In particular, we develop a real world coal transportation intermodal network across 15 states in the United States including highway, railway and inland waterway. The demand data were obtained from the Bureau of Transportation Statistics (BTS) under the US Department of Transportation (DOT). Four boundary models are built to evaluate the potential improvement of the network. The first boundary model is a typical minimum cost problem, where the total transportation cost is minimized while the flow balance and capacity restrictions are satisfied. An additional constraint that help obtain an upper bound on carbon emission is added in the second boundary model. Boundary model 3 minimizes the total emission with flow balance and capacity restrictions the same as boundary model 1. Boundary model 4 minimizes the total emission with an additional current cost restriction to achieve a less-aggressive lower bound for carbon emission. With a motivation to minimize the transportation and environmental costs simultaneously, we propose multi-objective optimization models to analyze intermodal transportation with economic, time performance and environmental considerations. Using data from fifteen selected states, the model determines the tonnage of coal to be transported on roadways, railways and waterways across these states. A time penalty parameter is introduced so that a penalty is incurred for not using the fastest transportation mode. Our analysis provides authorities with a potential carbon emission tax policy while minimizing the total transportation cost. In addition, sensitivity analysis allows authorities to vary waterway, railway and highway capacities, respectively, and study their impact on the total transportation cost. Furthermore, the sensitivity analysis demonstrates that an intermodal transportation policy that uses all the three modes can reduce the total transportation cost when compared to one that uses just two modes. In contrast with traditional vehicle routing problems, the second problem intends to find the most energy efficient vehicle route with minimum pollution by optimization of travel speed. A mixed integer nonlinear programming model is introduced and a heuristic algorithm based on a savings heuristic and Tabu Search is developed to solve the large case for this problem. Numerical experiments are conducted through comparison with a solution obtained by BONMIN in GAMS on randomly generated small problem instances to evaluate the performance of the proposed heuristic algorithm. To illustrate the impact of a time window constraint, travel speed and travel speed limit on total carbon emission, sensitivity analysis is conducted based on several scenarios. In the end, real world instances are examined to further investigate the impact of these parameters. Based on the analysis from the second problem, travel speed is an important decision factor in green vehicle routing problems to minimize the fuel cost. However, the actual speed limit on a road may have variance due to congestion. To further investigate the impact of congestion on carbon emission in the real world, we proposed a stochastic green vehicle routing problem as our third problem. We consider a green vehicle problem with stochastic speed limits, which aims to find the robust route with the minimum expected fuel cost. A two-stage heuristic with sample average approximation is developed to obtain the solution of the stochastic model. Computational study compares the solutions of robust and traditional mean-value green vehicle routing problems with various settings

Enrutamiento de almacenes cruzados considerando ventanas de tiempo y precios de ruta (estudio de caso: transporte de contenedores del puerto de Chabahar)

In this study, we develop a model for routing cross-docking centers considering time windows and pricing routs. In this model picking and delivery in several times is permitted and each knot can be serviced by more than one vehicle. Every truck can transport one or more product, in other words, we consider compatibility between product and vehicle. This model includes two goals: reducing the total cost and reducing the cost of carrying goods (freight fare). The total cost includes the cost required to traverse between the points, the cost of traversing the routes between the central cross-docking center and the first points after moving, and the cost to traverse the routes between the last points in each route and the depots that must be minimized. In general, the purpose of the model is to obtain the number of cross-docking center, the number of vehicles and the best route in the distribution network. We present a nonlinear programming model for this problem. We have solved the proposed model by GAMS. As the dimensions of the problem increase, the implementation time of the program increases progressively. So, in order to solve the model in medium and large scales, we proposed a genetic meta-heuristic algorithm. The results of examining different issues by the meta-heuristic approach show the very high efficiency of the developed algorithms in terms of the solution time and the answer of the problem.En esta investigación, se presenta un modelo para el enrutamiento entre almacenes con ventanas de tiempo y precios de ruta. En este modelo, se permite la recogida y entrega en varias ocasiones y cada nodo puede recibir servicio con más de un vehículo. Cada camión puede transportar uno o más tipos de mercancías, es decir, se considera la compatibilidad entre la mercancía y el vehículo. En este modelo, hay dos objetivos, que incluyen reducir el costo total y reducir el precio de envío de mercancías (flete). El costo total incluye el costo de recorrer los senderos entre los puntos, el costo de recorrer los senderos entre el almacén de la intersección central y los primeros puntos después de la salida, y el costo de recorrer los senderos entre los últimos puntos de cada sendero y los almacenes que deben minimizarse. En general, el propósito del modelo es obtener el número de almacenes, el número de vehículos y la mejor ruta en la red de distribución. Y presentamos un modelo de programación no lineal para este problema. Hemos resuelto el modelo propuesto con GAMS. A medida que aumenta el tamaño del problema, el tiempo de ejecución del programa aumenta considerablemente. Por tanto, para resolver el modelo en medianas y grandes dimensiones, presentamos el algoritmo genético metaheurístico. Los resultados de examinar varios problemas con metaheurísticas muestran la altísima eficiencia de los algoritmos propuestos en términos de tiempo de resolución de problemas

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

Enrutamiento de almacenes cruzados considerando ventanas de tiempo y precios de ruta (estudio de caso: transporte de contenedores del puerto de Chabahar)

In this study, we develop a model for routing cross-docking centers considering time windows and pricing routs. In this model picking and delivery in several times is permitted and each knot can be serviced by more than one vehicle. Every truck can transport one or more product, in other words, we consider compatibility between product and vehicle. This model includes two goals: reducing the total cost and reducing the cost of carrying goods (freight fare). The total cost includes the cost required to traverse between the points, the cost of traversing the routes between the central cross-docking center and the first points after moving, and the cost to traverse the routes between the last points in each route and the depots that must be minimized. In general, the purpose of the model is to obtain the number of cross-docking center, the number of vehicles and the best route in the distribution network. We present a nonlinear programming model for this problem. We have solved the proposed model by GAMS. As the dimensions of the problem increase, the implementation time of the program increases progressively. So, in order to solve the model in medium and large scales, we proposed a genetic meta-heuristic algorithm. The results of examining different issues by the meta-heuristic approach show the very high efficiency of the developed algorithms in terms of the solution time and the answer of the problem.En esta investigación, se presenta un modelo para el enrutamiento entre almacenes con ventanas de tiempo y precios de ruta. En este modelo, se permite la recogida y entrega en varias ocasiones y cada nodo puede recibir servicio con más de un vehículo. Cada camión puede transportar uno o más tipos de mercancías, es decir, se considera la compatibilidad entre la mercancía y el vehículo. En este modelo, hay dos objetivos, que incluyen reducir el costo total y reducir el precio de envío de mercancías (flete). El costo total incluye el costo de recorrer los senderos entre los puntos, el costo de recorrer los senderos entre el almacén de la intersección central y los primeros puntos después de la salida, y el costo de recorrer los senderos entre los últimos puntos de cada sendero y los almacenes que deben minimizarse. En general, el propósito del modelo es obtener el número de almacenes, el número de vehículos y la mejor ruta en la red de distribución. Y presentamos un modelo de programación no lineal para este problema. Hemos resuelto el modelo propuesto con GAMS. A medida que aumenta el tamaño del problema, el tiempo de ejecución del programa aumenta considerablemente. Por tanto, para resolver el modelo en medianas y grandes dimensiones, presentamos el algoritmo genético metaheurístico. Los resultados de examinar varios problemas con metaheurísticas muestran la altísima eficiencia de los algoritmos propuestos en términos de tiempo de resolución de problemas