Solving school bus routing and student assignment problems with heuristic and column generation approach.

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 time window constraints. We demonstrate the efficacy of heuristic methods as well as a column generation technique implemented to solve the problems using real data

School bus selection, routing and scheduling.

The aim of this thesis is to develop formulations and exact algorithms for the school bus routing and scheduling problem and to develop an integrated software implementation using Xpress-MP/CPLEX and ArcGIS of ESRI, a geographical information system software package. In this thesis, bus flow, single commodity flow, two-commodity flow, multi-commodity flow, and time window formulations have been developed. They capture all of the important elements of the School Bus Routing and Scheduling Problem (SBRSP) including homogeneous or heterogeneous bus fleets, the identification of bus stops from a large set of potential bus stops, and the assignment of students to stops and stops to routes. They allow for the one stop-one bus and one stop-multi bus scenarios. Each formulation of the SBRSP has a linear programming relaxation and we present the relationships among them. We present a Branch-and-Cut exact algorithm which makes use of new linearization techniques, new valid inequalities, and the first valid equalities. We develop an integrated software package that is based on Geographical Information System (GIS) map-based interface, linking to an Xpress-MP/CPLEX solver. The interface between GIS and Xpress-MP is written in VBA and VC++.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .K4. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6250. Thesis (Ph.D.)--University of Windsor (Canada), 2005

SOLVING MULTI-SCHOOL BUS ROUTING AND SCHEDULING PROBLEM

School bus routing and scheduling is of huge importance in school transportation system operations. It is usually treated as two separated problems and is solved sequentially. But it is shown that such separation will lead to a worse solution than solving them together with respect to the number of buses and travel time. The rationale behind it and the key point connecting routing and scheduling problem – trip compatibility – is thus deeply studied. A Mixed Integer Programming model is proposed along with a School Decomposition Algorithm. The model and algorithm are tested on eight sets of randomly-generated mid-size problems in comparison to the existing models. The results show that the proposed model and algorithm can find a better solution using up to 30% fewer buses than the best traditional models in a reasonable amount of time

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

A Cost Assessment of the Dayton Public Schools Vehicle Routing Problem

The routing and scheduling problem involves both constructing efficient routes to deliver goods or services to and from customers from a single depot or set of depots, as well as scheduling particular vehicles to these routes such that customers receive their goods within a specified time window. There have been several different methods developed to reduce the costs incurred in transporting goods or services (i.e. students) to customers (i.e. schools). This problem may be used to model many circumstances in logistics and public transportation. Several school districts do not utilize operations research techniques to minimize, as much as possible, the costs associated with the operation of its pupil transportation system. In contrast, Dayton Public Schools (DPS) employs the optimization software package VersaTrans to minimize its transportation expenses. However, due to the importance it has placed on customer satisfaction, DPS has ultimately been reduced to door-to-door pickups. This, combined with an open enrollment policy and higher fuel prices, has resulted in an explosion of transportation related costs. Though DPS has made many great strides to gain control of its spending, due primarily to better management, there is still much to accomplish. This thesis seeks to utilize the VersaTrans routing software available to the Dayton Public School district to construct efficient routes that are feasible under a consolidated bell schedule so that both bus usage and route times are minimized