This paper proposes a new formulation for the school bus scheduling problem (SBSP) which optimizes school start times and bus operation times to minimize transportation cost. Our goal is to minimize the number of buses to serve all bus routes such that each route arrives in a time window before school starts. We present a new time-indexed integer linear programming (ILP) formulation for this problem. Based on a strengthened version of the linear relaxation of the ILP, we develop a dependent randomized rounding algorithm that yields near-optimal solutions for large-scale problem instances. We also generalize our methodologies to solve a robust version of the SBSP.
We consider the school bus scheduling problem (SBSP) which simultaneously determines school bell times and route schedules. Often, the goal of the SBSP is to minimize the number of buses required by a school district. We extend a time-indexed integer programming model to incorporate additional considerations related to equity and efficiency. We seek to equitably reduce the disutilities associated with changing school start times via a minimax model, then propose a lexicographic minimax approach to improve minimax solutions. We apply our models to randomized instances based on a moderately-size…
Safely serving the school transportation demand with the minimum number of buses is one of the highest financial goals of school transportation directors. To achieve that objective, a good and efficient way to solve the routing and scheduling problem is required. Due to the growth of the computing power, the spotlight has been shed on solving the combined problem of the school bus routing and scheduling problem. We show that an integrated multi-school bus routing and scheduling can be formulated with the help of trip compatibility. A novel decomposition algorithm is proposed to solve the integ…
In the school bus scheduling problem, the main contributing factor to the cost is the number of buses needed for the operations. However, in the case of subcontracting the transportation of pupils, unbalanced tours can increase the costs significantly as the lengths of some tours can exceed the daily fixed driving goal and will result in over-hour charges. This paper proposes a Mixed Integer Programming (MIP) model and a matching-based heuristic algorithm to solve the balanced school bus scheduling problem in a multi-school setting. The heuristic is guaranteed to find the minimum number of bus…
Vehicle-based mobile sensing (a.k.a drive-by sensing) is an important means of surveying urban environment by leveraging the mobility of public or private transport vehicles. Buses, for their extensive spatial coverage and reliable operations, have received much attention in drive-by sensing. Existing studies have focused on the assignment of sensors to a set of lines or buses with no operational intervention, which is typically formulated as set covering or subset selection problems. This paper aims to boost the sensing power of bus fleets through active scheduling, by allowing instrumented b…
It is commonly seen that buses are blocked by the ones in front serving passengers and have to queue outside a curbside bus stop although there are vacant berths at the stop. The resultant bus delays degrade the service level of urban public transportation. A potential solution is to reschedule the arrivals of the buses at the stop for full utilization of the berths with the aid of connected vehicle technologies. This study proposes a mixed-integer linear programming model to optimize the scheduling of bus arrivals and the bus-berth matching at a curbside stop under connected vehicle environme…
We consider the Single School Routing Problem (SSRP) where students from a single school are picked up by a fleet of school buses, subject to a set of constraints. The constraints that are typically imposed for school buses are bus capacity, a maximum student walking distance to a pickup point, and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic …
The paper considers the problem of scheduling software modules on a multi-core processor, taking into account the limited bandwidth of the data bus and the precedence constraints. Two problem formulations with different levels of problem-specific detail are suggested and both shown to be NP-hard. A mixed integer linear programming (MILP) model is proposed for the first problem formulation, and a greedy algorithm is developed for the second one. An experimental comparison of the results of the greedy algorithm and the MILP solutions found by CPLEX solver is carried out.
Exploring the potential resource integration under passenger-freight shared mobility: collaborative optimization of multi-type bus scheduling and dynamic vehicle capacity allocation for urban-rural bus routes
The scheduling problem in Hurdle (1973) was formulated in a general form that simultaneously concerned the vehicle dispatching, circulating, fleet sizing, and patron queueing. As a constrained variational problem, it remains not fully solved for decades. With technical prowess in graphic analysis, the author unveiled the closed-form solution for the optimal dispatch rates (with key variables undetermined though), but only suggested the lower and upper bounds of the optimal fleet size. Additionally, such a graphic analysis method lacks high efficiency in computing specific scheduling problems, …
In this paper, a hierarchical distributed method consisting of two iterative procedures is proposed for optimal electric vehicle charging scheduling (EVCS) in the distribution grids. In the proposed method, the distribution system operator (DSO) aims at reducing the grid loss while satisfying the power flow constraints. This is achieved by a consensus-based iterative procedure with the EV aggregators (Aggs) located in the grid buses. The goal of aggregators, which are equipped with the battery energy storage (BES), is to reduce their electricity cost by optimal control of BES and EVs. As Aggs'…
The scheduling of films is a major problem for the movie theatre exhibition business. The problem is two-fold: movie exhibitors ideally would like to schedule films to screens in their various locations to maximize attendance and revenue, but would also like to schedule these films such that neighbouring theatre locations play the same films at different times thus giving guests a multitude of showtime options. We refer to this latter problem as the showtime \emph{staggering} problem. We give an exact formulation of this scheduling problem using binary integer linear optimization, and provide …
Integrated timetabling and scheduling of modular autonomous vehicles under uncertainty
Delft University of Technology（代尔夫特理工大学）；Department of Transport & Planning, Delft University of Technology（代尔夫特理工大学交通与规划系）；Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University（交通运输部综合交通运输大数据应用技术交通运输行业重点实验室，北京交通大学）
Security-constrained unit commitment (SCUC) is solved for power system day-ahead generation scheduling, which is a large-scale mixed-integer linear programming problem and is very computationally intensive. Model reduction of SCUC may bring significant time savings. In this work, a novel approach is proposed to effectively utilize machine learning (ML) to reduce the problem size of SCUC. An ML model using logistic regression (LR) algorithm is proposed and trained with historical nodal demand profiles and the respective commitment schedules. The ML outputs are processed and analyzed to reduce v…
