School Bus Routing Research Articles

A simulated annealing solution method for robust school bus routing

A simulated annealing solution method for robust school bus routing

Establishing school bus baseline emergency evacuation times for elementary school students

Emergency evacuation systems are critical to mass transportation vehicles such as school buses. Previous bus fire propagation tests indicate that the available time for successful evacuation is approximately 3–5min. Many school districts in the United States utilize school bus routes that exclusively transport children in kindergarten through second/third grade where the bus driver is the only adult onboard. Currently, no standards specify the maximum allowable evacuation time for school buses. Full-scale evacuation trials were performed to measure front door, rear door, and both door (simultaneous) evacuation flow rates for kindergarten through third grade students. The evacuation trials indicated that the grade level of school bus passengers, and available evacuation routes have a significant effect on flow rate (p<0.05). For evacuation trials with driver’s assistance mean flow rate through the front door was 29children/min, 21children/min for the rear emergency door, and 36children/min for evacuations using both doors simultaneously.

OPTIMIZATION MODEL FOR SCHOOL TRANSPORTATION DESIGN BASED ON ECONOMIC AND SOCIAL EFFICIENCY.

The purpose of this paper is to design a model that allows to suggest new planning proposals on school transport, so that greater efficiency operational will be achieved. It is a multi-objective optimization problem including the minimization of the cost of busing and minimizes the total travel time of all students. The foundation of the model is the planning routes made by bus due to changes in the starting time in schools, so the buses are able to perform more than one route. The methodology is based on the School Bus Routing Problem, so that routes from different schools within a given time window are connected, and within the restrictions of the problem, the system costs are minimized. The proposed model is programmed to be applied in any generic case. This is a multi-objective problem, in which there will be several possible solutions, depending on the weight to be assigned to each of the variables involved, economic point of view versus social point of view. Therefore, the proposed model is helpful for policy planning school transportation, supporting the decision making under conditions of economic and social efficiency. The model has been applied in some schools located in an area of Cantabria (Spain), resulting in 71 possible optimal options that minimize the cost of school transport between 2,7% and 35,1% regarding to the current routes of school transport, with different school start time and minimum travel time for students. DOI: http://dx.doi.org/10.4995/CIT2016.2016.4074

A mixed load capacitated rural school bus routing problem with heterogeneous fleet: Algorithms for the Brazilian context

A capacitated rural school bus routing problem featuring mixed loads, a heterogeneous fleet, and the same school starting time is here addressed. This is an important problem of the routing literature which has been attracting the attention of many researchers recently. The mixed load feature allows students from different schools to ride the same bus at the same time. Five meta-heuristic based algorithms were devised to solve the problem, and evaluated on solving four different datasets, one of them being based on a real case from Brazil. Four traditional local search neighborhood structures for vehicle routing problems were adapted and specialized to handle mixed loads and a heterogeneous fleet simultaneously. To the best of the authors knowledge, it is the first time that both features are treated jointly within an algorithm, and not as a post processing optimization step. The attained cost savings and reduction of fleet sizes suggest the suitability of a mixed load, heterogeneous fleet approach for sparsely populated rural areas. Moreover the devised framework has been embedded into a decision support system which is assisting several municipalities of the state of Minas Gerais, Brazil, to better plan their routes and reduce transportation costs.

A two-stage heuristic algorithm for the school bus routing problem with mixed load plan

The school bus routing problem (SBRP) seeks to the optimal routes for a fleet of school buses to transport students to schools. To share resources between schools, school bus routing problem with mixed load plan (SBRP-MLP) is proposed in this paper, in which school buses are allowed to pick up students of different schools and deliver them to their schools. This paper presents two modes, SBRP-MLP with virtual stops and SBRP-MLP with interscholastic transportation. To solve the two SBRP-MLPs efficiently, a two-stage heuristic algorithm is developed. The results of several tests suggest that the proposed SBRP-MLP modes take less time than the SBRP with single load plan. Moreover, it was found that the SBRP-MLP with virtual stops is suitable for small-scale cases, while the SBRP-MLP with interscholastic transportation is appropriate for large-scale cases. In addition, the results also indicate that the algorithm is feasible for solving the SBRP-MLP.

Optimizing School Bus Stop Placement in Howard County, Maryland

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.

Implementation of the Metaheuristic GRASP Applied to the School Bus Routing Problem

Implementation of the Metaheuristic GRASP Applied to the School Bus Routing Problem

Wearable mobile internet devices involved in big data solution for education

The big data in education faces one methodology problem, i.e., how to acquire, store and apply the big data, especially to find one mediator to associate and solve the problem overall. In this paper, we create our big data model for one school firstly, which includes the behaviour subject information model and its related activity model. The behaviour subjects include the school, class, teacher, students, parents, etc. The information model relates with the subjects' basic and the activity information. Secondly, the collection means of big data is presented, the detailed big data about the activities are acquired from the existing and extended school information systems, e.g., as the administration systems for student attendance, quiz, shopping, etc. Thirdly, the wearable mobile internet devices act as one new means to provide more information and one key to associate different data from heteronomous sources. Finally, we verify our big data model through new applications, such as school-bus route optimisation, timecost impact to learning, and parents' affection for students' development, etc.

Total Unidominating Functions of a Path

in graphs is an emerging area of research at present and it has applications to several fields such as School bus routing, Computer communication networks, Facility location problems, Locating radar stations problem etc. Recently dominating functions in domination theory have received much attention. The new concepts viz., unidominating functions and total unidominating functions have been introduced. In this paper some total unidominating functions of a path are presented and determined its total unidomination number. Also the number of total unidominating functions with minimum weight is investigated. KeywordsTotal unidominating function, Total unidomination number.

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem.

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.

Development of a Genetic Algorithm for the School Bus Routing Problem

The School Bus Routing Problem (SBRP) covers the issue of establishing plans to efficiently transport students distributed across a designated area to the relevant schools using defined resources. As with the similar Vehicle Routing Problem (VRP), the SBRP may have diverse constraints such as heterogeneous vehicles, the allotted time window and multiple depots. Many solutions for effectively solving the problem are currently being studied. By their nature, these routing problems are NP-Hard (non-deterministic polynomial-time hard) problems in which the search domains increase exponentially as they become larger, thus making it difficult to obtain solutions using an exact approach except for relatively simple and localized problems. Therefore the heuristic approach is being studied in many regions. In this study, an algorithm was developed using genetic algorithms, which stem from meta-heuristic algorithms, and the algorithm was tested against diverse problems to identify its performance and practicality.

Continuous approximation models for mixed load school bus routing

School bus routing is a complex and expensive transportation problem for many public school districts. Typical school bus routes serve a single school, but mixed load school bus routes carry students for more than one school at the same time. A mixed load policy reduces the number of stops and distance to pick up and drop off children, but it can increase travel distance by visiting multiple schools. This paper provides a general strategic analysis using continuous approximation models to assess the conditions under which mixed loading is likely to be beneficial. We also present a case study for a semi-rural Missouri school district to illustrate the application of the models in practice. Results show that mixed load routing is more beneficial for larger districts, when a large percentage of bus stops are shared by students of different schools, and when schools are closer together.

A hybrid column generation and clustering approach to the school bus routing problem with time windows

&lt;span&gt;This paper attempts to solve the School Bus Routing Problem with Time Windows that consists of finding the best set of routes to pick up students distributed geographically with constraints as capacity, time windows and maximum travel time. We formulated the problem as a classic Vehicle Routing Problem with Time Windows and solved it using an approach based on a clustering algorithm and column generation method. A real world case from a school in Bogotá, Colombiais presented including 600 students to pick up in near 400 nodes located in urban and rural areas. The obtained results demonstrate a reduction as the problem’s complexity and an improvement on the performance measures of the proposed method.&lt;/span&gt;

The school bus routing and scheduling problem with transfers.

In this article, we study the school bus routing and scheduling problem with transfers arising in the field of nonperiodic public transportation systems. It deals with the transportation of pupils from home to their school in the morning taking the possibility that pupils may change buses into account. Allowing transfers has several consequences. On the one hand, it allows more flexibility in the bus network structure and can, therefore, help to reduce operating costs. On the other hand, transfers have an impact on the service level: the perceived service quality is lower due to the existence of transfers; however, at the same time, user ride times may be reduced and, thus, transfers may also have a positive impact on service quality. The main objective is the minimization of the total operating costs. We develop a heuristic solution framework to solve this problem and compare it with two solution concepts that do not consider transfers. The impact of transfers on the service level in terms of time loss (or user ride time) and the number of transfers is analyzed. Our results show that allowing transfers reduces total operating costs significantly while average and maximum user ride times are comparable to solutions without transfers. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(2), 180–203 2015

Costs of school transportation: quantifying the fiscal impacts of encouraging walking and bicycling for school travel

National governments have provided subsidies for investments in increasing the safety and attractiveness of walking and biking to school. Evaluations of Safe Routes to School initiatives have found that they have been effective at changing behavior and reducing injuries. However, there has been little attention to the impacts of these programs on pupil transportation costs. This analysis assesses the potential economic benefits of Safe Routes to School programs in the US context by estimating the annual costs of using motorized transport for short trips to schools, examining real-world examples of the costs savings of SRTS programs, and evaluating land use impacts on school transportation costs using a simulation analysis of school bus routes. We find that there is potential for school districts and families to reduce transport expenditures through public sector investments in walking and biking infrastructure near schools. We also find that land use context matters and the most cost-effective investments would benefit schools where large numbers of children live within walking distance.

Two-phase branch-and-cut for the mixed capacitated general routing problem

The Mixed Capacitated General Routing Problem (MCGRP) is defined over a mixed graph, for which some vertices must be visited and some links must be traversed at least once. The problem consists of determining a set of least-cost vehicle routes that satisfy this requirement and respect the vehicle capacity. Few papers have been devoted to the MCGRP, in spite of interesting real-world applications, prevalent in school bus routing, mail delivery, and waste collection. This paper presents a new mathematical model for the MCGRP based on two-index variables. The approach proposed for the solution is a two-phase branch-and-cut algorithm, which uses an aggregate formulation to develop an effective lower bounding procedure. This procedure also provides strong valid inequalities for the two-index model. Extensive computational experiments over benchmark instances are presented.

Cuckoo Search Algorithm and its Application on School Bus Problem

In this paper, discusses the school bus problem, given the mathematical model of route optimization, put forward an improved cuckoo search algorithm. Finally, take school bus routes running problem of Gansu Normal College for Nationalities as an example, the algorithm was experimented and the experimental results show that the algorithm to be successful.

A heuristic approach to reduce carbon dioxide emissions

Transport accounts for 26% of global carbon dioxide emissions. The need to reduce greenhouse gas emissions, especially carbon dioxide, is thus becoming increasingly urgent and several approaches have been adopted to achieve this goal. Alternative sustainable technologies form one possible solution, and changes in driving styles could also contribute to a reduction in emissions. An alternative interesting approach is to reduce vehicle miles travelled. In this paper, the concept of vehicle miles travelled reduction based on a heuristic optimisation approach and geographical information system technology is introduced. The suitability of the concept was tested with the school bus routing problem. Working mechanisms of the adopted optimisation algorithms are explained. The results show that optimisation of bus stops, bus routes and driving schedules could significantly reduce the amount of vehicle miles travelled and, consequently, carbon dioxide emissions.

On constructing a family of student delivery routes in minimal time

We consider the school bus routing problem which is to construct the routes for delivering students after classes by multiple buses in minimal time. We show the corresponding linear partially integer model. Together with an exact algorithm we show a simple heuristic algorithm and present the results of a computational experiment.

A multi-start algorithm for a balanced real-world Open Vehicle Routing Problem

The aim of this paper is to solve a real-world problem proposed by an international company operating in Spain and modeled as a variant of the Open Vehicle Routing Problem in which the makespan, i.e., the maximum time spent on the vehicle by one person, must be minimized. A competitive multi-start algorithm, able to obtain high quality solutions within reasonable computing time is proposed. The effectiveness of the algorithm is analyzed through computational testing on a set of 19 school-bus routing benchmark problems from the literature, and on 9 hard real-world problem instances.