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.     

Charging infrastructure demands of shared-use autonomous electric vehicles in urban areas

Ride-hailing is a clear initial market for autonomous electric vehicles (AEVs) because it features high vehicle utilization levels and strong incentive to cut down labor costs. An extensive and reliable network of recharging infrastructure is the prerequisite to launch a lucrative AEV ride-hailing fleet. Hence, it is necessary to estimate the charging infrastructure demands for an AEV fleet in advance. This study proposes a charging system planning framework for a shared-use AEV fleet providing ride-hailing services in urban area. We first adopt an agent-based simulation model, called BEAM, to describe the complex behaviors of both passengers and transportation systems in urban cities. BEAM simulates the driving, parking and charging behaviors of the AEV fleet with range constraints and identifies times and locations of their charging demands. Then, based on BEAM simulation outputs, we adopt a hybrid algorithm to site and size charging stations to satisfy the charging demands subject to quality of service requirements. Based on the proposed framework, we estimate the charging infrastructure demands and calculate the corresponding economics and carbon emission impacts of electrifying a ride-hailing AEV fleet in the San Francisco Bay Area. We also investigate the impacts of various AEV and charging system parameters, e.g., fleet size, vehicle battery capacity and rated power of chargers, on the ride-hailing system’s overall costs.     

Examining the benefits of using bio-CNG in urban bus operations

Public service fleets offer an attractive option for introducing new renewable fuels on a large scale, which allow for the reduction of both greenhouse gas emissions and exhaust air pollutants. This study examines the use of biomethane (bio-CNG) and compressed natural gas for part of the bus fleet in Dublin, Ireland. The emissions produced from the 2008 fleet based at one of the city’s seven bus depots are compared to use of new diesel and bio-CNG buses. The optimum feedstock for bio-CNG production in Ireland was then investigated, as well as the quantity of feedstock needed to produce the required bio-CNG to fuel the bus fleet examined. As expected the results showed a substantial decrease in all exhaust emissions from the use of bio-CNG buses compared the 2008 fleet. Grass silage was chosen as the optimum feedstock for production of bio-CNG in Ireland.     

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.     

Numerical analysis of electric bus fast charging strategies for demand charge reduction

Electric transit buses have been recognized as an important alternative to diesel buses with many environmental benefits. Electric buses employing lithium titanate batteries can provide uninterrupted transit service thanks to their ability of fast charging. However, fast charging may result in high demand charges which will increase the fuel costs thereby limiting the electric bus market penetration. In this paper, we simulated daily charging patterns and demand charges of a fleet of electric buses in Tallahassee, Florida and identified an optimal charging strategy to minimize demand charges. It was found that by using a charging threshold of 60–64%, a $160,848 total saving in electricity cost can be achieved for a five electric bus fleet, comparing to a charging threshold of 0–28%. In addition, the impact of fleet sizes on the fuel cost was investigated. Fleets of 4 and 12 buses will achieve the lowest cost per mile driven when one fast charger is installed.     

Electric versus conventional vehicles: social costs and benefits in France

This article compares the social costs of electric vehicles with those of conventional, thermal vehicles for typical passenger use in the Ile-de-France region (Greater Paris), a case of particular interest because nearly 80% of the electricity is generated by nuclear power plants. A four-seat electric car is compared to a new conventional car of the same make and model; for the latter both the gasoline and the diesel version are considered because almost half of new car sales in France are diesel. These results are also compared to typical existing diesel and gasoline vehicles in the current French fleet. The methodology developed by the ExternE (External Costs of Energy) Project of the European Commission is used to estimate the costs associated with atmospheric pollution due to power plants, refineries and tail pipe emissions. Our discussion of externalities is limited to air pollution thus excluding others such as costs associated with noise or accidents. Our results imply that the external costs are large and significant, even when one considers the uncertainties. If internalized by government regulations, these externalities can render the total cost of an electric vehicle more competitive with that of currently available thermal vehicles in large urban centers if the electricity is produced by sources with low pollution. However, the current generation electric vehicles are so expensive that internalization of pollution damage would not give it a very clear advantage.     

Fuel cycle emissions and life cycle costs of alternative fuel vehicle policy options for the City of Houston municipal fleet

Municipal fleet vehicle purchase decisions provide a direct opportunity for cities to reduce emissions of greenhouse gases (GHG) and air pollutants. However, cities typically lack comprehensive data on total life cycle impacts of various conventional and alternative fueled vehicles (AFV) considered for fleet purchase. The City of Houston, Texas, has been a leader in incorporating hybrid electric (HEV), plug-in hybrid electric (PHEV), and battery electric (BEV) vehicles into its fleet, but has yet to adopt any natural gas-powered light-duty vehicles. The City is considering additional AFV purchases but lacks systematic analysis of emissions and costs. Using City of Houston data, we calculate total fuel cycle GHG and air pollutant emissions of additional conventional gasoline vehicles, HEVs, PHEVs, BEVs, and compressed natural gas (CNG) vehicles to the City's fleet. Analyses are conducted with the Greenhouse Gases, Regulated Emissions, and Energy use in Transportation (GREET) model. Levelized cost per kilometer is calculated for each vehicle option, incorporating initial purchase price minus residual value, plus fuel and maintenance costs. Results show that HEVs can achieve 36% lower GHG emissions with a levelized cost nearly equal to a conventional sedan. BEVs and PHEVs provide further emissions reductions, but at levelized costs 32% and 50% higher than HEVs, respectively. CNG sedans and trucks provide 11% emissions reductions, but at 25% and 63% higher levelized costs, respectively. While the results presented here are specific to conditions and vehicle options currently faced by one city, the methods deployed here are broadly applicable to informing fleet purchase decisions.     

The effectiveness and costs of speed reductions on emissions from international shipping

Greenhouse gas emissions from international shipping are an increasing concern. The paper evaluates whether vessel speed reduction can be a potentially cost-effective CO₂ mitigation option for ships calling on US ports. By applying a profit-maximizing equation to estimate route-specific, economically-efficient speeds, we explore policy impacts of a fuel tax and a speed reduction mandate on CO₂ emissions. The profit-maximizing function incorporates opportunity costs associated with speed reduction that go unobserved in more traditional marginal abatement cost analyses. We find that a fuel tax of about $150/ton fuel will lead to average speed-related CO₂ reductions of about 20–30%. Moreover, a speed reduction mandate targeted to achieve 20% CO₂ reduction in the container fleet costs between $30 and $200 per ton CO₂ abated, depending on how the fleet responds to a speed reduction mandate.     

The fleet size and mix pollution-routing problem

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO₂ emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one.     

Weather impact on containership routing in closed seas: A chance-constraint optimization approach

Weather conditions have a strong effect on the operation of vessels and unavoidably influence total time at sea and associated transportation costs. The velocity and direction of the wind in particular may considerably affect travel speed of vessels and therefore the reliability of scheduled maritime services. This paper considers weather effects in containership routing; a stochastic model is developed for determining optimal routes for a homogeneous fleet performing pick-ups and deliveries of containers between a hub and several spoke ports, while incorporating travel time uncertainties attributed to the weather. The problem is originally formulated as a chance-constrained variant of the vehicle routing problem with simultaneous pick-ups and deliveries and time constraints and solved using a genetic algorithm. The model is implemented to a network of island ports of the Aegean Sea. Results on the application of algorithm reveal that a small fleet is sufficient enough to serve network’s islands, under the influence of minor delays. A sensitivity analysis based on alternative scenarios in the problem’s parameters, leads to encouraging conclusions with respect to the efficiency and robustness of the algorithm.     

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.     

Cost benefit analysis of three different urban bus drive systems using real driving data

One of the CIVITAS-ELAN project measures in Ljubljana, Slovenia, was the introduction of alternative city bus propulsion systems (CNG, hydraulic hybrid buses) into the public transport and comparison of their performance in terms of costs and benefits with conventional (diesel) buses. A cost-benefit analysis was conducted to provide a model for identifying the most attractive alternative, with aim of aiding the decision making process for future rational up-scaling of the alternative propulsion technologies in PT fleet in Ljubljana. This paper focuses on presenting the key findings of this CBA, using real driving data, while demonstrating the sensitivity/variance of different parameters of a CBA, as well as the differentiation between uncertainties of parameters in an ex-ante analysis versus an ex-post analysis.     

Evaluation of fuel cell auxiliary power units for heavy-duty diesel trucks

A large number of heavy-duty trucks idle a significant amount. Heavy-duty line-haul truck engines idle about 20–40% of the time the engine is running, depending on season and operation. Drivers idle engines to power climate control devices (e.g., heaters and air conditioners) and sleeper compartment accessories (e.g., refrigerators, microwave ovens, and televisions) and to avoid start-up problems in cold weather. Idling increases air pollution and energy use, as well as wear and tear on engines. Efforts to reduce truck idling in the US have been sporadic, in part because it is widely viewed in the trucking industry that further idling restrictions would unduly compromise driver comfort and truck operations. The auxiliary power units (APUs) available to replace the idling of the diesel traction engine all have had limited trucking industry acceptance. Fuel cells are a promising APU technology. Fuel cell APUs have the potential to greatly reduce emissions and energy use and save money. In this paper, we estimate costs and benefits of fuel cell APUs. We calculate the payback period for fuel cell APUs to be about 2.6–4.5 years. This estimate is uncertain since future fuel cell costs are unknown and cost savings from idling vary greatly across the truck fleet. The payback period is particularly sensitive to diesel fuel consumption at idle. Given the large potential environmental and economic benefits of fuel cell APUs, the first major commercial application of fuel cells may be as truck APUs.     

Locating charging infrastructure for electric buses in Stockholm

Charging infrastructure requirements are being largely debated in the context of urban energy planning for transport electrification. As electric vehicles are gaining momentum, the issue of locating and securing the availability, efficiency and effectiveness of charging infrastructure becomes a complex question that needs to be addressed. This paper presents the structure and application of a model developed for optimizing the distribution of charging infrastructure for electric buses in the urban context, and tests the model for the bus network of Stockholm. The major public bus transport hubs connecting to the train and subway system show the highest concentration of locations chosen by the model for charging station installation. The costs estimated are within an expected range when comparing to the annual bus public transport costs in Stockholm. The model could be adapted for various urban contexts to promptly assist in the transition to fossil-free bus transport. The total costs for the operation of a partially electrified bus system in both optimization cases considered (cost and energy) differ only marginally from the costs for a 100% biodiesel system. This indicates that lower fuel costs for electric buses can balance the high investment costs incurred in building charging infrastructure, while achieving a reduction of up to 51% in emissions and up to 34% in energy use in the bus fleet.     

Developing green fleet management strategies: Repair/retrofit/replacement decisions under environmental regulation

The considerable cost of maintaining large fleets has generated interest in cost minimization strategies. With many related decisions, numerous constraints, and significant sources of uncertainty (e.g. vehicle breakdowns), fleet managers face complex dynamic optimization problems. Existing methodologies frequently make simplifying assumptions or fail to converge quickly for large problems. This paper presents an approximate dynamic programming approach for making vehicle purchase, resale, and retrofit decisions in a fleet setting with stochastic vehicle breakdowns. Value iteration is informed by dual variables from linear programs, as well as other bounds on vehicle shadow prices. Sample problems are based on a government fleet seeking to comply with emissions regulation. The model predicts the expected cost of compliance, the rules the fleet manager will use in deciding how to comply, and the regulation’s impact on the value of vehicles in the fleet. Stricter regulation lowers the value of some vehicle categories while raising the value of others. Such insights can help guide regulators, as well as the fleet managers they oversee. The methodologies developed could be applied more broadly to general multi-asset replacement problems, many of which have similar structures.     

Carrier collaboration with endogenous fleets and load factors when networks are complementary

This paper analyzes the effect of carrier collaboration on fleet capacity, fleet structures in terms of the number and the size of vehicles, and load factors. The model features complementary networks, scheduling, price elastic demands, and demand uncertainty. For the case of a given number of vehicles, the analysis shows that carrier collaboration increases vehicle sizes (thus, fleet capacity) if marginal seat costs are low while fleet capacity remains unchanged if marginal seat costs are high. If both vehicle sizes and vehicle numbers can be varied, then collaboration will always increase vehicle numbers and fleet capacity, while the effects on vehicle sizes and, thus, also load factors, are ambiguous and therewith hard to predict. Numerical simulations indicate that collaboration increases expected load factors also when the number of vehicles is endogenous.     

Switching service types for multi-region bus systems

Conventional fixed-route bus services are generally preferred to flexible-route services at high demand densities, and vice versa. This paper formulates the problem of integrating conventional and flexible services that connect a main terminal to multiple local regions over multiple time periods. The system’s vehicle size, route spacing (for conventional services), service area (for flexible services), headways and fleet sizes are jointly optimized to minimize the sum of supplier costs and user costs. The route spacing for conventional bus services and service area for flexible bus services are also optimized for each region. The proposed solution method, which uses a genetic algorithm and analytic optimization, finds good solutions quickly. Numerical examples and sensitivity analyses confirm that the single fleet variable-type bus service may outperform either the single fleet conventional bus service or the single fleet flexible bus service when demand densities vary substantially among regions and time periods.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

This paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley & Sons, Ltd.