School Bus Routing Problem Research Articles

Optimizing extracurricular activities assignment and related logistical deployment cost between collaborating schools

AbstractIn contemporary urban societies, where both parents are working full‐time, a significant number of schoolchildren engage in extra‐curricular activities after school. These activities can be organized by the school itself and take place in the school. However, sometimes few schoolchildren are interested in an activity organized by the school, or the schoolchildren's preferences do not match the school's offering at all, while on other occasions the school has limited availability for a popular activity. To expand the number of activities offered to their schoolchildren, some schools form a collaborating network, sharing their extracurricular activities and making them accessible to all schoolchildren. Thus, schoolchildren from any school may attend activities organized by other schools in the network. In this case, however, transport of the children between schools must also be organized. This problem can be framed as a school bus routing problem with some special features. A mixed‐integer linear optimization model is proposed for the integrated assignment of extracurricular activities and cost‐effective vehicle routing. The objective of the model is to minimize unmet demand for extracurricular activities while taking into account the constraints related to the facilities and transport. This model has been tested on a set of instances to analyze its performance, with the goal of deploying it for the projected levels of demand in a city of about 100,000 inhabitants. The results are compared with the current situation and the clustering of the set of schools.

The Review of Recent Trend for School Bus Routing Problem

The School Bus Routing Problem (SBRP) is a complex transportation challenge involving finding optimal bus routes. This review paper provides an overview of the recent developments in SBRP research and focuses on three sub-problems: Bus Route Generation, Bus Route Scheduling, and Bus Stop Selection. The paper examines recent publications from 57 relevant articles. It highlights the increasing focus on real-world and complex scenarios, as well as the growing popularity of metaheuristic approaches in addressing SBRP challenges. The analysis reveals the significance of bus route generation, bus route scheduling, and bus stop selection, showcasing the effectiveness of machine learning and heuristic or metaheuristic algorithms in improving route quality. This study also classifies SBRP problems based on the number of schools, service surroundings (urban or rural), mixed-load scenarios, and fleet mix (homogeneous or heterogeneous). Finally, the paper explores the objectives of SBRP research, including minimising the total cost, distance, time, and number of buses. Meanwhile, the constraints of this study are the capacity of a bus, the maximum riding time, time windows, the maximum walking time between two stops and so on. This comprehensive review paper aims to offer a framework for new researchers and provides valuable insights for future research directions in this transportation area.

The School bus routing problem: A systematic literature review

The School Bus Routing Problem (SBRP) is a classic optimization problem with a massive potential for real applications that have a high impact on society. Research interest in this problem is constantly rising. Previous review papers with a time-space between them of 10 years have helped understand the different features studied by the research community about this problem. In this systematic review, we consider two new categories not discussed before: the incorporation of a mixed load composed of multiple schools, along with the inclusion of a smart element related to the availability of user information and communication in real-time to join the smart mobility trend. In addition, we discuss the lack of real applications in the SBRP in university contexts with a focus on the multi-load problems.

The many costs of operating school buses in America

The research seeks to quantify the marginal cost impact of transportation cost drivers on the total operating cost of Texas's public schools and how these costs differ between district type and environment setting. The analysis tests the validity of often cited research findings examining the widely used School Bus Routing Problem (SBRP). We present results from fixed effects regressions with panel data for the total transportation operating cost. Finding the marginal cost of an additional student is 2.5 times greater for a rural district than for an urban district. Additionally, we compare mean average values of school bus transportation metrics between rural, town, suburban, and city districts. Concluding, on average, school bus transportation costs for Rural districts are 40% more per student than a City or Suburban district. The dataset includes eleven years of transportation operating costs from 998 Texas public school districts.

Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications

In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer network models, and school bus routing and facility location problems. If a fuzzy graph fails to obtain acceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in arbitrary real-world scenario. In this study, we consider the concept of domination as it relates to single-valued neutrosophic incidence graphs (SVNIGs). Given the importance of domination and its utilization in numerous fields, we propose the application of dominating sets in SVNIG with valid edges. We present some relevant definitions such as those of valid edges, cardinality, and isolated vertices in SVNIG along with some examples. Furthermore, we also show a few significant sets connected to the dominating set in an SVNIG such as independent and irredundant sets. We also investigate a relationship between the concepts of dominating sets and domination numbers as well as irredundant and independence sets in SVNIGs. Finally, a real-life deployment of domination in SVNIGs is investigated in relation to COVID-19 vaccination locations as a practical application.

Application of School Bus Routing Problem in GIS to Organize School Buses in Kandy City, Sri Lanka

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.

The cumulative school bus routing problem: Polynomial‐size formulations

AbstractThis article introduces the cumulative school bus routing problem, which concerns the transport of students from a school using a fleet of identical buses. The objective of the problem is to select a drop‐off point for each student among potential locations within a certain walking distance and to generate routes such that the sum of arrival times of all students from their school to their homes is minimized. The article describes six polynomial‐size mixed integer linear programming formulations based on original and auxiliary graphs, and the formulations are numerically compared on real instances. The article reports the results of computational experiments performed to evaluate the performance of the proposed models.

From School Buses to Carpooling: A Multifaceted Approach to Solving Vehicle Routing Problems in People Transportation

This paper delves into the complex realm of vehicle routing problems (VRPs) with a specific focus on the transportation of people, highlighting the nuanced challenges and optimization opportunities distinct from those associated with goods transportation. Among these, the Dial-a-Ride Problem (DARP) is emphasized as a pivotal area of study. DARP caters to providing personalized, accessible transportation services, particularly for individuals unable to use standard transit options, such as the elderly and handicapped. This research meticulously explores the mathematical formulation of DARP, and operational challenges and extends the discourse to encompass related VRPs in people transportation, thereby broadening the scope of investigation. Operational intricacies of DARP include managing time windows for pickups and deliveries, adhering to vehicle capacity limits, and ensuring tailored transportation solutions that optimally satisfy both operational costs and customer convenience. The paper reviews a wide spectrum of heuristic and metaheuristic solution methods developed over the years, tracing the evolution of these algorithms from their inception to the sophisticated techniques currently employed to address DARP's dynamic, static, and stochastic variants. Additionally, the research extends to related problems such as the School Bus Routing Problem (SBRP), which emphasizes the efficient and timely transportation of students, and the Carpooling Problem, focusing on organizing shared rides to reduce vehicle kilometers and enhance mobility. Demand Responsive Transportation (DRT) problems are also discussed, highlighting their importance in areas where fixed-route services are inefficient. Conclusively, the paper discusses the future scope of research in this domain, underscoring the necessity for novel solution concepts to address the growing complexity and scale of transportation demands. The integration of intermodal aspects, combining public transportation with demand-responsive services, and the advancement of hybrid algorithms are identified as key areas for future exploration. This comprehensive study not only contributes to the academic discourse on optimizing vehicle routing for people transportation but also aims to inform the development of more efficient, accessible, and customer-oriented transportation systems.

School accessibility evaluation under mixed-load school bus routing problem strategies

Mixed-load school bus routing problem (SBRP) strategy helps to improve the efficiency of school bus systems. School accessibility is a student-oriented measurement indicator that visually demonstrates the influence of mixed-load SBRP strategies on student commuting efficiency. In order to improve the convenience of students commuting to school while greatly reducing the operational cost of school buses, this paper proposes two mixed-load SBRP strategies (strategy 1: mixed-load mode and strategy 2: single-load mode). The bi-level programming model is constructed to model the two mixed-load SBRP strategies. In the bi-level programming model, the upper-level is to maximize school accessibility, and the lower-level optimizes school bus routes with the goal of minimizing the total number of school buses. The entropy-based weight method is introduced for comprehensive evaluation of strategies. Case studies are presented based on school bus data in Dalian, China to measure the performance of the two strategies. In computational experiments, the effect of weighted commuting time on school accessibility is also investigated. The results indicate that the SBRP strategy of mixed load mode (strategy 1) is the most effective in terms of comprehensive assessment of operating costs and school accessibility. In addition, it is found that the weighted commuting time has expanded the horizontal differentiation of school accessibility.

A School Bus Routing Heuristic Algorithm Allowing Heterogeneous Fleets and Bus Stop Selection

This paper addresses a school bus routing problem formulated as a capacitated and time-constrained open vehicle routing problem with a heterogeneous fleet and single loads. This problem incorporates several realistic features, such as student eligibility, maximum walking distances, bus stop selection, maximum riding times, different types of buses, multistops, and bus dwell times. A heuristic algorithm based on an iterated local search approach is proposed for this problem. It determines the selection of bus stops from a set of potential stops, the assignment of students to the selected bus stops, and the routes along the selected bus stops. The main objectives are minimizing the number of buses used, the total student walking distance, and the total route journey time. Other aims are balancing route journey times between buses and minimizing the total number of empty seats. A set of 20 real-world problem instances are used to evaluate the performance of the algorithm. Results indicate that the algorithm finds high-quality solutions in very short amounts of computational time.

An Android Application Using Machine Learning Algorithm for Clique Detection in Issues Related to Transportation

This paper presents the development of a new variant mobile application with a local search algorithm that has been designed to detect routes in school transportation. The School bus routing problem relates to designing the optimum distribution/collection routes for the school buses serving geographically scattered students, and has been the focus of many academics for a long time. The proposed application system selects the best route for the buses to pick up the students from their houses. The system determines the optimal route for designated locations using google maps endings in efficient use of time and fuel. In order to meet the tremendous distance and the complex geographic structure, the proposed method divide the geographic regions into cliques that contain close houses to each other. The application is implemented on Android operating system since android is currently broadly utilized. The proposed framework is integrated with Google API to handle access to map display, data downloading and Google Maps servers. To evaluate the proposed application a survey was conducted. The findings from the reviews were impressive and substantial. The proposed solution of the school bus routing problem can be applied to solve problems related to the vehicles of institutions and organizations

Conscious Exploration of Alpha-Cuts in the Parametric Solution of the School Bus Routing Problem with Fuzzy Walking Distance.

Combinatorial optimization problems allow for modeling multiple situations in which proper allocation of resources is needed. For some real-world problems, the use of fuzzy elements in the models allows for incorporating certain levels of uncertainty to better approximate such real-world situations. One way to solve combinatorial optimization problems with fuzzy elements is the parametric approach, where it is necessary to define how to explore different relaxation levels using alpha-cuts. Researchers tend to select such alpha-cuts uniformly. The current investigation proposes a novel strategy for selecting alpha-cuts in the School Bus Routing Problem with fuzzy students' maximum walking distance. This proposal bases its foundations on the number of student-bus stop pairs available according to the different levels of relaxations allowed. Results demonstrate how the proposed strategy gives attractive solutions with more diverse trade-offs, contrasted with other methods in the literature. Furthermore, it decreases the computational cost for those instances where the maximum relaxation does not provide new pairs of students-bus stops.

The routing problem for school buses considering accessibility and equity

School bus services play an important role in the daily commuting of students in small cities. In this paper, we research the school bus routing problem in Holingol, in which the accessibility of schools and the equity of schemes are considered. We measure the accessibility of schools by the average commuting time of students and the equity of schemes by the average detour time of students. The results show that applying the transfer strategy to solve the proposed problem can reduce the number of required school buses. Assigning more school buses to implement the second step of transfer strategy is conductive to improving the quality of solutions. Besides, the detour time for students is reduced to guarantee the equity of schemes. The findings highlight that policy makers should consider the long detour time of students and design schemes to overcome the observed inequity in small cities.

Proposal of a method for routing school buses in a small-sized county

The School Bus Routing Problem (SBRP) is widely discussed in the operations research literature and can be solved by several exact methods and heuristics. This problem seeks to designate the most efficient routes for a fleet of school buses, minimizing the total distance covered and considering variables such as bus stop locations, number of passengers, and the assigned destination for each of them. This study aims at solving a real case SBRP of a small-sized county located in the state of Paraná. The proposed method is based on the Capacitated Vehicle Routing Problem (CVRP) and Travelling Salesman Problem (TSP) combined with a heuristic correction that guarantees sequence constraints, in which the student has to be collected before visiting their destination school. It was possible to obtain two routes of 30.76 km and 17.42 km respectively and both with the total vehicles’ capacity of 24 students, which corresponds to the reduction of about 10% in the daily distance covered by two buses.

A partial evaluation approach for the School Bus Routing Problem

Several real-life optimization problems, such as the case of several instances of the School Bus Routing Problem (SBRP), are very complex and expensive to solve with exact algorithms. Metaheuristics are a good alternative in these situations because they are capable of generating good quality solutions to these problems in a reasonable time. Metaheuristics iterate thousands of times by introducing changes concerning the previous solutions. Each new solution must be evaluated, and sometimes, the new solutions have elements unchanged that are unnecessarily re-evaluated. However, an approach avoids repeatedly evaluating parts of different solutions known as partial evaluation. This work applies this technique to the SBRP to reduce its execution time. To apply the partial evaluation approach in this problem, each solution contains the information of the change that was made concerning the solution from which it originates. With this information, when evaluating the objective function, it will be only necessary to analyze the routes that changed. In the literature reviewed, no previous work was found in which the partial evaluation approach has been applied in the context of SBRP. In this paper we apply it in order to reduce the computational cost of SBRP solutions based on metaheuristics. The results show that it is possible to decrease the execution time in 80% of the instances, reducing the execution time on average by 73.6%.

Integrated student to school assignment and school bus routing problem for special needs students

In this paper, we address the combined problem of assigning students to schools and generating school bus routes for special needs students. Special needs students typically require additional accommodations, both in terms of the services available at school and during pick-ups and drop-offs. This introduces additional complexities to the problems of assignment and routing for students. We develop a mathematical model that jointly addresses these problems, and incorporate multi-loads and heterogeneous bus fleet features. The model simultaneously assigns special needs students to schools based on their level of need and the availability of resources, and generates efficient routes to transport them to their designated schools. We propose a two-phase heuristic approach using the capacitated clustering problem, which is capable of generating high-quality solutions. We evaluate our proposed methodology using several randomly generated instances, and a real-world case study in Fort Smith, Arkansas. The results from the case study demonstrate that the proposed methodology can reduce the total miles traveled by buses by over 35% on average, when compared to previously developed heuristics in the literature for the same case study.

A New School Bus Routing Problem Considering Gender Separation, Special Students and Mix Loading: A Genetic Algorithm Approach

In developing countries, whereas the urban bus network is a major part of public transportation system, it is necessary to try to find the best design and routing for bus network. Optimum design of school bus routes is very important. Non-optimal solutions for this problem may increase traveling time, fuel consumption, and depreciation rate of the fleet. A new bus routing problem is presented in this study. A multi-objective mixed integer model is proposed to handle the associated problem. Minimization of transportation cost as well as traveling time is the main objectives. The main contributions of this paper are considering gender separation as well as mixed-loading properties in the school bus routing problem. Moreover, special and handicapped students are considered in this problem. The proposed model is applied in a real case study including 4 schools in Tehran. The results indicate the efficiency of the proposed model in comparison with the existing system. This comparison shows that the students’ travelling time is reduced by 28% for Peyvand middle smart school, 24% for Tehran international school, 13% for Hemmat School and 21% for Nikan High school. A customized Genetic Algorithm (GA) is proposed to solve the model. Penalty functions are used to handle the several constraints of the problem in Genetic Algorithm. The results justify the applicability and efficacy of the both proposed model and solution approach.

School Bus Routing Problem with a Mixed Ride, Mixed Load, and Heterogeneous Fleet

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.

Improved Genetic Algorithm (VNS-GA) using polar coordinate classification for workload balanced multiple Traveling Salesman Problem (mTSP)

The multiple traveling salesman problem (mTSP) is an extension of the traveling salesman problem (TSP), which has wider applications in real life than the traveling salesman problem such as transportation and delivery, task allocation, etc. In this paper, an improved genetic algorithm (VNS-GA) that uses polar coordinate classification to generate the initial solutions is proposed. It integrates the variable neighbourhood algorithm to solve the multiple objective optimization of the mTSP with workload balance. Aiming to workload balance, the first design of this paper is about generating initial solutions based on the polar coordinate classification. Then a distance comparison insertion operator is designed as a neighbourhood action for allocating paths in a targeted manner. Finally, the neighbourhood descent process in the variable neighbourhood algorithm is fused into the genetic algorithm for the expansion of search space. The improved algorithm is tested on the TSPLIB standard data set and compared with other genetic algorithms. The results show that the improved genetic algorithm can increase computational efficiency and obtain a better solution for workload balance and this algorithm has wild applications in real life such as multiple robots task allocation, school bus routing problem and other optimization problems.

A metaheuristic for the rural school bus routing problem with bell adjustment

This paper addresses the school bus routing problem with bell adjustments. This problem extends the traditional school bus routing problem by having the school working times as decision variables instead of input data. Adjusting schools working times (bell adjustment) increases managerial flexibility to lower transportation costs. On the other hand, this comes at the price of having to deal with more complex solution design and greater computational complexity, as underlaid by the scarce literature on the theme. Here we propose different bell adjustment strategies for a rural variant of the problem which has particular importance both economically and socially for developing countries that usually have schooling with multiple shifts and budget restrictions. The memetic algorithm combines an iterated local search with specialized neighborhood structures arranged in a variable neighborhood descent strategy and enriched with a diversification scheme that relies on an elite set to solve large scale real instances. Different bell adjustment strategies are richly explained, tested, and analyzed thoroughly. The results of statistical analysis show significant cost savings for both cases with or without multi-loading. The new strategy achieved up to 9% savings and 2.55% savings on the consolidated results. Instances with a lower number of vehicles and a higher number of schools presented higher savings.