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A Quadratically Constrained Mixed-Integer Non-linear Programming Model for Multiple Sink Distributions
Abstract
Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 (1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.
Sustainably powering agricultural systems including greenhouses, irrigation, and farm equipment relies on the Pulsation Free Current Circulation System's (PFCC) efficient use of solar energy reserves. Improving the distribution of solar power reserves in light of the fact that solar energy output varies over time is the primary goal of this research. Energy reserve expenses are reduced and storage battery operating life is extended using an interval linear programming technique. Power distribution that is both dependable and efficient is achieved by use of the system's models, which take into consideration factors like allocation costs, power reserve and network losses. Through the use of a two-tiered structural approach, the optimization procedure guarantees balanced dispatching and rapid responsiveness to fluctuating energy needs by managing distribution and reserve capacity in tandem. Enhancing the sustainability of solar-powered agricultural systems, the suggested technology minimizes battery deterioration and ensures energy availability during important agricultural activities. Multi power reserve systems are also used to reduce distributed energy swings,which makes the system even more reliable and stable. According to the findings of the tests, the technology has the power to greatly improve the efficiency and longevity of solar energy in farming, with an output efficiency of 0.99(in decimal). This strategy tackles the problem of energy management and sets the stage for renewable energy solutions that can be easily scaled and adjusted for use in agriculture. This will guarantee the sustainability and effectiveness of these solutions in the long run.
In view of the pressing need to reduce the negative environmental impact of freight transportation we argue that it is essential to take account of the organization of the freight transportation system when considering how to address various individual activities and parts of the system. To support a transition to a more sustainable freight transportation system this paper examines the way in which different parts of the system interact and the way this can impact the scope for profound change. Taking loosely coupled systems (Weick, 1976) as a starting point, we scrutinize the couplings within and between three system layers of the freight transportation system: the supply chain layer, the transportation layer, and the infrastructure layer. In addition, we address two interfaces connecting these layers: the market for transportation services, and the traffic using the infrastructure. We find that tight couplings dominate in the supply chain and infrastructure layers and that these couplings depend on loose couplings in the transportation layer and the two interfaces. The pattern of couplings identified in the freight transportation system can explain several positive outcomes, such as flexibility and efficiency. But there are also major negative aspects of the loosely coupled nature of the system that create resistance to change and present a barrier in the drive for increased sustainability. The paper concludes that the identified couplings and system features have important implications for policies aiming to change the freight transportation system in ways that lead to significant reduction in the reliance on oil.
Currently, the number of deliveries handled by transportation logistics is rapidly increasing because of the significant growth of the e-commerce industry, resulting in the need for improved functional vehicle routing measures for logistic companies. The effective management of vehicle routing helps companies reduce operational costs and increases its competitiveness. The vehicle routing problem (VRP) seeks to identify optimal routes for a fleet of vehicles to deliver goods to customers while simultaneously considering changing requirements and uncertainties in the transportation environment. Due to its combinatorial nature and complexity, conventional optimization approaches may not be practical to solve VRP. In this paper, a new optimization model based on reinforcement learning (RL) and a complementary tree-based regression method is proposed. In our proposed model, when the RL agent performs vehicle routing optimization, its state and action are fed into the tree-based regression model to assess whether the current route is feasible according to the given environment, and the response received is used by the RL agent to adjust actions for optimizing the vehicle routing task. The procedure repeats iteratively until the maximum iteration is reached, then the optimal vehicle route is returned and can be utilized to assist in decision making. Multiple logistics agency case studies are conducted to demonstrate the application and practicality of the proposed model. The experimental results indicate that the proposed technique significantly improves profit gains up to 37.63% for logistics agencies compared with the conventional approaches.
Fruits and vegetables are highly nutritious agricultural produce with tremendous human health benefits. They are also highly perishable and as such are easily susceptible to spoilage, leading to a reduction in quality attributes and induced food loss. Cold chain technologies have over the years been employed to reduce the quality loss of fruits and vegetables from farm to fork. However, a high amount of losses (≈50%) still occur during the packaging, pre-cooling, transportation, and storage of these fresh agricultural produce. This study highlights the current state-of-the-art of various advanced tools employed to reducing the quality loss of fruits and vegetables during the packaging, storage, and transportation cold chain operations, including the application of imaging technology, spectroscopy, multi-sensors, electronic nose, radio frequency identification, printed sensors, acoustic impulse response, and mathematical models. It is shown that computer vision, hyperspectral imaging, multispectral imaging, spectroscopy, X-ray imaging, and mathematical models are well established in monitoring and optimizing process parameters that affect food quality attributes during cold chain operations. We also identified the Internet of Things (IoT) and virtual representation models of a particular fresh produce (digital twins) as emerging technologies that can help monitor and control the uncharted quality evolution during its postharvest life. These advances can help diagnose and take measures against potential problems affecting the quality of fresh produce in the supply chains. Plausible future pathways to further develop these emerging technologies and help in the significant reduction of food losses in the supply chain of fresh produce are discussed. Future research should be directed towards integrating IoT and digital twins for multiple shipments in order to intensify real-time monitoring of the cold chain environmental conditions, and the eventual optimization of the postharvest supply chains. This study gives promising insight towards the use of advanced technologies in reducing losses in the postharvest supply chain of fruits and vegetables.
Resilience of transportation systems has been extensively studied in the past decade. This paper aims to provide a synthesis of the up-to-date literature on resilient transportation, focusing on concepts and methodologies. A systematic literature search method integrating database search, related journal search, and citation supplement is proposed to select all the appropriate articles. Based on the selected core papers, the definition of resilience is examined, and some related concepts are compared. The main body of the review is devoted to the review of metrics and mathematical models used to measure resilience and the strategies used to enhance resilience. Several popular subtopics are identified and discussed. Finally, current research gaps and challenges are addressed, and some potential research directions are presented.
This article focuses upon multi-modal transportation systems (MMTS) and their capacity assessment. To perform this task, a linear programming model (LP) denoted by MMTS_CAP has been developed. This model determines the maximum flow of vehicles and commodities that can be accommodated, over a given time period, on different transportation modes within the MMTS. It chooses how to move commodities between different origin destination pairs (ODP) and facilitates the transfer of commodities across different modes. The proposed model can facilitate a variety of capacity planning and querying activities and provides a mechanism to quickly analyse the effect of structural and parametric changes within MMTS. The model has been applied to several scenarios, including a real life case study. Our numerical testing indicates that it is effective, highly flexible and extendable. Our analysis suggests that the proposed capacity assessment techniques are worthwhile and may help transportation planners build better MMTS.
Transportation plays a very significant role when it comes to the costs of a company representing on average 60% of logistics costs, so its management is very important for any company. The transportation modal choice is one of the most important transportation decisions. The purpose of this article is to select the transportation mode which is able to minimize total costs, and consistent with the objectives of customer service on the coolant import, which is used in plasma cutting machines. With the installation of a distribution center in Brazil and the professionalization of the logistics department of the company, it was decided to re-evaluate the transportation mode previously chosen to import some items. To determine the best mode of transportation was used basic compensation costs, in other words the cost compensation of using the shuttle service to the indirect cost of inventory related to the modal performance. Through the study, it was possible to observe it may be possible to save up to 73% on the coolant international transportation by changing the transportation mode used by the company.
The public-transport (transit) operation planning process commonly includes four basic activities, usually performed in sequence: network design, timetable development, vehicle scheduling, and crew scheduling. This work addresses two activities: timetable development and vehicle-scheduling with different vehicles types. Alternative timetables are constructed with either even headways, but not necessarily even passenger loads or even average passenger loads, but not even headways. A method to construct timetables with the combination of both even-headway and even-load concepts is developed for multi-vehicle sizes. The vehicle-scheduling problem is based on given sets of trips and vehicle types arranged in decreasing order of vehicle cost. This problem can be formulated as a cost-flow network problem with an NP-hard complexity level. Thus, a heuristic algorithm is developed. A few examples are used as an expository device to illustrate the procedures developed. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee.
Hydrogen transport over long distances is a critical cost component, and it can involve many complex pathways. We have developed a model and an associated framework that can be used to determine the cost of transport methods for both land and land-and-sea scenarios. The model assesses the transportation of liquid and gaseous hydrogen by truck, rail, and barge; as well as gaseous hydrogen pipelines. Our results show that for large scale and long-distance hydrogen transport, the only feasible gaseous hydrogen transport option are pipelines. For example, a well-planned pipeline can keep hydrogen transportation costs below $3 per kg for distances up to 7000 km so long as the demand is greater than 150 tonnes per day. Liquid hydrogen transport is feasible and efficient for long distance transport, especially when used alongside rail travel providing less than 50 tonnes per day.
The Internet of Things technology is an important part of modern intelligent systems. It plays an important role in the development of information, and it is also indispensable in industry, trade, manufacturing and daily life. The explosive development of e-commerce in recent years has contributed to the rapid growth of the logistics industry. However, due to the substantial increase in online orders, serious environmental pollution has also appeared in the logistics industry, and the society is paying more and more attention to it. The reliability assessment of the supply chain and the analysis of the green logistics innovation strategy have improved the environmental pollution of the logistics industry and reduced the vehicle emissions in transportation by 26.9%. In addition, the data system for green packaging and green warehousing has been updated, and the accuracy of information circulation has increased by 45.97%. Effectively reduce costs in all aspects of the logistics industry, and the first to develop green logistics will undoubtedly take the initiative in the development of the logistics industry. Green logistics is considered to be one of the trends in the future development of logistics industry.
Transportation and inventory are essential to hazardous materials logistics, while different classes of hazardous materials are often transported over a network simultaneously. Despite their in-transit and storage incompatibility, the superimposed risks among different materials, which results from possible chemical reaction once accidents (e.g., leakage, explosion) happen, further complicate the comprehensive plans. In this study, we introduce a new multi-class hazmat distribution network design problem with inventory and superimposed risks (MHND) in a multi-echelon supply chain, where the planning of locations, inventory, and routes are made together. The long-term detour cost/risk and the cyclic time windows penalty costs under the time-dependent (periodic) road closure policy are explicitly formulated. We further propose a new population-based risk definition that evaluates the risk for the population at any location and any time with respect to its multi-class hazmat logistics system. In particular, to capture the interactions between different types of materials, we introduce risk superposition coefficients to capture possible superimposed risks among different hazmat that accommodate a general system with more than two hazmat types. We develop a knowledge-based NSGA-II algorithm with cyclic dissimilarity-based elitist selection (NSGA-II-CD) to solve the problem. The devised cyclic dissimilarity-based elitist selection (CD) operator can tackle the issue of speeding proliferation, which greatly improves the solution quality. Our model is applied to a metropolitan-wide real-world case study in Guangzhou, China. The results suggest that, from the perspective of the traffic management sector, the periodic road closures policy in Guangzhou could be possibly upgraded to a full-time prohibition. Moreover, the results provide the following insights to authorities (1) there is a positive convex relation between risk minimization and risk equilibration. The authorities should not try to find a perfect distribution of risk, and they should make a trade-off between the risk equity and total exposed risk; (2) there is a positive correlation between the level of service and total risk. Thus, in practice, the agencies should make a trade-off between economic viability of the system, exposed risk, and maintaining good service for customers; and (3) the interactions between different types of hazmat considerably affect the distribution network design; specifically, the route overlapping ratio for different types of hazmat decreases when their interactions intensify.
The grocery market, especially the perishable product market is under amazing developments in China, accounting for half of overall food expenditure. However, the supply chain of perishable products has encountered serious problems, including significant freight losses, high inventory and transportation costs, etc. To solve these problems, the current paper proposes an integrated approach for simultaneously optimizing the decisions involved in the supply chain, typically including location, inventory, and routing strategy. A three-echelon supply chain including suppliers, DCs and retailers is structured in this paper, with the impacts of whether allowing direct shipment from supplier to retailer being considered. Two typical problems are investigated: location-inventory problem (LIP) and location-inventory-routing problem (LIRP). Mixed integer nonlinear programming model for LIP is proposed while Mixed integer linear programming models for LIRP is proposed, with the objective of minimizing the overall costs of supply chain, which are composed of infrastructure construction costs, transportation costs, inventory costs, and freight losses. CPLEX is used for LIP model solution and a two-stage heuristic algorithm based on Simulated Annealing is designed to solve the LIRP model. The proposed mathematical models and solution method are then applied to a real supply chain network for fresh milk. The optimized results suggest that considering the direct shipment from supplier to retailer is beneficial in terms of reducing the overall supply chain costs by 31%, with 43% reductions in transportation costs, 69.4% reductions in freight losses, 99.4% increases in inventory costs. With the developments of e-retailers for perishable products, allowing the direct shipment from supplier to retailer will bring more benefits in the future.
Urbanization growth, together with the limited capacity of the road network, has worsened traffic congestion inside the cities. To improve the urban traffic conditions, it is essential to better understand and measure urban-traffic behavior not only on different period time of a day (e.g., morning or evening peaks) but also on different days (i.e., Monday to Sunday). Using real and recent data from the Google Maps API, this paper proposes a new approach to estimate the speeds within defined geographical areas (i.e. zip codes) per daytime and per weekday. Using this input, a statistical analysis including k-means clustering is adopted to classify and define different urban-congestion levels according to the estimated speeds the number of inhabitants the zone types and the type of roads in each zip code. In order to validate our approach, we conduct an experimental analysis in Boston, US. Our results provide managerial insights for key stakeholders (i.e., Carriers, Consumers, and Government) to improve the efficiency of the road network and reduce traffic congestion in cities.
The cell expresses various genes in specific contexts with respect to internal and external perturbations to invoke appropriate responses. Transcription factors (TFs) orchestrate and define the expression level of genes by binding to their regulatory regions. Dysregulated expression of TFs often leads to aberrant expression changes of their target genes and is responsible for several diseases including cancers. In the last two decades, several studies experimentally identified target genes of several TFs. However, these studies are limited to a small fraction of the total TFs encoded by an organism, and only for those amenable to experimental settings. Experimental limitations lead to many computational techniques having been proposed to predict target genes of TFs. Linear modeling of gene expression is one of the most promising computational approaches, readily applicable to the thousands of expression datasets available in the public domain across diverse phenotypes. Linear models assume that the expression of a gene is the sum of expression of TFs regulating it. In this chapter, I introduce mathematical programming for the linear modeling of gene expression, which has certain advantages over the conventional statistical modeling approaches. It is fast, scalable to genome level and most importantly, allows mixed integer programming to tune the model outcome with prior knowledge on gene regulation.
Optimizing the trade-off between crucial decisions has been a prominent issue to help decision-makers for synchronizing the production scheduling and distribution planning in supply chain management. In this article, a bi-objective integrated scheduling problem of production and distribution is addressed in a production environment with identical parallel machines. Besides, two objective functions are considered as measures for customer satisfaction and reduction of the manufacturer's costs. The first objective is considered aiming at minimizing the total weighted tardiness and total operation time. The second objective is considered aiming at minimizing the total cost of the company's reputational damage due to the number of tardy orders, total earliness penalty, and total batch delivery costs. First, a mathematical programming model is developed for the problem. Then, two well-known meta-heuristic algorithms are designed to spot near-optimal solutions since the problem is strongly NP-hard. A multi-objective particle swarm optimization (MOPSO) is designed using a mutation function, followed by a non-dominated sorting genetic algorithm (NSGA-II) with a one-point crossover operator and a heuristic mutation operator. The experiments on MOPSO and NSGA-II are carried out on small, medium, and large scale problems. Moreover, the performance of the two algorithms is compared according to some comparing criteria. The computational results reveal that the NSGA-II performs highly better than the MOPSO algorithm in small scale problems. In the case of medium and large scale problems, the efficiency of the MOPSO algorithm was significantly improved. Nevertheless, the NSGA-II performs robustly in the most important criteria.
We introduce a multi-period location-inventory-routing problem with time windows and fuel consumption, which simultaneously optimizes the location, routing, and inventory decisions for both the distribution center and customers in a multi-echelon supply chain. To better reflect reality, the fuel consumption is also incorporated into the variable transportation cost. The problem is formulated as a mixed integer nonlinear programming model. We then propose a two-stage hybrid metaheuristic algorithm to address this problem. In the first stage, a customized genetic algorithm is proposed. In the second stage, a gradient descent algorithm is used to improve the inventory decision to further reduce the total cost. Results of numerical experimentations on generated instances confirm the effectiveness of the algorithm. Results show that inventory management activities contribute considerably to total cost saving. Given the cost trade-off between transportation and inventory, the retailers’ inventory level shows more shortages after post-optimization, while the inventory level in the distribution centers can be either reduced or increased, depending on the spatial distribution of retailers in the vicinity of the distribution center. Sensitivity analysis on the model parameters is also conducted to provide managerial insights.
Determining the type of vehicles to transport goods between multiple factories and numerous distributors with different demands is one of the major logistic decisions that have to be made by industry players to reduce the cost of operations. A Mixed-Integer Quadratic Programming (MIQP) model was used to optimally distribute goods to 105 distributors from two factories across Ghana. The formulated model and analysis show that the existence of multiple vehicles in a fleet purposely for long hauling of goods also renders an optimal minimum cost as compared to a single-vehicle fleet. This optimum minimum cost accounts for 0.2066 of the total cost incurred by the two factories. This resulted in a 25% reduction in transportation cost. Again, a single-vehicle fleet with loading capacity within the mean value of all individual demands gave a minimum cost next to the optimal minimum.
In emergency logistics, it is important to allocate available assets to operations effectively due to the resource scarcity. This paper considers a supply chain network which includes local and global suppliers of medical relief items, regional and central distribution centers, and many customer demand points. Either pre-positioned resources at distribution centers or new assembly operations at them can fulfill resources demands. Moreover, a capacitated multi-stage operations scheduling problem is presented, in which renewable (medical teams) as well as non-renewable resources (standard or customized medical kits) are required in an emergency supply chain. In addition, a new mixed integer programming model is presented, and solved for small-sized problems. Further, for solving large-sized problems, a particle swarm optimization (PSO) algorithm is developed. Finally, the performance of the proposed solution method is evaluated, and some sensitivity analyses are conducted on the more important parameters.
Online vehicle routing is an important task of the modern transportation service provider. Contributed by the ever-increasing real-time demand on the transportation system, especially small-parcel last-mile delivery requests, vehicle route generation is becoming more computationally complex than before. The existing routing algorithms are mostly based on mathematical programming, which requires huge computation time in city-size transportation networks. To develop routes with minimal time, in this paper, we propose a novel deep reinforcement learning-based neural combinatorial optimization strategy. Specifically, we transform the online routing problem to a vehicle tour generation problem, and propose a structural graph embedded pointer network to develop these tours iteratively. Furthermore, since constructing supervised training data for the neural network is impractical due to the high computation complexity, we propose a deep reinforcement learning mechanism with an unsupervised auxiliary network to train the model parameters. A multisampling scheme is also devised to further improve the system performance. Since the parameter training process is offline, the proposed strategy can achieve a superior online route generation speed. To assess the proposed strategy, we conduct comprehensive case studies with a real-world transportation network. The simulation results show that the proposed strategy can significantly outperform conventional strategies with limited computation time in both static and dynamic logistic systems. In addition, the influence of control parameters on the system performance is investigated.
The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental-related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time.
This paper addresses the vehicle routing and selection problem of single and multi-compartment vehicles for grocery distribution. Retailers used to rely on single-compartment vehicles (SCV), and transported only one temperature-specific product segment with this vehicle type. Retailers now have the option of using multi-compartment vehicles (MCV) due to technological advances. Products requiring differing temperature zones can be transported jointly as the loading area is split into separate compartments. Both vehicle types cause different costs for loading, transportation and unloading. In literature either the use of SCVs or MCVs has been considered without a distinction between vehicle-dependent costs and the use of both vehicle types in the fleet to achieve a cost-optimal fleet mix. We therefore identify vehicle-dependent costs within empirical data collection and present an extended multi-compartment vehicle routing problem (MCVRP) for the vehicle selection. We solve the problem with a Large Neighborhood Search. Our numerical experiments are based on the insights we draw from a real-life case with a retailer. In further experiments we show that the mixed fleet is always better than an exclusive fleet of SCVs or MCVs and state which factors influence the cost reduction. A mixed fleet can reduce costs by up to 30%. As a result, mixed fleets are advisable in grocery distribution and vehicle selection should be part of the MCVRP.
In the context of vehicle usage decisions, there are two important choice dimensions namely, the choice of vehicle from household fleet that will be utilized for trips and second, the distance traveled to pursue the planned activities. There are interrelationships between these two choice dimensions with one dimension potentially influencing the other. The direction of the interrelationship has important implications for transportation planning and policy analyses. In an effort to explore the interrelationships, a latent segmentation-based modeling approach is proposed in this paper. The approach allows for exploring alternative interrelationship structures between choice dimensions in the same modeling framework. The methodology is demonstrated using data from the latest wave of the National Household Travel Survey (NHTS) in the United States. The results show the need for accommodating alternative structures between choice dimensions to accurately describe the vehicle usage decision processes exhibited by individuals.
The split delivery vehicle routing problem (SDVRP) is a relaxed version of the classic capacitated vehicle routing problem (CVRP). Customer demands are allowed to split among vehicles. This problem is computationally challenging and the state-of-the-art heuristics are often complicated to describe and difficult to implement, and usually have long computing times. All these hinder their application by practitioners to solve real-world problems. We propose a novel, efficient, and easily implemented approach to solve the SDVRP using an a priori split strategy, that is, each customer demand is split into small pieces in advance. Our computational experiments on 82 benchmark instances show that our algorithm is overall much more efficient and produces results that are comparable to those from the state-of-the-art approaches.
This paper provides a review on the most relevant research works conducted to solve natural gas transportation problems via pipeline systems. The literature reveals three major groups of gas pipeline systems, namely gathering, transmission, and distribution systems. In this work, we aim at presenting a detailed discussion of the efforts made in optimizing natural gas transmission lines.
There is certainly a vast amount of research done over the past few years on many decision-making problems in the natural gas industry and, specifically, in pipeline network optimization. In this work, we present a state-of-the-art survey focusing on specific categories that include short-term basis storage (line-packing problems), gas quality satisfaction (pooling problems), and compressor station modeling (fuel cost minimization problems). We discuss both steady-state and transient optimization models highlighting the modeling aspects and the most relevant solution approaches known to date.
Although the literature on natural gas transmission system problems is quite extensive, this is, to the best of our knowledge, the first comprehensive review or survey covering this specific research area on natural gas transmission from an operations research perspective. The paper includes a discussion of the most important and promising research areas in this field. Hence, this paper can serve as a useful tool to gain insight into the evolution of the many real-life applications and most recent advances in solution methodologies arising from this exciting and challenging research area of decision-making problems.
Overviews and Surveys.- Routing a Heterogeneous Fleet of Vehicles.- A Decade of Capacitated Arc Routing.- Inventory Routing.- The Period Vehicle Routing Problem and its Extensions.- The Split Delivery Vehicle Routing Problem: A Survey.- Challenges and Advances in A Priori Routing.- Metaheuristics for the Vehicle Routing Problem and Its Extensions: A Categorized Bibliography.- Parallel Solution Methods for Vehicle Routing Problems.- Recent Developments in Dynamic Vehicle Routing Systems.- New Directions in Modeling and Algorithms.- Online Vehicle Routing Problems: A Survey.- Modeling and Solving the Capacitated Vehicle Routing Problem on Trees.- Using a Genetic Algorithm to Solve the Generalized Orienteering Problem.- An Integer Linear Programming Local Search for Capacitated Vehicle Routing Problems.- Robust Branch-Cut-and-Price Algorithms for Vehicle Routing Problems.- Recent Models and Algorithms for One-to-One Pickup and Delivery Problems.- One-to-Many-to-One Single Vehicle Pickup and Delivery Problems.- Challenges and Opportunities in Attended Home Delivery.- Chvatal-Gomory Rank-1 Cuts Used in a Dantzig-Wolfe Decomposition of the Vehicle Routing Problem with Time Windows.- Vehicle Routing Problems with Inter-Tour Resource Constraints.- From Single-Objective to Multi-Objective Vehicle Routing Problems: Motivations, Case Studies, and Methods.- Practical Applications.- Vehicle Routing for Small Package Delivery and Pickup Services.- Advances in Meter Reading: Heuristic Solution of the Close Enough Traveling Salesman Problem over a Street Network.- Multiperiod Planning and Routing on a Rolling Horizon for Field Force Optimization Logistics.- Health Care Logistics, Emergency Preparedness, and Disaster Relief: New Challenges for Routing Problems with a Focus on the Austrian Situation.- Vehicle Routing Problems and Container Terminal Operations - An Update of Research.
The papers in this Special Issue on 'Efficient Algorithms for Large Scale Scientific Computations' are mainly devoted to the efficient solutions related to the selection of numerical algorithms. The selected papers deal mainly with the important topics, such as, finite element methods applied in the discretization of several types of PDEs or systems of PDEs. Other topics include papers on iterative methods for the solution of large systems of linear algebraic equations arising after the discretization of elliptic PDEs, application of finite volume schemes for studying particle dispersion in open channel flow, algorithms for applying observation data in an attempt to improve the quality of the calculated by the mathematical models results, treatment of reaction diffusion models for studying ecosystems composed by one predator and two prey populations, and efficient application of splitting procedures. The papers will certainly contribute to the selection of promising numerical methods and computational devices.
This paper deals with two interrelated questions, namely the optimum size of a vehicle or vessel, and the structure of transport costs with respect to haulage distance. The relationship between these two questions has not been coherently dealt with previously in the literature, and the heuristic attempts at doing so have lead to both theoretical and empirical anomalies. This paper adopts an inventory optimisation approach in order to show that both of these questions can be treated in a unified manner and this allows us to show, first, that under very general conditions the optimum size of a ship increases with the haulage distance and haulage weight, and second, that the observed structure of transport costs with respect to the haulage distance and quantity is itself a result of this optimisation problem.
Ghana: Weddi africa invests in tomato processing
- F X Branthome
Solution of two vehicle cost varying interval transportation problem-a new approach
- G Ramesh
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G. Ramesh, G. Sudha, K. Ganesan, Solution of two vehicle cost varying interval transportation problem-a new approach, Int. J. Pure Appl. Math. (2018) 363-372.
Developed method for optimal solution of transportation problem
- Davda
P. Davda, J. Patel, Developed method for optimal solution of transportation problem, Int. J. Res. Eng. Technol. 6 (3) (2019) 1880-1882.
The Vehicle Routing Problem with Time Windows, Flexible Service Locations and Time-Dependent Location Capacity
- A Jungwirth
- M Frey
- R Kolisch
A. Jungwirth, M. Frey, R. Kolisch, The Vehicle Routing Problem with Time Windows, Flexible Service Locations and Time-Dependent Location Capacity, 2020.
Introduction to Multi-Modal Transportation Planning, Victoria Transport Policy Institute Canada
- T Litman
T. Litman, Introduction to Multi-Modal Transportation Planning, Victoria Transport Policy Institute Canada, 2017.
Solution of two vehicle cost varying interval transportation problem-a new approach
- Ramesh