Modelling and optimization of average travel time for a metro line by simulation and response surface methodology

This research presents a modelling and solution approach based on discrete-event simulation and response surface methodology for dealing with average passenger travel time optimization problem inherent to the metro planning process. The objective is to find the headways optimizing passenger average travel time with a satisfactory rate of carriage fullness. Due to some physical constraints, traffic safety and legal requirements, vehicle speeds cannot be raised any further to decrease travel time. But travel time can be optimized by arranging headways (i.e. the time period between the departure times of two consecutive transportation vehicles) in a timetable. In the presented approach, simulation metamodels that best fit the data collected from the simulated experiments are constructed to describe the relationship between the responses (average travel time and rate of carriage fullness) and input factors (headways). Then, the Derringer–Suich multi-response optimization procedure is used to determine the optimal settings of the input factors that produce the minimum value of the average travel time by providing a proper rate of carriage fullness. This methodology is applied for a real metro line, and good quality solutions are obtained with reduced number of experiments that needed to provide sufficient information for statistically acceptable results.     

A pro-active real-time control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods

This paper proposes a new pro-active real-time control approach for dynamic vehicle routing problems in which the urgent delivery of goods is of utmost importance. Without assuming any distribution, stochastic knowledge about future requests is generated using past request information. The generated knowledge is integrated into the transportation process, which is controlled by a Tabu Search algorithm, in order to actively guide vehicles to request-likely areas before requests arrive there. By analyzing the results attained for various test settings, we identify structural diversity as a crucial criterion for classifying the quality of stochastic knowledge attainable from past request information. This criterion provides a promising starting point for assessing the quality of past request information in order to efficiently use the derived stochastic knowledge in real-time control approaches. We prove the efficiency of our approach by a direct comparison with a deterministic approach on test scenarios with varying structural diversity. Thanks to the proposed classification of structural diversity, differences in results obtained among the tested scenarios become explainable.     

A Multi-Class Dynamic User Equilibrium Model for Queuing Networks with Advanced Traveler Information Systems

This paper presents a formulation and solution algorithm for a composite dynamic user-equilibrium assignment problem with multi-user classes, in order to assess the impacts of Advanced Traveler Information Systems (ATIS) in general networks with queues. Suppose that users equipped with ATIS will receive complete information and hence be able to choose the best departure times and routes in a deterministic manner, while users not equipped with ATIS will have incomplete information and hence may make decisions on departure times and routes in a stochastic manner. This paper proposes a discrete-time, finite-dimensional variational inequality formulation that involves two criteria regarding the route and departure time choice behaviors, i.e., the deterministic dynamic user equilibrium and the nested logit-based stochastic dynamic user equilibrium. The formulation is then converted to an equivalent “zero-extreme value” minimization problem. A heuristic algorithm based on route/time-swapping process is proposed, which iteratively adjusts the route and departure time choices to reach closely to an extreme point of the minimization problem. A numerical example is used to demonstrate the effectiveness of the proposed approach for assessing the ATIS impacts such as changes in individual travel costs, departure times, route inflows, queuing peaks and total network travel cost. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measuring Risk for Income Streams

A measure of risk is introduced for a sequence of random incomes adapted to some filtration. This measure is formulated as the optimal net present value of a stream of adaptively planned commitments for consumption. The new measure is calculated by solving a stochastic dynamic linear optimization problem which, for finite filtrations, reduces to a deterministic linear programming problem.We analyze properties of the new measure by exploiting the convexity and duality structure of the stochastic dynamic linear problem. The measure depends on the full distribution of the income process (not only on its marginal distributions) as well as on the filtration, which is interpreted as the available information about the future. The features of the new approach are illustrated by a numerical example.     

基于鲁棒优化的随机时变网络最优路径研究

交通事故、恶劣天气以及偶发的交通拥堵等都会导致道路交通网络中行程时间的不确定性,极大地影响了道路交通系统的可靠性,同时给日常生活中出行计划的制定以及出行路径的选择带来了不便。因此,本次研究将综合考虑道路交通网络中由于交通流量的全天变化所导致的路径行程时间的时变特征,以及由于事故、天气等不确定因素所导致的路径行程时间的随机特征,并以此作为路网环境的假设条件,对出行路径选择问题进行研究。具体地,首先建立行程时间的动态随机变量,并在此基础上模拟构建了随机时变网络。随后,定义了该网络环境下路径选择过程中所考虑的成本费用,并通过鲁棒优化的方法,将成本费用鲁棒性最强的路径视为最优路径。随后,在随机一致性条件下,通过数学推导证明了该模型可以简化为解决一个确定性时变网络中的最短路径问题。最终,具有多项式时间计算复杂度的改进Dijkstra算法被应用到模型的求解中,并通过小型算例验证模型及算法的有效性。结果表明,本研究中所提出的方法可以被高效率算法所求解,并且不依赖于先验行程时间概率分布的获取,因此对后续的大规模实际城市道路网络应用提供了良好的理论基础。此外,由于具有行程时间随机时变特征的交通网络更接近实际道路情况,因此本次研究的研究成果具有较高的实际意义和应用价值。     

Modelling Intra-City Time-Dependent Travel Speeds for Vehicle Scheduling Problems

Many research papers have presented mathematical models for vehicle scheduling. Several of these models have been embedded in commercial decision support systems for intra-city vehicle scheduling for launderies, grocery stores, banks, express mail customers, etc. Virtually all of these models ignore the important issue of time-dependent travel speeds for intra-city travel. Travel speeds (and times) in nearly all metropolitan areas change drastically during the day because of congestion in certain parts of the city road network. The assumption of constant (time-independent) travel speeds seriously affects the usefulness of these models. This is particularly true when time windows (earliest and latest stop time constraints) and other scheduling issues are important. This research proposes a parsimonious model for time-dependent travel speeds and several approaches for estimating the parameters for this model. An example is presented to illustrate the proposed modelling approach. The issue of developing algorithms to find near-optimal vehicle schedules with time-dependent travel speeds is also discussed. The modelling approach presented in this paper has been implemented in a commercial courier vehicle scheduling system and was judged to be ‘very useful’ by users in a number of different metropolitan areas in the United States.     

Dynamic system optimal performances of shared autonomous and human vehicle system for heterogeneous travellers

ABSTRACT

Autonomous vehicles (AV) can solve vehicle relocation problems faced by traditional one-way vehicle-sharing systems. This paper explores the deterministic time-dependent system optimum of mixed shared AVs (SAV) and human vehicles (SHV) system to provide the benchmark for the situation of mixed vehicle flows. In such a system, the system planner determines vehicle-traveller assignment and optimal vehicle routing in transportation networks to serve predetermined travel demand of heterogeneous travellers. Due to large number of vehicles involved, travel time is considered endogenous with congestion. Using link transmission model (LTM) as a traffic flow model, the deterministic time-dependent system optimum is formulated as linear programming (LP) model to minimize the comprehensive cost including travellers’ travel time cost, waiting time cost and empty vehicle repositioning time cost. Numerical examples are conducted to show system performances and model effectiveness.     

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.      

Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem

The stochastic uncapacitated single allocation p-hub center problem is an extension of the deterministic version which aims to minimize the longest origin-destination path in a hub and spoke network. Considering the stochastic nature of travel times on links is important when designing a network to guarantee the quality of service measured by a maximum delivery time for a proportion of all deliveries. We propose an efficient reformulation for a stochastic p-hub center problem and develop exact solution approaches based on variable reduction and a separation algorithm. We report numerical results to show effectiveness of our new reformulations and approaches by finding global solutions of small-medium sized problems. The combination of model reformulation and a separation algorithm is particularly noteworthy in terms of computational speed.     

Optimizing the release of passenger flow guidance information in urban rail transit network via agent-based simulation

The passenger flow guidance is an effective demand management strategy to alleviate the excessive congestion in the urban rail transit network. In order to determine the scope and the timing, a simulation-based optimization model is proposed to optimize the release of passenger flow guidance information in the rail transit network in this paper. In the optimization model, we mainly focus on three aspects namely; where, when and what type of the guidance information should be released to the passengers. In the simulation model, the passenger choice behavior is captured by the agent-based simulation method, which responses to the congestion and the guidance information. Based on this, the dynamic passenger flow distribution can be derived. Furthermore, the adoption rate of the displayed guidance information on passenger information system as well as its impact on passenger travel behavior are also considered in the model. A hybrid heuristic solution algorithm, integrated with passenger simulator and genetic algorithm, is developed to solve the proposed simulation-based optimization model. Finally, a case study of Beijing subway is carried out with the large-scale smart card data. The numerical study shows that the passenger flow demand affects the guidance effect significantly and the best guidance effect can be met with sufficiently high passenger flow demand. And the guidance rate is also found to affect the guidance results. The results also show that the proposed model can provide a detailed guidance scheme for every station at selected time intervals. The results show that the dynamic releasing scheme can save up to a total of 46,319 min in passenger travel time during a single guidance period.     

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.This author's work was supported in part by the National Science Foundation under Grants ECS 88-15101, ECS 92-16819, and SES 92-11937.This author's work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-5489 and by the UK Engineering and Physical Sciences Research Council under Grants J90855 and K17897.     

Vehicle routing problems with alternative paths: An application to on-demand transportation

The class of vehicle routing problems involves the optimization of freight or passenger transportation activities. These problems are generally treated via the representation of the road network as a weighted complete graph. Each arc of the graph represents the shortest route for a possible origin–destination connection. Several attributes can be defined for one arc (travel time, travel cost, etc.), but the shortest route modeled by this arc is computed according to a single criterion, generally travel time. Consequently, some alternative routes proposing a different compromise between the attributes of the arcs are discarded from the solution space. We propose to consider these alternative routes and to evaluate their impact on solution algorithms and solution values through a multigraph representation of the road network. We point out the difficulties brought by this representation for general vehicle routing problems, which drives us to introduce the so-called fixed sequence arc selection problem (FSASP). We propose a dynamic programming solution method for this problem. In the context of an on-demand transportation (ODT) problem, we then propose a simple insertion algorithm based on iterative FSASP solving and a branch-and-price exact method. Computational experiments on modified instances from the literature and on realistic data issued from an ODT system in the French Doubs Central area underline the cost savings brought by the proposed methods using the multigraph model.     

A Stochastic Model for Combined Activity/Destination/Route Choice Problems

In travel behavior modeling, an important topic is to investigate what drives people to travel. A systematic analysis should examine why, where and when various activities are engaged in, and how activity engagement is related to the spatial and institutional organization of an urban area. In view of this, this paper presents a stochastic model for solving the combined activity/destination/route choice problem. It is a time-dependent model for long-term transport planning such as travel demand forecasting. The activity/destination choices are based on multinomial logit formulae and, the route choice is governed by stochastic user equilibrium principle. The solution algorithm is proposed together with a numerical example for demonstration. It is shown that the proposed modeling approach provides a powerful tool for fully understanding and predicting the complex travel behavior at strategic level. The work described in this paper was substantially supported by the grants from the National Natural Science Foundation of China (Project No. 79825101), the Chinese Academy of Sciences (MADIS Research Project) and the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU5077/97E).     

A Deterministic Approach To Stochastic Optimal Control With Application To Anticipative Control

Using the decomposition of solution of SDE, we consider the stochastic optimal control problem with anticipative controls as a family of deterministic control problems parametrized by the paths of the driving Wiener process and of a newly introduced Lagrange multiplier stochastic process (nonanticipativity equality constraint). It is shown that the value function of these problems is the unique global solution of a robust equation (random partial differential equation) associated to a linear backward Hamilton-Jacobi-Bellman stochastic partial differential equation (HJB SPDE). This appears as limiting SPDE for a sequence of random HJB PDE's when linear interpolation approximation of the Wiener process is used. Our approach extends the Wong-Zakai type results [20] from SDE to the stochastic dynamic programming equation by showing how this arises as average of the limit of a sequence of deterministic dynamic programming equations. The stochastic characteristics method of Kunita [13] is used to represent the value function. By choosing the Lagrange multiplier equal to its nonanticipative constraint value the usual stochastic (nonanticipative) optimal control and optimal cost are recovered. This suggests a method for solving the anticipative control problems by almost sure deterministic optimal control. We obtain a PDE for the “cost of perfect information” the difference between the cost function of the nonanticipative control problem and the cost of the anticipative problem which satisfies a nonlinear backward HJB SPDE. Poisson bracket conditions are found ensuring this has a global solution. The cost of perfect information is shown to be zero when a Lagrangian submanifold is invariant for the stochastic characteristics. The LQG problem and a nonlinear anticipative control problem are considered as examples in this framework     

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).     

Doubly uncertain transportation network: Degradable capacity and stochastic demand

This study developed a methodology to model doubly uncertain transportation network with stochastic link capacity degradation and stochastic demand. We consider that the total travel demand comprises of two parts, infrequent travelers and commuters. The traffic volume of infrequent travelers is stochastic, which adds to the network traffic in a random manner based on fixed route choice proportions. On the other hand, the traffic volume of commuters is stable or deterministic. Commuters acquire the network travel time variability from past experiences, factor them into their route choice considerations, and settle into a long-term habitual route choice equilibrium in which they have no incentive of switching away. To define this equilibrium, we introduce the notion of “travel time budget” to relate commuters’ risk aversion on route choices in the presence of travel time variability. The travel time budget varies among commuters according to their degrees of risk aversion and requirements on punctual arrivals. We then developed a mixed-equilibrium formulation to capture these stochastic considerations and illustrated its properties through some numerical studies.     

A NEW DETERMINISTIC FORMULATION FOR DYNAMIC STOCHASTIC PROGRAMMING PROBLEMS AND ITS NUMERICAL COMPARISON WITH OTHERS

A new deterministic formulation, called the conditional expectation formulation, is proposed for dynamic stochastic programming problems in order to overcome some disadvantages of existing deterministic formulations. We then check the impact of the new deterministic formulation and other two deterministic formulations on the corresponding problem size, nonzero elements and solution time by solving some typi     

Models and model value in stochastic programming

Finding optimal decisions often involves the consideration of certain random or unknown parameters. A standard approach is to replace the random parameters by the expectations and to solve a deterministic mathematical program. A second approach is to consider possible future scenarios and the decision that would be best under each of these scenarios. The question then becomes how to choose among these alternatives. Both approaches may produce solutions that are far from optimal in the stochastic programming model that explicitly includes the random parameters. In this paper, we illustrate this advantage of a stochastic program model through two examples that are representative of the range of problems considered in stochastic programming. The paper focuses on the relative value of the stochastic program solution over a deterministic problem solution.The author's work was supported in part by the National Science Foundation under Grant DDM-9215921.     

Stochastic uncapacitated hub location

We study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs. We show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem (EVP), in which random variables are replaced by their expectations. In the case of uncertain independent transportation costs, the corresponding stochastic problem is not equivalent to its EVP and specific solution methods need to be developed. We describe a Monte-Carlo simulation-based algorithm that integrates a sample average approximation scheme with a Benders decomposition algorithm to solve problems having stochastic independent transportation costs. Numerical results on a set of instances with up to 50 nodes are reported.     

Planning logistics operations in the oil industry

In this paper we apply stochastic programming modelling and solution techniques to planning problems for a consortium of oil companies. A multiperiod supply, transformation and distribution scheduling problem—the Depot and Refinery Optimization Problem (DROP)—is formulated for strategic or tactical level planning of the consortium's activities. This deterministic model is used as a basis for implementing a stochastic programming formulation with uncertainty in the product demands and spot supply costs (DROPS), whose solution process utilizes the deterministic equivalent linear programming problem. We employ our STOCHGEN general purpose stochastic problem generator to ‘recreate’ the decision (scenario) tree for the unfolding future as this deterministic equivalent. To project random demands for oil products at different spatial locations into the future and to generate random fluctuations in their future prices/costs a stochastic input data simulator is developed and calibrated to historical industry data. The models are written in the modelling language XPRESS-MP and solved by the XPRESS suite of linear programming solvers. From the viewpoint of implementation of large-scale stochastic programming models this study involves decisions in both space and time and careful revision of the original deterministic formulation. The first part of the paper treats the specification, generation and solution of the deterministic DROP model. The stochastic version of the model (DROPS) and its implementation are studied in detail in the second part and a number of related research questions and implications discussed.