A model of an urban transportation system formulated as a multiobjective mathematical programming problem under uncertainty

An urban transportation system formulated in terms of a multiobjective mixed integer linear fractional programming (MOMILFP) problem under uncertainty is considered. The system is based on two means of public transportation i.e., trams and buses. One takes into account the factors of both passengers' and operator's concern, whose objectives are, generally, in conflict. The real uncertainty and imprecision of data is modeled by L-R type fuzzy numbers. To solve the fuzzy MOMILFP problem an interactive method is utilized. As an illustration of that approach an application to Poznan's urban transportation system is presented.     

Vehicle scheduling under stochastic trip times: An approximate dynamic programming approach

Due to unexpected demand surge and supply disruptions, road traffic conditions could exhibit substantial uncertainty, which often makes bus travelers encounter start delays of service trips and substantially degrades the performance of an urban transit system. Meanwhile, rapid advances of information and communication technologies have presented tremendous opportunities for intelligently scheduling a bus fleet. With the full consideration of delay propagation effects, this paper is devoted to formulating the stochastic dynamic vehicle scheduling problem, which dynamically schedules an urban bus fleet to tackle the trip time stochasticity, reduce the delay and minimize the total costs of a transit system. To address the challenge of “curse of dimensionality”, we adopt an approximate dynamic programming approach (ADP) where the value function is approximated through a three-layer feed-forward neural network so that we are capable of stepping forward to make decisions and solving the Bellman’s equation through sequentially solving multiple mixed integer linear programs. Numerical examples based on the realistic operations dataset of bus lines in Beijing have demonstrated that the proposed neural-network-based ADP approach not only exhibits a good learning behavior but also significantly outperforms both myopic and static polices, especially when trip time stochasticity is high.     

An optimal aircraft fleet management decision model under uncertainty

Decision planning for an efficient fleet management is crucial for airlines to ensure a profit while maintaining a good level of service. Fleet management involves acquisition and leasing of aircraft to meet travelers' demand. Accordingly, the methods used in modeling travelers' demand are crucial as they could affect the robustness and accuracy of the solutions. Compared with most of the existing studies that consider deterministic demand, this study proposes a new methodology to find optimal solutions for a fleet management decision model by considering stochastic demand. The proposed methodology comes in threefold. First, a five‐step modeling framework, which is incorporated with a stochastic demand index (SDI), is proposed to capture the occurrence of uncertain events that could affect the travelers' demand. Second, a probabilistic dynamic programming model is developed to optimize the fleet management model. Third, a probable phenomenon indicator is defined to capture the targeted level of service that could be achieved satisfactorily by the airlines under uncertainty. An illustrative case study is presented to evaluate the applicability of the proposed methodology. The results show that it is viable to provide optimal solutions for the aircraft fleet management model. Copyright © 2013 John Wiley & Sons, Ltd.     

A constraint programming model with time uncertainty for cooperative flight departures

The lack of a proper integration of strategic Air Traffic Management decision support tools with tactical Air Traffic Control interventions usually generates a negative impact on the Reference Business Trajectory adherence, and in consequence affects the potential of the Trajectory-Based Operations framework. In this paper, a new mechanism relaying on Reference Business Trajectories as a source of data to reduce the amount of Air Traffic Controller interventions at the tactical level while preserving Air Traffic Flow Management planned operations is presented. Artificial Intelligence can enable Constraint Programming as it is a powerful paradigm for solving complex, combinatorial search problems. The proposed methodology takes advantage of Constraint Programming and fosters adherence of Airspace User’s trajectory preferences by identifying tight interdependencies between trajectories and introducing a new mechanism to improve the aircraft separation at concurrence events considering time uncertainty. The underlying philosophy is to capitalize present degrees of freedom between layered Air Traffic Management planning tools, when sequencing departures at the airports by considering the benefits of small time stamp changes in the assigned Calculated Take-Off Time departures and to enhance Trajectory-Based Operations concepts.     

A carbon footprint-based closed-loop supply chain model under uncertainty with risk analysis: A case study

The management of products’ end-of-life and the recovery of used products has gained significant importance in recent years. In this paper, we address the carbon footprint-based problem that arises in a closed-loop supply chain where returned products are collected from customers. These returned products can either be disposed of or be remanufactured to be resold as new ones. Given this environment, an optimization model for a closed-loop supply chain (CLSC) in which carbon emission is expressed in terms of environmental constraints, i.e., carbon emission constraints, is developed. These constraints aim to limit the carbon emission per unit of product supplied with different transportation modes. Here, we design a closed-loop network where capacity limits, single-item management and uncertainty on product demands and returns are considered. First, fuzzy mathematical programming is introduced for uncertain modeling. Then, the statistical approach to the possibility to synthesize fuzzy information is utilized. Therefore, using a defined possibilistic mean and variance, we transform the proposed fuzzy mathematical model into a crisp form to facilitate efficient computation and analysis. Finally, the risk caused by violating the estimated resource constraints is analyzed so that decision makers (DMs) can trade off between the expected cost savings and the expected risk. We utilize data from a company located in Iran.     

A multiobjective hierarchical model for locating public facilities on a transportation network: A goal programming approach

This paper introduces a Multiobjective Hierarchical Model (MOHLM) for locating public facilities on a transportation network. The proposed model combines the multiobjective nature of the location-allocation problem with the hierarchical character of some public service systems, such as health care delivery. The model examines both maximum and total weighted travel time, facility utilization, and total travel time from the master facility to the attached subordinate facilities. An iterative goal programing algorithm is used to solve the problem. An example related to the location of health care facilities in a rural area of Greece is used to illustrate the application of the proposed model.     

Multi-period planning of closed-loop supply chain with carbon policies under uncertainty

Climate change and greenhouse gases emissions have caused countries to implement various carbon regulatory mechanisms in some industrial sectors around the globe to curb carbon emissions. One effective method to reduce industry environmental footprint is the use of a closed-loop supply chain (CLSC). The decision concerning the design and planning of an optimal network of the CLSC plays a vital role in determining the total carbon footprint across the supply chain and also the total cost. In this context, this research proposes an optimization model for design and planning a multi-period, multi-product CLSC with carbon footprint consideration under two different uncertainties. The demand and returns uncertainties are considered by means of multiple scenarios and uncertainty of carbon emissions due to supply chain related activities are considered by means of bounded box set and solve using robust optimization approach. The model extends further to investigate the impact of different carbon policies such as including strict carbon cap, carbon tax, carbon cap-and-trade, and carbon offset on the supply chain strategic and operational decisions. The model captures trade-offs that exist among supply chain total cost and carbon emissions. Also, the proposed model optimizes both supply chain total cost and carbon emissions across the supply chain activities. The numerical results reveal some insightful observations with respect to CLSC strategic design decisions and carbon emissions under various carbon policies and at the end we highlighted some managerial insights.     

A multiobjective land development optimization model: the case of New Castle County,Delaware

This paper develops a multiobjective optimization model to consider transportation impacts of the future development of land. The output of the model is the best location and type of land use that has minimal negative transportation effects and uses the maximum available public transportation infrastructure. It provides tools for both planners and transportation engineers and enables them to consider different scenarios of possible policies and land development. Since multiple objectives and their nonlinear structures are considered, the model is solved using mixed integer nonlinear programming. The final results are shown in both tabular and graphical format. The effectiveness of the model is applied to the northern part of New Castle County, Delaware. The results show that the model successfully finds the best locations for both residential and commercial land uses in order to meet several criteria discussed in the paper.     

A multiobjective model for maximizing fleet availability under the presence of flight and maintenance requirements

Every aircraft, military or civilian, must be grounded for maintenance after it has completed a certain number of flight hours since its last maintenance check. In this paper, we address the problem of deciding which available aircraft should fly and for how long, and which grounded aircraft should perform maintenance operations, in a group of aircraft that comprise a combat unit. The objective is to achieve maximum availability of the unit over the planning horizon. We develop a multiobjective optimization model for this problem, and we illustrate its application and solution on a real life instance drawn from the Hellenic Air Force. We also propose two heuristic approaches for solving large scale instances of the problem. We conclude with a discussion that gives insight into the behavior of the model and of the heuristics, based on the analysis of the results obtained.     

Future planning for benchmarking and ranking sustainable suppliers using goal programming and robust double frontiers DEA

Decision-making for selecting sustainable suppliers has become an intricate duty. To rank sustainable suppliers and select benchmarks this paper proposes an efficiency improvement plan. Two levels of improvement plans including goals and benchmarks are presented for the suppliers. To this end, the first-level goals are obtained using goal programming (GP) and data envelopment analysis (DEA). Since inputs and outputs of the first-level goals might be imprecise, robust Charnes-Cooper-Rhodes (CCR) model is run. As a result, the benchmarks of the second-level are obtained. Then, a robust CCR inefficiency model is applied for ranking the suppliers. In fact, such a ranking capability is made by creating double-frontiers including CCR efficiency and inefficiency frontiers. Accordingly, the suppliers are ranked using the first-level goals. In the new ranking, uncertainty of the goals is considered by running robust optimization technique. The proposed approach provides technical and planning capabilities which are demonstrated by a case study.     

Capacity investment model for airport facilities under demand uncertainty

This paper addresses strategic airport facility planning under demand uncertainty. Existing studies are improved by (1) allowing capacity contraction and (2) adopting more flexible delay functions. A mixed‐integer nonlinear program, which incorporates scale economies in construction, time value of money, nonlinear congestion effect, and other factors, is proposed for optimizing the capacity expansion/contraction decisions over time for multiple airport components. The stochastic problem is converted into its deterministic equivalent because the number of demand scenarios considered is finite. A discrete approximation technique is used to remove the nonlinearities. Numerical studies are presented to demonstrate the capability of the proposed model and the computational efficiency of the solution method. The “Flaw of Averages” due to faulty decisions based on the average future condition is illustrated, and trade‐offs among various costs are discussed in the numerical analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Rolling horizon stochastic optimal control strategy for ACC and CACC under uncertainty

This paper presents a rolling horizon stochastic optimal control strategy for both Adaptive Cruise Control and Cooperative Adaptive Cruise Control under uncertainty based on the constant time gap policy. Specifically, uncertainties that can arise in vehicle control systems and vehicle sensor measurements are represented as normally-distributed disturbances to state and measurement equations in a state-space formulation. Then, acceleration sequence of a controlled vehicle is determined by optimizing an objective function that captures control efficiency and driving comfort over a predictive horizon, constrained by bounded acceleration/deceleration and collision protection. The optimization problem is formulated as a linearly constrained linear quadratic Gaussian problem and solved using a separation principle, Lagrangian relaxation, and Kalman filter. A sensitivity analysis and a scenario-based analysis via simulations demonstrate that the proposed control strategy can generate smoother vehicle control and perform better than a deterministic feedback controller, particularly under small system disturbances and large measurement disturbances.     

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.     

Multi-scale robustness model for highway networks under flood events

Transportation system infrastructure often experiences severe flood-related disruptions such as overtopping, erosion, and scour. The ensuing damages can result in enormous direct and indirect economic losses to the traffic network and consequently the individuals through conditions like inaccessibility to commuters and reduction in traffic safety. Many studies have claimed that a robust transportation system could significantly prevent such consequences from natural hazards such as floods, highlighting the importance of robustness measures that could be used by decision-makers to properly manage flooded transportation system. Most available measures related to network robustness assessment are qualitative, and while some recent studies have focused on such evaluation using quantitative assessment approaches related to environmental or social-economic operations, they lack the holistic view towards robustness under flood events. This study develops a composite multi-scale transportation-system robustness model considering flood hazards by synthesizing geographical damage recognition, topological functionality analysis, network operation evaluation, and traffic-user loss estimation. This integrated model has been applied in a real-world highway network, mainly revealing that a given intensive flood occurrence at different locations may result in a variety of after-flood disruptions in the transportation network. To assist the asset owners with developing more reasonable prevention and recovery plans, the developed multi-scale robustness index presents both visible multi-denominational flood consequences and an overall post-event transportation-system robustness indicator.     

A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

A bi-objective dynamic programming approach for airline green fleet planning

Ensuring a fleet of green aircraft is a basic step in mitigating aviation pollution issues that are expected to be worsen in the coming years due to rapid air traffic growth. This study proposed a novel methodology in green fleet planning in which both profit and green performance of airline are considered simultaneously and explicitly. To do this, a Green Fleet Index (GFI) is derived as an indicator to quantify the green performance of airline’s fleet. It measures the degree of airline compliance with a standard requirement in terms of emission, noise, and fuel consumption. A bi-objective dynamic programming model is then formulated to find optimal aircraft acquisition (lease or purchase) decision by minimizing GFI and maximizing profit. Several interesting results are obtained: (1) considering environmental issue as secondary objective yields a greener fleet; (2) airline’s profit is affected, but could be recovered from environmental cost savings; (3) increasing load factor is an effective operational improvement strategy to enhance airline’s green performance and raise profit level. It is anticipated that the framework developed in this study could assist airlines to make a smart decision when considering the need to be green.     

A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty

In densely populated and congested urban areas, the travel times in congested multi‐modal transport networks are generally varied and stochastic in practice. These stochastic travel times may be raised from day‐to‐day demand fluctuations and would affect travelers' route and mode choice behaviors according to their different expectations of on‐time arrival. In view of these, this paper presents a reliability‐based user equilibrium traffic assignment model for congested multi‐modal transport networks under demand uncertainty. The stochastic bus frequency due to the unstable travel time of bus route is explicitly considered. By the proposed model, travelers' route and mode choice behaviors are intensively explored. In addition, a stochastic state‐augmented multi‐modal transport network is adopted in this paper to effectively model probable transfers and non‐linear fare structures. A numerical example is given to illustrate the merits of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

A mathematical programming technique for matching time-stamped records in logistics and transportation systems

Time-stamped data for transportation and logistics are essential for estimating times on transportation legs and times between successive stages in logistic processes. Often these data are subject to recording errors and omissions. Matches must then be inferred from the time stamps alone because identifying keys are unavailable, suppressed to preserve confidentiality, or ambiguous because of missing observations. We present an integer programming (IP) model developed for matching successive events in such situations and illustrate its application in three problem settings involving (a) airline operations at an airport, (b) taxi service between an airport and a train station, and (c) taxi services from an airport. With data from the third setting (where a matching key was available), we illustrate the robustness of estimates for median and mean times between events under different random rates for “failure to record”, different screening criteria for outliers, and different target times used in the IP objective. The IP model proves to be a tractable and informative tool for data matching and data cleaning, with a wide range of potential applications.     

Robust single-track train dispatching model under a dynamic and stochastic environment: A scenario-based rolling horizon solution approach

After a major service disruption on a single-track rail line, dispatchers need to generate a series of train meet-pass plans at different decision times of the rescheduling stage. The task is to recover the impacted train schedule from the current and future disturbances and minimize the expected additional delay under different forecasted operational conditions. Based on a stochastic programming with recourse framework, this paper incorporates different probabilistic scenarios in the rolling horizon decision process to recognize (1) the input data uncertainty associated with predicted segment running times and segment recovery times and (2) the possibilities of rescheduling decisions after receiving status updates. The proposed model periodically optimizes schedules for a relatively long rolling horizon, while selecting and disseminating a robust meet-pass plan for every roll period. A multi-layer branching solution procedure is developed to systematically generate and select meet-pass plans under different stochastic scenarios. Illustrative examples and numerical experiments are used to demonstrate the importance of robust disruption handling under a dynamic and stochastic environment. In terms of expected total train delay time, our experimental results show that the robust solutions are better than the expected value-based solutions by a range of 10-30%.     

A basic mathematical model for evacuation problems in urban areas

Real life situations like floods, hurricanes or chemical accidents may cause the evacuation of a certain area to rescue the affected population. To enable a fast and a safe evacuation a basic mixed-integer evacuation model has been developed that provides a reorganization of the traffic routing of a certain area for the case of an evacuation. This basic problem of evacuation minimizes the evacuation-time while prohibiting conflicts within intersections. Our evacuation model is a dynamic network flow problem with additional variables for the number and direction of used lanes and with additional complicating constraints.Because of the size of the time-expanded network, the computational effort required by standard software is already very high for tiny instances. To deal with realistic instances we propose a heuristic approach.