ارائۀ مدلی برای مسئلۀ مسیریابی اتوبوس مدرسه با درنظرگرفتن تفکیک جنسیتی

In the current system, school bus stops in Howard County, Maryland are manually placed along the school bus routes based on safety, cost-efficiency, and many other variables. With such liberal placement, bus stops are sometimes placed unnecessarily. This issue is prevalent in many school districts and often results in needlessly close bus stop proximity. In this study, the authors implemented a GIS-based heuristic to assist school officials in optimizing their districts bus stop placement. They also estimated the proportion of county-wide bus stops that could be eliminated by this approach. Following the constraints determined by State and local guidelines, the ArcGIS Network Analyst Extension was used to identify unnecessary bus stops across the study area. The initial output was re-evaluated by school officials in order to determine if those bus stops would be eliminated. The results indicate that approximately 30% of the existing bus stops were marked as “candidates for elimination” by the GIS process. After a review of these candidates, it was determined that at least 15% of the total school bus stops could be eliminated. Statistical estimates lent credence to the benefit of a re-evaluation of these bus stops. The method developed in this study can easily be replicated. Hence, it may inspire other school systems to exercise the same approach. Additionally, the results provide a gateway for future studies in examining more efficient school bus routes with less travel time, as well as investigating how much the carbon footprint of school bus fleets can be reduced.

A school bus problem is one of the most important logistical issues faced by governments and school administrations, which is widely depends on route optimization and scheduling. This study presents a mathematical model for the single-load school bus problem for urban areas, which considers bus stop selection, bus route generation, and school bus scheduling simultaneously. This model considers the possibility of demand outsourcing (e.g., students using parallel systems for transportation) and time windows in the school bus routing and scheduling (SBRS) problem. Each vehicle transports students from a bus stop to their school under the given constraints. Our goal is to maximize the transportation firm’s profits and increase the quality of service provided for students. To validate the presented model, the problem is solved by GAMS software, and the results are shown and analyzed. Finally, some sensitivity analyses are performed to show the efficiency of the presented model.

In this dissertation, we solve a school bus routing problem of transporting students including special education (handicapped) students and assigning them in Oldham county education district. The main contribution of this research is that we consider special education students (Type-2) along with other students (Type-1) and design a comprehensive school bus schedule to transport both kinds of students at the same time. Also, a student assignment mathematical model is presented to optimize the number of bus stops in use as well as one important measure of service quality, the total student walking distance. Comparing to the classic clustering methods, heuristic methods, or other methods from previous literatures, a mathematical optimization model is developed to solve a student assignment problem and to obtain the global optimal solution. The modeling constraints include budget limit, travel time limit, equity, school time window, and etc. Especially, the main difference between our model and other models is that it takes Type-2 students into consideration along with critical constraints accordingly, and solves the resulting more complex problem. Moreover, the school bus routing model in this work is one of the most general optimization models representing the school bus routing problem. On the other hand, similar to all existing models, the developed model considers the total system cost as the objective function value to minimize, different bus capacities, and common vehicle routing constraints such as flow conservation on routes and subtour elimination. Furthermore, another main difference is that the bus scheduling and school time window is also considered and solved in the model. With two different types of students, both Type-1 and Type-2, the time restrictions are varying, resulting in more complexity and additional constraints. The results in this work present the difficulties of meeting the requirement of Type-2 student riding time limit and school time window simultaneously. Also, the constraints regarding service equity and quality are provided and they can be used by decision makers if necessary. Either densely populated urban areas or sparsely populated rural areas, the school bus routing problem is difficult to solve due to a large number of students or long travel distance. The school bus routing problem falls under vehicle routing problem (VRP) with additional requirements because each student represents one unit of capacity. In this dissertation, we present a modeling framework that solves a student assignment problem with bus stop selection, and subsequently a school bus routing problem with school

Special education students are usually routed on different buses than non-disabled general education students. To make the routes more efficient, this study proposes serving general students and special education students on the same bus at the same time (mixed ride) while allowing heterogeneous fleets and mixed loads. ESRI Location-Allocation tools and Google OR-Tools are used for bus stop selection, route generation, and bus stop optimization. Parallel cheapest insertion heuristic and metaheuristic, simulated annealing, are adopted to generate school bus routes. The effectiveness of the mixed ride approach is tested for three schools with 178 synthetic students’ locations data (including 12 with wheelchair) in New York City using a fleet of 14 buses spread over four types. The results show the mixed ride approach achieved 14.32% reduction in total travel distance and 10.46% reduction in total travel time. The mixed ride approach tends to return solutions with fewer vehicles and fewer bus stops, less average travel distance, and shorter average travel time.

This paper proposes a School Bus Stop location and Routing Problem with Walking Accessibility and Mixed Load (SBSLRP-WA-ML), where the individual difference of walking accessibilities among students and the possibility of serving students attending different schools with the same bus simultaneously are considered. We first develop a mixed integer programming model for SBSLRP-WA-ML with the objective of minimizing the total commuting time, including walking time from the residence to school, in-vehicle travel time, and service time at stops. A two-stage solution method is then developed. In stage 1, an iterative clustering method based on k-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is used to locate bus stops aiming at minimizing the number of stops subject to various walking accessibilities. In stage 2, an improved ant colony optimization algorithm (IACO) integrating two local search operators is devised, which is used to generate bus routes with minimal total commuting time. A number of instances of different sizes are generated to verify the solution approach, and the influential factors with respect to total commuting time are analyzed. The model is also compared to the door-to-door school bus services. Comparison to similar methods and sensitivity analysis of parameters are also conducted to analyze the performance and robustness of the proposed approach.

Solving Integer Linear Programming (ILP) models generally lies in the category of NP-hard problems. Therefore, as the size of ILP models grows, the efficiency of exact algorithms for solving the models reduced significantly and for large models it is not possible to have the result. Genetic Algorithm (GA) is a metaheuristic method capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. Still GA has huge search space for large models and parallelization is a suitable technique to tackle this problem. This paper presents a scalable parallel GA to solve large ILP models derived from behavioral synthesis of digital circuits. We show that although models have non-binary variables, only binary variables are sufficient for coding chromosomes. We also use ”unknown” values for some genes to decrease the likelihood of inconsistency in the encoded constraints. Our experiments verify the efficiency and scalability of the proposed algorithm on multicore platforms. The proposed method outperforms IBM ILOG CPLEX 12.6 and MI-LXPM algorithm where the ILP models include 550 to 2258 int / binary decision variables. Also, the results indicate that the saturation point of using parallel processing elements for solving the large ILP models is at least 60.

Feeder buses provide a small but important part of the public transport system by carrying people between residential areas and transport interchanges. A feeder bus to a train station planned in advance will attract new residents of a housing development to use the bus. The bus route can influence the location choice of a buyer concerned about access for children, the elderly or anyone not wishing to drive a car. Our bus route modelling starts with the bus stops – not the route – to be reached from each dwelling by the shortest possible walk. In demand terms, people locating close to bus stops are more likely to use the service than those choosing more distant locations, and the nearby residences have higher values. The stops-first application determines a feeder bus route to enhance an irregular residential plan covering an area of one square kilometre. The planned road and housing lot locations provide the data for calculating the access measure from each dwelling to each potential bus stop, the closest stop being used. A genetic algorithm tests potential bus stops to find demand maximizing locations, the propensity to use the bus being formulated as an exponential (increasing elasticity) function of walking distance. Then a ‘travelling salesman’ genetic algorithm finds the shortest route linking the stops, so that an efficient circuit route is generated for each alternative number of bus stops, ranging from 7 to 11. More stops not only give better access but also increase the route length, so that total accessibility must be assessed against route length. The distribution of walking distances shows most between 150 and 240 metres, with none more than 400 metres. The results indicate that planning policy should require prior design of a bus route to achieve good walking accessibility, so that residents become accustomed to the convenience of using the bus. This study shows that, at the planning stage, estimating a bi-objective model giving a Pareto front between accessibility and route length can reveal a policy compromise that shortens the route with little reduction in expected patronage.

Generally, Kandy city and traffic congestion go hand in hand. This situation becomes worse during school time. The geographical location of the city, the limited number of entrances and the large number of schools located within a small area are contributing to this condition. This study attempts to propose a new model to reduce school time traffic congestion using School Bus Routing Problem (SBRP) method. Network analysis in GIS facilitates the build of this system. SBRP seeks to plan an efficient schedule for school buses to pick up students from a bus stop and drop them to school by satisfying various constraints like; school time window, maximum walking distance and riding time, and the traffic. SBRP selects the nearest bus stops, generates suitable bus routes and visualizes traffic congestion on roads in Kandy city. Vehicle Routing Problem (VRP), closest facility, and location-allocation tools identify GIS-based solutions to SBRP. The proposed model selected suitable bus stops to drop students to a school and to generate the fastest bus route for the school buses. Visualizing a 12-hour daytime traffic in Kandy City, all schools are covered by the 56 fastest bus routes. The maximum riding time and distance limits to 59 minutes and 16 km respectively. Historical traffic data identifies 6.00 am to 8.00 am and 12.00 pm to 2.00 pm as the most traffic-congested time in the city. Finally, all problems of SBRP are solved and a systematic method is introduced to transport school students by optimizing the traveling time of students with existing traffic congestion.

Bus stops are key links in the journeys of transit patrons with disabilities. Inaccessible bus stops prevent people with disabilities from using fixed-route bus services, thus limiting their mobility. The Americans with Disabilities Act (ADA) of 1990 prescribes the minimum requirements for bus stop accessibility by riders with disabilities. Due to limited budgets, transit agencies can only select a limited number of bus stop locations for ADA improvements annually. These locations should preferably be selected such that they maximize the overall benefits to patrons with disabilities. In addition, transit agencies may also choose to implement the universal design paradigm, which involves higher design standards than current ADA requirements and can provide amenities that are useful for all riders, like shelters and lighting. Many factors can affect the decision to improve a bus stop, including rider-based aspects like the number of riders with disabilities, total ridership, customer complaints, accidents, deployment costs, as well as locational aspects like the location of employment centers, schools, shopping areas, and so on. These interlacing factors make it difficult to identify optimum improvement locations without the aid of an optimization model. This dissertation proposes two integer programming models to help identify a priority list of bus stops for accessibility improvements. The first is a binary integer programming model designed to identify bus stops that need improvements to meet the minimum ADA requirements. The second involves a multi-objective nonlinear mixed integer programming model that attempts to achieve an optimal compromise among the two accessibility design standards. Geographic Information System (GIS) techniques were used extensively to both prepare the model input and examine the model output. An analytic hierarchy process (AHP) was applied to combine all of the factors affecting the benefits to patrons with disabilities. An extensive sensitivity analysis was performed to assess the reasonableness of the model outputs in response to changes in model constraints. Based on a case study using data from Broward County Transit (BCT) in Florida, the models were found to produce a list of bus stops that upon close examination were determined to be highly logical. Compared to traditional approaches using staff experience, requests from elected officials, customer complaints, etc., these optimization models offer a more objective and efficient platform on which to make bus stop improvement suggestions.

By using the system analysis method. and game theory of governmental placement of urban bus stops, operation of transit enterprises, and travelers choice of trip mode, transit line, and bus stop location, the research objectives of this study are to solve the bi-level programming problem for optimized urban bus stop placement with elastic demand and to establish a bi-level programming model. The upper-level goal of the government and transit enterprises for choosing bus stops from possible selections is to minimize travelers total travel cost, to minimize bus operating cost, and to maximize the bus trip volume. The lower-level goal of the traveler for choosing travel mode, transit lines, and final bus stop is to minimize his generalized cost within equilibrium of the traffic assignment. A genetic algorithm is adopted in the concrete optimization solution. The game analysis of different decision agents and the concrete restriction of bus stop location are considered using the bi-level programming method for ultimate selection of the bus stops. Moreover, the feasibility and correctness of the method. are proved.

Developing model-based software to optimise wheat storage and transportation: A real-world application

Saturation flow under mixed traffic conditions is affected by vehicular mix and its characteristics, approach grade, driver behaviour, roadway geometry, and road side frictions in the vicinity of intersection. Side friction arises from pedestrian movement, activities of public transport vehicles, and parking of vehicles on road premises. Due to the influence of these factors, realistic estimation of saturation flow is a complex task under heterogeneous traffic conditions. Road side friction arising from stopping of public transport adjacent to signalised intersection tends to interfere with vehicular discharge at intersections. This paper attempts to analyse the impact of far side (down stream side) and near side (upstream side) bus stops on saturation flow rate. As a first step towards quantifying the effect of bus stops, saturation flow of approaches that satisfies the base conditions set for the study were estimated in PCU/hr using area occupancy concept. Mathematical model for the prediction of base saturation flow was proposed. Effect of bus stops on saturation flow rate was then determined by analysing saturation flow rates of approaches where bus stops are located adjacent to intersections. Adjustment factors were introduced to incorporate the effect of far side bus stop (Ffb) and near side bus stop (Fnb) on saturation flow rate. Linear regression models were developed for the prediction of adjustment factors based on data generated using a micro simulation programme. The results of the study showed that adjustment factors vary with distance of bus stop from stop line, width of approach and proportion of green time blocked. The study also revealed that the reduction in saturation flow rate is more when bus stops are located in the upstream side (near side bus stop).

A column generation approach for a school bus routing problem with resource constraints

School bus routing involves transporting students from predefined locations to school using a fleet of buses with varying capacity. This paper describes a real-life problem of the school bus routing. The overall goal of this study is to develop a route plan for the school bus service so that it is able to serve the students in an efficient and economical manner with maximum utilization of the capacity of buses using hybrid genetic algorithm.KeywordsSchool bus routing problemGenetic algorithmVehicle routing problem with time windows

The article deals with the influence of the infrastructure for public transport on the delay time of private and public transport in the city. The study employed the methods of simulation, mathematical modeling and field research. Imitation microscopic modeling determined the parameters of mathematical models of the delay time of private and public transport for various parameters of the bus lane, the length of the bus stop loading area, and its distance from the signalized intersection. Calculations determined the total delay time, taking into account the number of passengers in public and private transport on the section of the main street of regulated traffic. Determining the optimum parameters of the public transport infrastructure requires considering not only public transport passengers, but also drivers and passengers of private vehicles. Over-improving parameters of the bus lane has no effect on public transport, but traffic parameters for all other road users degrade. At high traffic intensity, the dependences of the total delay time on the length of the marking lines 1.11 and 1.5 are described by the parabola equation. The values for a road with three lanes have been determined, marking lines 1.11 and 1.5 at which the total delay time is minimal. For a highway with a high intensity, minimum bus stop parameters lead to significant increases in delay time.