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1. Estimating and Mitigating the Congestion Effect of Curbside Pick-ups and Drop-Offs: A Causal Inference Approach

   https://doi.org/10.1287/trsc.2022.0195  

   Liu, Xiaohui ; Qian, Sean ; Teo, Hock-Hai ; Ma, Wei ( December 2023 , Transportation Science)

   Curb space is one of the busiest areas in urban road networks. Especially in recent years, the rapid increase of ride-hailing trips and commercial deliveries has induced massive pick-ups/drop-offs (PUDOs), which occupy the limited curb space that was designed and built decades ago. These PUDOs could jam curbside utilization and disturb the mainline traffic flow, evidently leading to significant negative societal externalities. However, there is a lack of an analytical framework that rigorously quantifies and mitigates the congestion effect of PUDOs in the system view, particularly with little data support and involvement of confounding effects. To bridge this research gap, this paper develops a rigorous causal inference approach to estimate the congestion effect of PUDOs on general regional networks. A causal graph is set to represent the spatiotemporal relationship between PUDOs and traffic speed, and a double and separated machine learning (DSML) method is proposed to quantify how PUDOs affect traffic congestion. Additionally, a rerouting formulation is developed and solved to encourage passenger walking and traffic flow rerouting to achieve system optimization. Numerical experiments are conducted using real-world data in the Manhattan area. On average, 100 additional units of PUDOs in a region could reduce the traffic speed by 3.70 and 4.54 miles/hour (mph) on weekdays and weekends, respectively. Rerouting trips with PUDOs on curb space could respectively reduce the system-wide total travel time (TTT) by 2.44% and 2.12% in Midtown and Central Park on weekdays. A sensitivity analysis is also conducted to demonstrate the effectiveness and robustness of the proposed framework.

   Funding: The work described in this paper was supported by the National Natural Science Foundation of China [Grant 52102385], grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [Grants PolyU/25209221 and PolyU/15206322], a grant from the Otto Poon Charitable Foundation Smart Cities Research Institute (SCRI) at the Hong Kong Polytechnic University [Grant P0043552], and a grant from Hong Kong Polytechnic University [Grant P0033933]. S. Qian was supported by a National Science Foundation Grant [Grant CMMI-1931827].

   Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0195 .

    

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2. Polynomial Voting Rules

   https://doi.org/10.1287/moor.2023.0080  

   Tang, Wenpin ; Yao, David D. ( February 2024 , Mathematics of Operations Research)

   We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading.

   Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.

    

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3. Disruption and Rerouting in Supply Chain Networks

   https://doi.org/10.1287/opre.2022.2409  

   Birge, John R. ; Capponi, Agostino ; Chen, Peng-Chu ( December 2022 , Operations Research)

   We study systemic risk in a supply chain network where firms are connected through purchase orders. Firms can be hit by cost or demand shocks, which can cause defaults. These shocks propagate through the supply chain network via input-output linkages between buyers and suppliers. Firms endogenously take contingency plans to mitigate the impact generated from disruptions. We show that, as long as firms have large initial equity buffers, network fragility is low if both buyer diversification and supplier diversification are low. We find that a single-sourcing strategy is beneficial for a firm only if the default probability of the firm’s supplier is low. Otherwise, a multiple-sourcing strategy is ex post more cost effective for a firm. Funding: J.R. Birge acknowledges financial support from the University of Chicago Booth School of Business. The research of A. Capponi has been supported by the NSF/CMMI CAREER-1752326 award. P.-C. Chen acknowledges financial support from the Research Grant Council of Hong Kong [Early Career Scheme Grant 27210118]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2409 . 

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4. Constrained Information Design

   https://doi.org/10.1287/moor.2022.1346  

   Doval, Laura ; Skreta, Vasiliki ( January 2023 , Mathematics of Operations Research)

   We provide tools to analyze information design problems subject to constraints. We do so by extending an insight by Le Treust and Tomala to the case of multiple inequality and equality constraints. Namely, that an information design problem subject to constraints can be represented as an unconstrained information design problem with additional states, one for each constraint. Thus, without loss of generality, optimal solutions induce as many posteriors as the number of states and constraints. We provide results that refine this upper bound. Furthermore, we provide conditions under which there is no duality gap in constrained information design, thus validating a Lagrangian approach. We illustrate our results with applications to mechanism design with limited commitment and persuasion of a privately informed receiver.

   Funding: L. Doval acknowledges the support of the National Science Foundation through [Grant SES-2131706]. V. Skreta acknowledges the support from the National Science Foundation through [Grant SES-1851729] and from the European Research Council (ERC) through consolidator [Grant 682417].

   Supplemental Material: The e-companion is available at https://doi.org/10.1287/moor.2022.1346 .

    

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5. A Riemannian Smoothing Steepest Descent Method for Non-Lipschitz Optimization on Embedded Submanifolds of Rn

   https://doi.org/10.1287/moor.2022.0286  

   Zhang, Chao ; Chen, Xiaojun ; Ma, Shiqian ( August 2023 , Mathematics of Operations Research)

   In this paper, we study the generalized subdifferentials and the Riemannian gradient subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds of [Formula: see text]. We then propose a Riemannian smoothing steepest descent method for non-Lipschitz optimization on complete embedded submanifolds of [Formula: see text]. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary point associated with the smoothing function employed in the method, which is necessary for the local optimality of the original non-Lipschitz problem. We also prove that any accumulation point of the sequence generated by our method that satisfies the Riemannian gradient subconsistency is a limiting stationary point of the original non-Lipschitz problem. Numerical experiments are conducted to demonstrate the advantages of Riemannian [Formula: see text] [Formula: see text] optimization over Riemannian [Formula: see text] optimization for finding sparse solutions and the effectiveness of the proposed method.

   Funding: C. Zhang was supported in part by the National Natural Science Foundation of China [Grant 12171027] and the Natural Science Foundation of Beijing [Grant 1202021]. X. Chen was supported in part by the Hong Kong Research Council [Grant PolyU15300219]. S. Ma was supported in part by the National Science Foundation [Grants DMS-2243650 and CCF-2308597], the UC Davis Center for Data Science and Artificial Intelligence Research Innovative Data Science Seed Funding Program, and a startup fund from Rice University.

    

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