The economic speed of an oceangoing vessel in a dynamic setting

The optimal (economic) speed of oceangoing vessels has become of increased importance due to the combined effect of low freight rates and volatile bunker prices. We examine the problem for vessels operating in the spot market in a tramp mode. In the case of known freight rates between origin destination combinations, a dynamic programming formulation can be applied to determine both the optimal speed and the optimal voyage sequence. Analogous results are derived for random freight rates of known distributions. In the case of independent rates the economic speed depends on fuel price and the expected freight rate, but is independent of the revenue of the particular voyage. For freight rates that depend on a state of the market Markovian random variable, economic speed depends on the market state as well, with increased speed corresponding to good states of the market. The dynamic programming equations in our models differ from those of Markovian decision processes so we develop modifications of standard solution methods, and apply them to small examples.     

高速铁路列车运行图均衡性研究

以相邻间隔时间期望方差及相间间隔时间均值和方差为计算指标,描述车站的列车分布及顺序均衡性。运用均衡性指标矩阵及均衡度指标向量来评价列车实际与计划运行图的均衡性。结果表明,由于干扰影响列车间隔时间大小波动明显,列车到达均衡性整体优于列车出发均衡性,长沙南站时间间隔分布及顺序均衡性最差,衡山西站、株洲西站、长沙南站到发均衡度最差,应结合列车晚点情况重点考虑运行图结构优化。     

Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions

The aim of this paper is to remove the known limitations of Deterministic and Stochastic User Equilibrium (DUE and SUE), namely that only routes with the minimum cost are used in DUE, and that all permitted routes are used in SUE regardless of their costs. We achieve this by combining the advantages of the two principles, namely the definition of unused routes in DUE and of mis-perception in SUE, such that the resulting choice sets of used routes are equilibrated. Two model families are formulated to address this issue: the first is a general version of SUE permitting bounded and discrete error distributions; the second is a Restricted SUE model with an additional constraint that must be satisfied for unused paths. The overall advantage of these model families consists in their ability to combine the unused routes with the use of random utility models for used routes, without the need to pre-specify the choice set. We present model specifications within these families, show illustrative examples, evaluate their relative merits, and identify key directions for further research.     

Integrating congestion pricing and transit investment planning

This paper develops a mathematical model and solution procedure to identify an optimal zonal pricing scheme for automobile traffic to incentivize the expanded use of transit as a mechanism to stem congestion and the social costs that arise from that congestion. The optimization model assumes that there is a homogenous collection of users whose behavior can be described as utility maximizers and for which their utility function is driven by monetary costs. These monetary costs are assumed to be the tolls in place, the per mile cost to drive, and the value of their time. We assume that there is a system owner who sets the toll prices, collects the proceeds from the tolls, and invests those funds in transit system improvements in the form of headway reductions. This yields a bi-level optimization model which we solve using an iterative procedure that is an integration of a genetic algorithm and the Frank–Wolfe method. The method and solution procedure is applied to an illustrative example.     

An analysis of airport–airline vertical relationships with risk sharing contracts under asymmetric information structures

We analyze the double moral hazard problem at the joint venture type airport–airline vertical relationship, where two parties both contribute efforts to the joint venture but neither of them can see the other’s efforts. With the continuous-time stochastic dynamic programming model, we show that by the de-centralized utility maximizations of two parties under very strict conditions, i.e., optimal efforts’ cost being negligible and their risk averse parameters both asymptotically approaching to zero, the vertical contract could be agreed as the optimal sharing rule, which is the linear function of the final state with the slope being the product of their productivity difference and uncertainty (diffusion rate) level index.If both parties’ productivities are same, or the diffusion rate of the underlying process is unity, optimal linear sharing rule do not depend on the final state. If their conditions not dependent on final state are symmetric as well, then risk sharing disappears completely. In numerical examples, we illustrate the complex impact of uncertainty increase and end-of-period load factor improvement on the optimal sharing rule, and the relatively simple impact on total utility levels.     

Accounting for dynamic speed limit control in a stochastic traffic environment: A reinforcement learning approach

This paper proposes a novel dynamic speed limit control model accounting for uncertain traffic demand and supply in a stochastic traffic network. First, a link based dynamic network loading model is developed to simulate the traffic flow propagation allowing the change of speed limits. Shockwave propagation is well defined and captured by checking the difference between the queue forming end and the dissipation end. Second, the dynamic speed limit problem is formulated as a Markov Decision Process (MDP) problem and solved by a real time control mechanism. The speed limit controller is modeled as an intelligent agent interacting with the stochastic network environment stochastic network environment to assign time dependent link based speed limits. Based on different metrics, e.g. total network throughput, delay time, vehicular emissions are optimized in the modeling framework, the optimal speed limit scheme is obtained by applying the R-Markov Average Reward Technique (R-MART) based reinforcement learning algorithm. A case study of the Sioux Falls network is constructed to test the performance of the model. Results show that the total travel time and emissions (in terms of CO) are reduced by around 18% and 20% compared with the base case of non-speed limit control.     

The time-dependent vehicle routing problem with soft time windows and stochastic travel times

This paper studies a vehicle routing problem with time-dependent and stochastic travel times. In our problem setting, customers have soft time windows. A mathematical model is used in which both efficiency for service as well as reliability for customers are taken into account. Depending on whether service times are included or not, we consider two versions of this problem. Two metaheuristics are built: a Tabu Search and an Adaptive Large Neighborhood Search. We carry out our experiments for well-known problem instances and perform comprehensive analyses on the numerical results in terms of the computational time and the solution quality. Experiments confirm that the proposed procedure is effective to obtain very good solutions to be performed in real-life environment.     

The fleet renewal problem with regional emission limitations: Case study from Roll-on/Roll-off shipping

In this paper, the maritime fleet renewal problem (MFRP) is extended to include regional limitations in the form of emission control areas. The motivation for including this aspect is that strengthening of emission regulations in such areas is expected to be challenging for deep sea shipping in the years to come. In the proposed model, various means to cope with these stricter emission regulations are evaluated for new vessels, and the possibility of upgrading existing vessels with new emission reduction technology is introduced. We consider future fuel prices to be important for the problem, and have chosen to treat them as uncertain, and thus, a stochastic programming model is chosen. A fleet renewal problem faced by the liner shipping operator Wallenius Wilhelmsen Logistics, concerning whether to use low sulphur fuel or have an exhaust gas scrubber system installed to comply with sulphur regulation in emission control areas from 2015, is used as a case study. Furthermore, tests show that the savings from including the aspect of emission control areas in the MFRP are substantial.     

Multi-scenario optimization approach for assessing the impacts of advanced traffic information under realistic stochastic capacity distributions

In this study, to incorporate realistic discrete stochastic capacity distribution over a large number of sampling days or scenarios (say 30–100 days), we propose a multi-scenario based optimization model with different types of traveler knowledge in an advanced traveler information provision environment. The proposed method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions (and related reliability measure) across a large number of different sampling days. Using a gap function framework or describing the mixed user equilibrium under different information availability over a long-term steady state, a nonlinear programming model is formulated to describe the route choice behavior of the perfect information (PI) and expected travel time (ETT) user classes under stochastic day-dependent travel time. Driven by a computationally efficient algorithm suitable for large-scale networks, the model was implemented in a standard optimization solver and an open-source simulation package and further applied to medium-scale networks to examine the effectiveness of dynamic traveler information under realistic stochastic capacity conditions.