Uncertainty modeling for bus selection and allocation in a private transportation system

ABSTRACT

This paper describes the development of a probabilistic formulation that provides global optimum selection and allocation of a fleet of buses in a private transportation system of an organization where a third party is hired to provide transportation for its employees and their dependents. In this private transportation system, a fleet of buses is to be selected and allocated to serve employees and their independents on different prescheduled trips along different routes from the organization’s headquarters and residential compound where round-trip times of scheduled trips are subject to uncertainty due to random delays. We propose a probabilistic approach based on 0-1 integer programming for the selection and allocation to determine the optimal number and size of buses assigned to a set of prescheduled trips in a particular time interval. Examples and a case study are presented to illustrate the applicability and suitability of the proposed approach.     

Reduction of capacity and projected costs associated with seat belt installation on school buses

This study examines the potential effects the installation of seat belts on school buses would have on the fleet capacity in Alabama and the resulting cost implications. The study also documents the myriad research studies and professional opinions offered on the potential safety effects of equipping school buses with safety restraints/seat belts. Four seat configurations for the school buses were analyzed. The first configuration represents the most common current bus seating configuration without seat belts, 3 seats on each side of the aisle and 12 rows (3/3-12). The physical space required for seat belt hardware may result in a loss of a row of seats and may reduce the number of students seated per row. Thus, three more configurations were studied: loss of a row of seats (3/3-11), loss of one seat per row (3/2-12), and loss of both a row of seats and a seat per row (3/2-11). The capacity for each configuration for each bus using current pupil loads was determined. The costs associated with installation of seat belts, and purchase and operation of new buses were obtained. Should school bus seat belts become mandatory in Alabama, the results obtained in this study can be used by any school system to determine the optimum configuration for their pupils, which will identify the number of additional buses that must be purchased by the school system. This study found that many of the buses that would become overloaded due to seat belt installation and the resultant loss of seating will be carrying only a few excess pupils. Transportation supervisors may be able to handle such overloads by transferring these pupils to other buses or by adjusting their bus routes to minimize purchase of new buses. Additional suggestions for handling bus overloads were offered in the body of this report.     

A segregated urban busway system

A transport system has been proposed using buses operating over ordinary roads and over special reserved tracks (busways) on which they might be automatically guided. Using cost and performance data resulting from an earlier technical study (not reported here), a hypothetical network of routes and services in the West Midlands conurbation is studied. Estimates of patronage diverted from public and private transport enable the profitability of the system and its costs and benefits to be assessed. It is concluded that the system could be attractive both in commercial and in cost/benefit terms, providing acceptable means could be found for handling the buses around and through the inner central areas of cities. The net environmental changes, which would result from additional fixed plant permitting more efficient use of mobile plant, have not been quantified.     

The allocation of buses in heavily utilized networks with overlapping routes

Many transit systems outside North America are characterized by networks with extensively overlapping routes and buses frequently operating at, or close to, capacity. This paper addresses the problem of allocating a fleet of buses between routes in this type of system; a problem that must be solved recurrently by transit planners. A formulation of the problem is developed which recognizes passenger route choice behavior, and seeks to minimize a function of passenger wait time and bus crowding subject to constraints on the number of buses available and the provision of enough capacity on each route to carry all passengers who would select it. An algorithm is developed based on the decomposition of the problem into base allocation and surplus allocation components. The base allocation identifies a feasible solution using an (approx.) minimum number of buses. The surplus allocation is illustrated for the simple objective of minimizing the maximum crowding level on any route. The bus allocation procedure developed in this paper has been applied to part of the Cairo bus system in a completely manual procedure, and is proposed to be the central element of a short-range bus service planning process for that city.     

Exposure to noise inside transit buses in Kuwait: Measurements and passenger attitudes

Noise levels were measured, for the first time, inside 115 randomly selected transit buses, operating on 12 sample representative routes in Metropolitan Kuwait. Simultaneously with the monitoring of noise levels, the attitudes of 679 riders concerning the annoyance and long-term health impacts of noise were also surveyed. The noise and passenger attitude data were collected over 10 months (March - December 2000). The percentile distribution, equivalent noise level, traffic noise index and noise pollution levels inside four types of transit buses are presented. Riders' perceived annoyance and awareness of the long-term health impacts of noise were also determined and are discussed. The level of service and performance deficiencies of the public transit system in Kuwait, as perceived by its passengers, are also identified. A number of recommendations end the paper.     

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.     

“Comparing guideway transit implementation plans,including the impact on road traffic”

A methodology for comparing phased implementation plans for a new fixed guideway transit system in an urban area is presented. Four assumptions are made: (1) the guideway system replaces existing or planned bus service, (2) superior service on the new system results in increased ridership when compared to buses; (3) presence of the guideway facility redirects outward urban growth resulting in additional ridership, and (4) conversely, the absence of any action on the new guideway facility reinforces a diffuse urban growth pattern that creates an irreversible loss of transit ridership. The economic comparision of alternative plans includes total as well as “relative” inflation of principal cost components. A key feature of the proposed methodology is including in the comparisons the costs of private automobile mileage that could have been replaced by transit. These costs are expressed as “fuel” and “all other” automobile costs; favorable transit system implementation schedules can then be identified as a function of parametrically assumed values for these two unit costs. A hypothetical example demonstrates the proposed method.     

Optimizing bus-size and headway in transit networks

Optimization models for calculating the best size for passenger carrying vehicles in urban areas were popular during the 1980s. These studies were abandoned in the ‘90s concluding that it was more efficient to use smaller buses at higher frequencies. This article returns to this controversial question, starting from the point of view that any calculation of bus size can only be made after considering the demand for each of the routes on the system. Therefore, an optimization model for sizing the buses and setting frequencies on each route in the system is proposed in accordance with the premises detailed below. The proposed model is a bi-level optimization model with constraints on bus capacity. The model allows buses of different sizes to be assigned to public transport routes optimizing the headways on each route in accordance with observed levels of demand. At the upper level the model considers the optimization of the system’s social and operating costs, these are understood to be the sum of the user’s and operator’s costs. At the lower level there is an assignment model for public transport with constraints on vehicle capacity which balances the flows for bus sizes and headways at each iteration. By graphically representing the results of the model applied to a real case, a series of useful conclusions are reached for the management and planning of a fleet of public transport vehicles.     

Energy consumption and cost-benefit analysis of hybrid and electric city buses

This paper presents a cost-benefit analysis (CBA) of hybrid and electric city buses in fleet operation. The analysis is founded on an energy consumption analysis, which is carried out on the basis of extensive simulations in different bus routes. A conventional diesel city bus is used as a reference for the CBA. Five different full size hybrid and electric city bus configurations were considered in this study; two parallel and two series hybrid buses, and one electric city bus. Overall, the simulation results indicate that plug-in hybrid and electric city buses have the best potential to reduce energy consumption and emissions. The capital and energy storage system costs of city buses are the most critical factors for improving the cost-efficiency of these alternative city bus configurations. Furthermore, the operation schedule and route planning are important to take into account when selecting hybrid and electric city buses for fleet operation.     

Bus Rapid Transit System in Istanbul: A Success Story or Flawed Planning Decision?

Abstract

There is a growing tendency in cities around the world to invest in Bus Rapid Transit (BRT) systems in an attempt to improve the capacity and quality of public transport services. The appeal of BRTs is based on their ability to combine the service level of rail transit systems with the flexibility of buses at relatively lower investment costs, and this was the motivation behind the opening of such a system in the Turkish city of Istanbul in 2007. This system has attracted mixed opinions as to its performance, as while passenger ridership figures are extremely high, proving the effectiveness of the system, there is an argument that the corridor should have been developed with rail technology, and that the BRT is failing to meet the demand. The paper presents a comprehensive analysis of this system, assessing its planning and performance through a comparative analysis of a number of BRTs in the world and Istanbul's metro and tram systems. The analysis confirms the success of the system in terms of passenger statistics, but also highlights a number of problems in certain planning decisions that should be addressed, thus taking the discussion beyond a simplified comparison of bus and rail technologies.     

An optimization model for bus fleet replacement with budgetary and environmental constraints

ABSTRACT

As maintenance and operation costs increase with usage over time, equipment is replaced when the value of new equipment is more attractive. Some methods have been developed to solve this problem. In the public transport sector, such problems are frequently analyzed by fleet managers and determined by bus age restriction regulations. We propose an Integer Programming model that integrates both budgetary and environmental constraints (CO₂ emissions) which, as far as we know, have not previously been studied in conjunction. The study aims to determine the optimal replacement plan for a fleet of diesel buses of different size, age, maintenance costs and emissions rates, with new (less polluting) diesel buses over a time horizon of 50 years. The results indicate that it is possible to reduce emissions with a low annual budget using an optimal replacement policy.     

The Vehicle Routing Problem: The Case of the Hong Kong Postal Service

Abstract

With the growth in population and development of business activities in Hong Kong, the range and level of services provided by Hongkong Post have multiplied. However, the schedule of its postal vehicles, including mail collection and delivery, is still constructed manually on a daily basis, based on the experience of staff and transportation reviews. In this paper, the problem of scheduling a set of n collection points (District Post Offices) from a depot (General Post Office) in Hong Kong Island is addressed. The objectives pursued are the maximization of resource utilization and minimization of operation costs. In other words, the variable cost is expected to be reduced. To achieve these goals, an integer linear programming (IP) model of the vehicle routing problem (VRP) is developed in an effort to obtain optimal solutions. As the model involves computational complexity, a commercial software package CPLEX is used to solve the problems efficiently. The results show that the proposed model can produce optimal vehicle routes and schedules.     

Optimization of emergency crossovers and signals for emergency operations in rail rapid transit

This paper presents a methodology for designing rail transit systems to meet operating requirements when track maintenance or failure cause sections of tracks to be unavailable for service. The methodology can be also used to establish the requirements for the continuity of operations during construction. The main objective of the paper is to develop a tool which performs trade-offs between system costs and level of services during emergencies/construction. Several alternatives, including various signal and control systems, number and types of crossovers and corresponding operating strategies, are developed and evaluated against capital investments. Operating measures and strategies for the selected alternative can be recommended before the design phase is completed, because the designer, by using this methodology, is aware of the capacities attained during emergencies and construction.     

Daily newspaper distribution planning with integer programming: an application in Turkey

Abstract

This paper concerns the newspaper distribution problem. It addresses the transportation of newspapers from printing plant to newsagents with distribution vehicles under various particular constraints. The objective is to minimize the distance traveled by the vehicles and/or the number of vehicles. In this study, the routes for vehicles of a leading newspaper distributor company in the Turkish press sector are examined. The problem is defined as determining optimal delivery routes for a fleet of homogeneous vehicles, starting and ending at the printing plant that is required to serve a number of geographically dispersed newsagents with known demands under capacity and time constraints, while minimizing the total distribution cost. An integar linear programming model is proposed as a solution using Cplex. Computational results demonstrate that the proposed model is fast and able to find optimal solutions for problem scenarios with up to 55 newsagents within reasonable computing times. It was found that the proposed model reduced the delivery cost by 21% on average when compared to the current manual method. The results show that this model is adequate for medium-sized distribution problems.     

Integrating bus services with mixed fleets

Conventional bus service (with fixed routes and schedules) has lower average cost than flexible bus service (with demand-responsive routes) at high demand densities. At low demand densities flexible bus service has lower average costs and provides convenient door-to-door service. Bus size and operation type are related since larger buses have lower average cost per passenger at higher demand densities. The operation type and other decisions are jointly optimized here for a bus transit system connecting a major terminal to local regions. Conventional and flexible bus sizes, conventional bus route spacings, areas of service zones for flexible buses, headways, and fleet sizes are jointly optimized in multi-dimensional nonlinear mixed integer optimization problems. To solve them, we propose a hybrid approach, which combines analytic optimization with a Genetic Algorithm. Numerical analysis confirms that the proposed method provides near-optimal solutions and shows how the proposed Mixed Fleet Variable Type Bus Operation (MFV) can reduce total cost compared to alternative operations such as Single Fleet Conventional Bus (SFC), Single Fleet Flexible Bus (SFF), Mixed Fleet Conventional Bus (MFC) and Mixed Fleet Flexible Bus (MFF). With consistent system-wide bus sizes, capital costs are reduced by sharing fleets over times and over regions. The sensitivity of results to several important parameters is also explored.     

Intermodal Transit System Coordination

In urban areas where transit demand is widely spread, passengers may be served by an intermodal transit system, consisting of a rail transit line (or a bus rapid transit route) and a number of feeder routes connecting at different transfer stations. In such a system, passengers may need one or more transfers to complete their journey. Therefore, scheduling vehicles operating in the system with special attention to reduce transfer time can contribute significantly to service quality improvements. Schedule synchronization may significantly reduce transfer delays at transfer stations where various routes interconnect. Since vehicle arrivals are stochastic, slack time allowances in vehicle schedules may be desirable to reduce the probability of missed connections. An objective total cost function, including supplier and user costs, is formulated for optimizing the coordination of a general intermodal transit network. A four-stage procedure is developed for determining the optimal coordination status among routes at every transfer station. Considering stochastic feeder vehicle arrivals at transfer stations, the slack times of coordinated routes are optimized, by balancing the savings from transfer delays and additional cost from slack delays and operating costs. The model thus developed is used to optimize the coordination of an intermodal transit network, while the impact of a range of factors on coordination (e.g., demand, standard deviation of vehicle arrival times, etc) is examined.     

A fuzzy-stochastic optimization model for the intermodal fleet management problem of an international transportation company

ABSTRACT

In this paper, a fuzzy-stochastic optimization model is developed for an intermodal fleet management system of a large international transportation company. The proposed model integrates various strategic, tactical and operational level decisions simultaneously. Since real-life fleet planning problems may involve different types of uncertainty jointly such as randomness and fuzziness, a hybrid chance-constrained programming and fuzzy interactive resolution-based approach is employed. Therefore, stochastic import/export freight demand and fuzzy transit times, truck/trailer availabilities, the transport capacity of Ro-Ro vessels, bounds on block train services, etc. can also be taken into account concurrently. In addition to minimize overall transportation costs, optimization of total transit times and CO₂ emission values are also incorporated in order to provide sustainable fleet plans by maximizing customer satisfaction and environmental considerations. Computational results show that effective and efficient fleet plans can be produced by making use of the proposed optimization model.     

The implications of school choice on travel behavior and environmental emissions

We examine the implications of school choice on walkability, school travel mode and overall environmental emissions. In developing this proof-of-concept model we show—and quantify—differences between city-wide schools and their neighborhood school counterpart. Our analysis demonstrates how children attending city-wide schools may have heightened travel distance, greenhouse gas emissions, and exposure to bus fumes. Using available data along with a series of informed assumptions we figure the city-wide school had six times fewer children walking, 4.5 times as many miles traveled, 4.5 times the system cost, and 3–4.5 times the amount of criteria air pollutants and greenhouse gas emissions. By providing bus service, the overall miles traveled (and resulting emissions) decreased 30–40% compared to the scenario without bus service, however system costs were higher for both the neighborhood and city-wide school (no pollution externality costs were factored in).     

The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems

Most of the studies address issues relating to the delivery from satellites to customers, which is throughout the end part of the linehaul-delivery system. Differing from the long-term strategic problems including the two-echelon vehicle routing problem (2E-VRP), the two-echelon location routing problem (2E-LRP) and the truck and trailer routing problem (TTRP) which make location decisions in depots or satellites, the paper introduces a short-term tactical problem named the two-echelon time-constrained vehicle routing problem in linehaul-delivery systems (2E-TVRP) that does not involve location decisions. The linehaul level and the delivery level are linked through city distribution centers (CDCs) located on the outskirts of cities. The 2E-TVRP has inter-CDC linehaul on the first level and urban delivery from CDCs to satellites on the second level. Vehicle routes on different levels are interacted by time constraints. A mixed integer nonlinear programming model for the 2E-TVRP is put forward, and a mixed integer linear programming model is used as the benchmark model. The Clarke and Wright savings heuristic algorithm (CW) improved by a local search phase is adopted. The 2E-TVRP formulations and the heuristic algorithm are tested by using 140 randomly-generated instances with up to 10 CDCs and 500 satellites. The computational results indicate that the heuristic can effectively solve various instances of the 2E-TVRP.     

Bus maintenance systems and maintenance scheduling: model formulations and solutions

This paper deals with the problem of scheduling bus maintenance activities. The scheduling of maintenance activities is an important component in bus transit operations planning process. The other components include network route design, setting timetables, scheduling vehicles, and assignment of drivers. This paper presents a mathematical programming approach to the problem. This approach takes as input a given daily operating schedule for all buses assigned to a depot along with available maintenance resources. It, then, attempts to design daily inspection and maintenance schedules for the buses that are due for inspection so as to minimize the interruptions in the daily bus operating schedule, and maximize the utilization of the maintenance facilities. Three integer programming formulations are presented and different properties of the problem are discussed. Several heuristic methods are presented and tested. Some of these procedures produce very close to optimal solutions very efficiently. In some cases, the computational times required to obtain these solutions are less than 1% of the computational time required for the conventional branch and bound algorithm. Several small examples are offered and the computational results of solving the problem for an actual, 181-bus transit property are reported.