Ship Routing Design for the Oily Liquid Waste Collection

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

Public consciousness on environmental sustainability and industry impact on environment has been increasing for the last few decades. As a result, more and more companies are taking pollution factor into account when planning their logistic activities. Pollution Routing Problem (PRP) is an extension of the classical Vehicle Routing Problem with Time Windows by determining a set of optimal routes and vehicle speed on each route segment for a fleet of vehicles serving a set of customers within specific time windows. In practice, many vehicle routing problems are addressed by a fleet of heterogeneous vehicles with different capacities and travel costs. Emission levels vary by vehicle type due to differences in curb weight and capacity. Therefore, Heterogeneous Fleet Pollution Routing Problem (HFPRP) has been proposed as an extension of Pollution Routing Problem (PRP). Its goal is to minimize the total costs of fuel, greenhouse gas (GHG) emissions, and vehicle variable cost put together in a more comprehensive objective function. This research developed a mathematical model and proposed a Simulated Annealing (SA) heuristic for HFPRP. The performance of the proposed SA heuristic was first verified using benchmark data of the Pollution Routing Problem. The result shows that SA performs better for 7 instances than previous method. SA was then used to solve HFPRP and the results were compared to those obtained by CPLEX. We found that the consideration of a heterogeneous fleet reduces total costs for all instances.

In real life situations most companies that deliver or collect goods own a heterogeneous fleet of vehicles. Their goal is to find a set of vehicle routes, each starting and ending at a depot, making the best possible use of the given vehicle fleet such that total cost is minimized. The specific problem can be formulated as the Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP), which is a variant of the classical Vehicle Routing Problem. This paper describes a variant of the threshold accepting heuristic for the HFFVRP. The proposed metaheuristic has a remarkably simple structure, it is lean and parsimonious and it produces high quality solutions over a set of published benchmark instances. Improvement over several of previous best solutions also demonstrates the capabilities of the method and is encouraging for further research.

In Southeast Asian cities, it is common for logistic companies to operate a heterogeneous fleet of delivery vehicles with motorcycles being the preferred vehicle to handle the final phase of delivery. In such scenarios, heterogeneous fleet vehicle routing problem (HFVRP) is generally applied to plan an optimal delivery. However, in many downtown cores of large and rapidly developing Southeast Asian cities, HFVRP is neither viable nor reliable because of road usage restrictions. The purpose of this article is to develop and test a different approach that accurately takes these restrictions into account and provides viable and more sustainable results. Restrictions in this paper refer to situations of urban areas in Vietnam where (i) certain vehicle types are prohibited in specified areas or where narrow alleyways limit the utilization of vehicles that exceed the road capacity and (ii) certain roads are exclusive to certain vehicle types. In networks, limited access and exclusive lanes are represented as links, or arcs, exclusive to one or another. Taking these limitations into consideration, we have developed a unique model, which we have termed Vehicle Routing Problem with Exclusive Links (VRP-EL). The model was validated and tested for its performance on scenarios with varying ratios of exclusive links. Scenarios up to 500 customers were tested on a meta-heuristic algorithm, simulated annealing. VRP-EL produces realistic outcomes. Limiting certain links to be selected according to vehicle types increases overall travel distance. However, this increase outweighs the cost of re-planning and rerouting had they not been constrained initially. The reduction in traveling distance leads to fossil fuel reduction for the overall system. The estimation of reduced carbon emissions through applying the proposed model is presented. Considering the severe traffic congestion and carbon emissions caused by motorcycles in Vietnam, the proposed model leads to a sustainable road environment.

The classic vehicle routing problem (VRP) is generally concerned with the optimal design of routes by a fleet of vehicles to service a set of customers by minimizing the overall cost, usually the travel distance for the whole set of routes. Although the problem has been extensively studied in the context of operations research and optimization, there is little research on solving the VRP, where distributed vehicles need to compute their respective routes in a decentralized fashion. Our first contribution is a synchronous distributed approximation algorithm that solves the VRP. Using the duality theorem of linear programming, we show that the approximation ratio of our algorithm is O(n · (ρ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/n</sup> log(n + m)), where ρ is the maximum cost of travel or service in the input VRP instance, n is the size of the graph, and m is the number of vehicles. We report results of simulations and discuss implementation of our algorithm on a real fleet of unmanned aerial systems (UASs) that carry out a set of tasks.

The vehicle routing problem (VRP) is a crucial group of transportation problems, and traditional capacitated VRP (CVRP) directly handles external logistics with a homogeneous vehicle fleet. This paper examines the CVRP from an in-plant logistic view with a heterogeneous fleet in an automotive factory. The homogeneous and heterogeneous vehicle fleets are compared to address the factory's actual in-plant logistics issues. Firstly, simulated annealing (SA), tabu search (TS) algorithms and mathematical modeling were utilized. Then, a hybrid approach was proposed, and all suggested meta-heuristic algorithms were evaluated for homogeneous and heterogeneous vehicle fleets. According to the results, the reduction rates using CVRP with the heterogeneous fleet are 17% and 36% for fleet area and distribution costs, respectively. Also, to examine the effect of the hybrid algorithm parameters on the result, traveling distance was calculated for different scenarios, and multiple regression analyses were applied. According to the multiple regression analysis, the hybrid algorithm's most affected parameter was the cooling coefficient.

In the last decade interest in environment preservation is increasing and environmental aspects play an important role in strategic and operational policies. Therefore, environmental targets are to be added to economic targets, to find the right balance between these two dimensions. Green logistics extend the traditional definition of logistics by explicitly considering external factors associated mainly with climate change, air pollution, noise, vibration and accidents. Among the logistical activities, the vehicle routing problem (VRP) is one of the most widely researched and has mainly focused on economic objectives, not considering explicitly environmental issues. In this chapter, a realistic variant of the VRP with heterogeneous vehicle fleets in which vehicles are characterized by different capacities and costs, has been considered and external costs have been estimated using international research projects, and have been included as part of a mixed-integer linear programming model to solve a realistic variant of the VRP. To solve medium to large-size VRP instances, heuristic approaches are necessary. An impressive number of heuristic have been proposed for the VRP in the literature. In this chapter, one heuristic is developed to find good solutions to the proposed eco-efficiency model: a savings heuristic when time windows are not considered. Since there are no instances for this problem variant, the algorithm is validated with benchmarking problems adapted from the literature, offering good solutions and quickness. The selection of eco-efficiency routes can help to reduce the emissions of air pollutants, noises and greenhouse gases, without losing competitiveness in transport companies.KeywordsVehicle routing problemSustainabilityExternalitiesGreen logisticsEnvironmental costs

This paper discusses a vehicle routing problem with multiple trips, time windows, and simultaneous delivery-pickup (VRPMTTWSDP). This problem is a variant of the basic vehicle routing problem (VRP) including the following characteristics: multiple trips, time windows, and simultaneous delivery-pickup. In this paper, a solution approach based on tabu search (TS) is proposed. In the proposed TS, the sequential insertion (SI) algorithm is used to construct an initial solution. A neighbor structure is generated by applying an operator order consisting of eleven operators of relocation, exchange, and crossover operators. A tabu solution code (TSC) method is applied as a tabu restriction mechanism. Computational experiments are carried out to examine the performance of the proposed TS using hypothetical instances. The performance of the proposed TS is compared to the local search (LS) and the genetic algorithm (GA). The comparison shows that the proposed TS is better in terms of the objective function value.

The Capacitated Vehicle Routing Problem with Time-Dependent Demands (CVRPTD) is a significant optimization challenge in the logistics and transportation domain, characterized by dynamic customer demands, strict time windows, and heterogeneous vehicle fleets. This study focuses on urban parcel delivery operations as the primary object of research. The problem addressed involves the inefficiency of conventional vehicle routing strategies in adapting to time-varying customer demands and operational constraints, which often lead to increased costs and service delays. This study aims to minimize total operational costs while ensuring compliance with capacity constraints, service continuity, and demand fluctuations. A comprehensive mathematical model is developed based on a fully connected, directed acyclic graph G=(V, A), incorporating decision variables that represent vehicle routing sequences, timing, and vehicle type assignments. This study addresses the Capacitated Vehicle Routing Problem with Time-Dependent Demands (CVRPTD) in urban parcel delivery, where traditional routing methods struggle with dynamic demands and operational constraints. A mathematical model using a directed acyclic graph is developed, optimized via a gradient-based method with Hessian approximation, LU decomposition, and quasi-Newton techniques. Experiments on datasets with up to 200 customers and 20 vehicles with reductions ranging from 1.79% to 12.75%. The most significant improvement was observed in Sidorame Timur, where the optimization distance decreased by 12.75%, indicating high accuracy in route optimization. For the SCP, the proposed algorithm achieved a 6.46% improvement in solution quality over traditional greedy algorithms

The simulated trading heuristic for solving vehicle routing problems

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a real-world situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Pareto-optimal solution with the e-constraint method is obtained. Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.

The constant increase in the consumption of goods and the high costs of transport operations make decisions related to logistics increasingly more relevant. In this context, the Vehicle Routing Problem (VRP) has been in focus. In order to solve this problem, we aim to set the best routes for a fleet of vehicles to ensure that all clients will be served. The routing problems often have particular characteristics. In this work, we will address a variant of the PRV called the vehicle routing problem with heterogeneous fleet and multiple trips, in which we consider different types of vehicles and the possibility of making more than a single trip. Initially, a mathematical model, adapted from the literature, was developed. The first computational tests showed that only small instances can be solved in reasonable computational time, using commercial optimization software. Then, we present a heuristic method for the solution of the problem. The algorithm has three main steps: obtaining an initial solution (constructive heuristic), searching for local minimums (ILS), and improving the solution (coverage model). In sequence, a second objective that seeks to minimize the time of the longest route is approached. We conclude the dissertation with the presentation of a biobjective approach to the problem, which is solved using three techniques: weighting the objective function, epsilon -restricted method and Pareto-ILS. With that we aim to propose mono and bi objective approaches to solve the problem.

This study develops a Green Vehicle Routing Problem (GVRP) model to address key logistics challenges, including time windows, simultaneous pickup and delivery, heterogeneous vehicle fleets, and multiple trip allocations. The model incorporates emissions-related costs, such as carbon taxes, to encourage sustainable supply chain operations. Emissions are calculated based on the total shipment weight and the travel distance of each vehicle. The objective is to minimize operational costs while balancing economic efficiency and environmental sustainability. A Genetic Algorithm (GA) is applied to optimize vehicle routing and allocation, enhancing efficiency and reducing costs. A Liquid Petroleum Gas (LPG) distribution case study in Yogyakarta, Indonesia, validates the model’s effectiveness. The results show significant cost savings compared to current route planning methods, alongside a slight increase in carbon. A sensitivity analysis was conducted by testing the model with varying numbers of stations, revealing its robustness and the impact of the station density on the solution quality. By integrating carbon taxes and detailed emission calculations into its objective function, the GVRP model offers a practical solution for real-world logistics challenges. This study provides valuable insights for achieving cost-effective operations while advancing green supply chain practices.

In this paper, we address the distribution problem of liquefied petroleum gas (LPG). In particular we are targeting the optimization of pickup and split delivery of gas bottles to a set of customers with loading constraints. The problem combines the loading of a heterogeneous fleet of vehicles through a set of different size racks and then the establishment of divisible deliveries (split delivery: SDVRP). The problem discussed in this paper can be presented as a Multi-depot Two-Loading Split Delivery and Pickup using Heterogeneous fleet of Vehicles with Time Windows vehicle Routing Problem and with Multi-Product (2L-SDP-HVRPTW-MP). After proposing a mathematical formulation for this problem (MILP), we tested our model firstly by a small instances using ILOG CPLEX solver following this by testing and discussing numerical results.

In this paper, we consider the waste collection problem from customers’ location with assumptions that are closer to real life applications of the problem. The fleet of vehicles is heterogeneous and vehicles have separated compartments, namely they have different capacity for each type of waste. Also, the vehicles have different traveling time limitation and different variable and fixed cost according to their types. As well as, the multi-depot vehicle routing problem and the mixed close-open vehicle routing problem are combined together. The objective of the problem is minimizing the cost of servicing to customers with respect to customers’ demands and available constraints. A new mathematical MIP model is proposed and to deal with this problem, three meta-heuristic algorithms are investigated and the results are compared with the results of CPLEX solver. The results of experiments show that the proposed Meta-heuristic algorithms are able to produce satisfied solutions with regard to the MIP solver CPLEX.