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The emergence of bike-sharing systems has considerably improved last- and first-mile transportation systems. To ensure attractiveness to end users, operators aim to design effective service-oriented operational strategies to meet the desired service targets for users. Most existing studies focus on the service efficiency of bike-sharing systems, while service equity is overlooked. In this study, we propose a target-based stochastic distributionally robust optimization (TSDRO) model that addresses both the efficiency and equity of the service level in docked bike-sharing systems under demand uncertainty. We first employ a dissatisfaction risk measure to jointly quantify the probability and magnitude of user dissatisfaction in a zone. Then, we apply a lexicographic-order approach to define the objective function to achieve equity of service among different zones. This lexicographic approach optimizes the worst-off individual and the second-worst zone in an iterative manner. To address demand ambiguity, we use a data-driven method to explore the relationship between the demand distribution and several exogenous factors, including weather and weekends, and then construct a scenario-based distributionally robust optimization model. Based on duality theory and linear decision approximation, this model can be reformulated as a tractable equivalent deterministic model, which can be solved via a bisection-search approach to optimality. Numerical experiments based on real operational data show that compared with the benchmark models, the TSDRO model achieves (i) better out-of-sample performance in terms of service efficiency and (ii) higher service equity among users in different zones. Moreover, setting a lower target level may generate a better solution. • We propose a target-based service efficiency and equity optimization model. • We consider the spatial service equity by employing the lexicographic approach. • We address demand uncertainty by a stochastic distributionally robust approach. • Numerical experiments show that our model has good out-of-sample performance. [ABSTRACT FROM AUTHOR]

Over the past two decades, bike-sharing systems have grown significantly worldwide. Compared with that of other business sectors, the means by which revenue is obtained in the bike-sharing industry is unique. When the market in a region or city is saturated, an efficient way for a firm to increase revenue is to enter a new market. In this study, we design a revenue maximization-oriented decision tool to support the operational decisions of a new competitor firm entering into competition against a local firm. It is assumed that operational-level information from the local firm is unknown to the competitor firm. A new multi-stage max–min–max robust maximization model is proposed. It aims to optimize the dynamic bike inventory to maximize the worst-case revenue that the competitor firm may achieve. The worst-case revenue is treated as the baseline revenue for the competitor firm according to which rational decisions can be made. Specifically, we construct an uncertainty set to capture the uncertainty in the bike distribution of the local firm. To work with this nonconvex model, we design a myopic method, inspired by a special two-stage model that can be solved with a customized constraint-and-column approach, for obtaining the upper and lower bounds of the potential optimal revenue in our multistage model. The results of numerical experiments illustrate that the approximation approach has satisfactory computational efficiency and generates a tight bound of the optimal baseline revenue. Sensitivity analyses show that the new competitor firm should not increase its investment in bikes when the local firm increases its quantity of bikes because of high depreciation costs. Moreover, the two firms would allocate a similar proportion of bikes to each zone when either of them provides a large number of bikes. When the firms both provide a small number of bikes, the allocation of bikes by the new competitor firm is widely dispersed, while the local firm tends to allocate bikes across several zones with high demand. Furthermore, on the premise of a given target, increasing the bike acquisition can improve the robustness of revenue estimation for the competitor firm. • A revenue-oriented model is presented for a new firm entering into competition against a local firm. • An uncertainty set is defined to capture the uncertainty in the bike distribution of the local firm. • A customized myopic method with CC&G approach is designed to obtain suboptimal solutions. • The results show the new firm may decrease the number of bikes as the local firm provides more bikes. [ABSTRACT FROM AUTHOR]

Travel time is one of the most intuitive pieces of traffic information to help decision makers to control real-time traffic conditions and to guide travelers to choose a reasonable route. An optimal sensor location scheme can obtain reliable route travel time information. Most current travel-time-oriented sensor location models are deterministic and assume a given and correct travel time probability density function. Nevertheless, due to widespread observational and systematic errors, prior travel time information is not accurate or reliable. In our study, a novel data-driven link-based network sensor location method is proposed to maximize travel time information gain. The effect of route differentiation is considered, and the sensors are located at links rather than at nodes. In addition, to account for the uncertainty in the prior travel time distribution, the distributionally robust travel time information gain sensor location (DRTTIGSL) model is presented. The prior distribution information is taken into account based on a statistical measure called ϕ -divergence. The ϕ -divergence is used to construct the uncertainty set. The reformulation of DRTTIGSL is dependent on the choice of ϕ -divergence and is tractable. Extensive numerical experiments are conducted to verify the effectiveness of the DRTTIGSL model. Compared with the optimal solutions for the deterministic model, the optimal solutions for the DRTTIGSL model can reduce the worst-case situation with a small price of the average objective value, especially when the total budget is not large. [ABSTRACT FROM AUTHOR]

Path flow identification is of particular interest for a number of traffic applications, such as OD demand estimation, link flow inference, and toll freeway revenue management. Optimal positioning of active sensors can help to identify path flows. Due to the stochastic nature of transportation systems, we propose a scenario based two stage stochastic programming framework which considers the uncertainty of the link-path matrix. The first stage model aims to minimize the total traffic sensor installation cost and the expected penalty for uncovered and undifferentiated paths. The second stage model attempts to minimize uncovered and undifferentiated paths for a given sensor location pattern and a specific scenario. In addition, a mean risk measure is also incorporated into the two stage stochastic programming framework, and consequently a mean risk two stage stochastic programming model is proposed. Both models have the same structure, where the first stage and second stage decision variables are binary. The second stage decision variable can be relaxed to a continuous variable without changing the nature of the model. To solve the two stochastic programming models, a branch and bound based integer L-shaped algorithm is presented. Finite steps convergence is guaranteed for the algorithm. To handle the problem with a large number of scenarios, a sampling technique is introduced, and the confidence bound is analyzed with respect to the scenario size. Extensive numerical experiments are conducted to verify the effectiveness of the proposed models and algorithm. The most important numerical results are as follows: (i) the stochastic programming framework is capable of capturing the reality more efficiently and accurately, (ii) the path differentiation factor is more critical than the path coverage factor in determining the sensor placement pattern, and (iii) in the partial parameter setting case, the mean risk based stochastic programming model results in a significantly different sensor placement pattern compared to the normal stochastic programming model. The study contributes to practical sensor placement design. [ABSTRACT FROM AUTHOR]

A new traffic sensor location problem is developed and solved by strategically placing both passive and active sensors in a transportation network for path reconstruction. Passive sensors simply count vehicles, while active sensors can recognize vehicle plates but are more expensive. We developed a two-stage heterogeneous sensor location model to determine the most cost-effective strategies for sensor deployment. The first stage of the model adopts the path reconstruction model defined by Castillo et al. (2008b) to determine the optimal locations of active sensors in the network. In the second stage, an algebraic framework is developed to strategically replace active sensors so that the total installation cost can be reduced while maintaining path flow observation quality. Within the algebraic framework, a scalar product operator is introduced to calculate path flows. An extension matrix is generated and used to determine if a replacement scheme is able to reconstruct all path flows. A graph model is then constructed to determine feasible replacement schemes. The problem of finding the optimal replacement scheme is addressed by utilizing the theory of maximum clique to obtain the upper bound of the number of replaced sensors and then revising this upper bound to generate the optimal replacement scheme. A polynomial-time algorithm is proposed to solve the maximum clique problem, and the optimal replacement scheme can be obtained accordingly. Three numerical experiments show that our proposed two-stage method can reduce the total costs of transportation surveillance systems without affecting the system monitor quality. The locations of the active sensors play a more critical role than the locations of the passive sensors in the number of reconstructed paths. [ABSTRACT FROM AUTHOR]