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We consider a minimization variant on the classical prophet inequality with monomial cost functions. A firm would like to procure some fixed amount of a divisible commodity from sellers that arrive sequentially. Whenever a seller arrives, the seller’s cost function is revealed, and the firm chooses how much of the commodity to buy. We first show that if one restricts the set of distributions for the coefficients to a family of natural distributions that include, for example, the uniform and truncated normal distributions, then there is a thresholding policy that is asymptotically optimal in the number of sellers. We then compare two scenarios based on whether the firm has in-house production capabilities or not. We precisely compute the optimal algorithm’s competitive ratio when in-house production capabilities exist and for a special case when they do not. We show that the main advantage of the ability to produce the commodity in house is that it shields the firm from price spikes in worst-case scenarios. Funding: This work was supported by NSF Grants [CNS-2146814, CPS-2136197, CNS-2106403, NGSDI-2105648]. 

This paper considers off-street parking for the cruising vehicles of transportation network companies (TNCs) to reduce the traffic congestion. We propose a novel business that integrates the shared parking service into the TNC platform. In the proposed model, the platform (a) provides interfaces that connect passengers, drivers and garage operators (commercial or private garages); (b) determines the ride fare, driver payment, and parking rates; (c) matches passengers to TNC vehicles for ride-hailing services; and (d) matches vacant TNC vehicles to unoccupied parking garages to reduce the cruising cost. A queuing-theoretic model is proposed to capture the matching process of passengers, drivers, and parking garages. A market-equilibrium model is developed to capture the incentives of the passengers, drivers, and garage operators. An optimization-based model is formulated to capture the optimal pricing of the TNC platform. Through a realistic case study, we show that the proposed business model will offer a Pareto improvement that benefits all stakeholders, which leads to higher passenger surplus, higher drivers surplus, higher garage operator surplus, higher platform profit, and reduced traffic congestion. 

The value created by aggregating behind-the-meter distributed energy storage devices for grid services depends on how much storage is in the system and the power network operation conditions. To understand whether market-driven distributed storage investment will result in a socially desirable outcome, we formulate and analyze a network storage investment game. By explicitly characterizing the set of Nash equilibria (NE) for two examples, we establish that the uniqueness and efficiency of NE depend critically on the power network conditions. Furthermore, we show it is guaranteed that NE support social welfare for general power networks, provided we include two modifications in our model. These modifications suggest potential directions for regulatory interventions. 

Frequency regulation is crucial for balancing the supply and demand of modern electricity grids. To provide regulation services, it is important to understand the capability of flexible resources to track regulation signals. This paper studies the problem of submitting capacity bids to a forward regulation market based on historical regulation signals. We consider an aggregator who manages a group of flexible resources with linear dynamic constraints. He seeks to find the optimal capacity bid, so that real-time regulation signals can be followed with an arbitrary guaranteed probability. We formulate this problem as a chance-constrained program with unknown regulation signal distributions. A sampling and discarding algorithm is proposed. It provably provides near-optimal solutions at a guaranteed probability of success without knowing the distribution of the regulation signals. This result holds for resources with arbitrary linear dynamics and allows arbitrary intra-hour data correlations. We validate the proposed algorithm with real data via numerical simulations. Two cases are studied: (1) CAISO market, where providers separately submit capacity estimates for regulation up and regulation down signals, (2) PJM market, where regulation up and down capacities are the same. Simulation results show that the proposed algorithm provides near-optimal capacity estimates for both cases. 

In the classical risk limiting dispatch (RLD) formulation, the system operator dispatches generators relying on information about the distribution of demand. In practice, such information is not readily available and therefore is estimated using historical demand and auxiliary information (or features) such as weather forecasts. In this paper, instead of using a separated estimation and optimization procedure, we propose learning methods that directly compute the RLD decision rule based on historical data. Using tools from statistical learning theory, we then develop generalization bounds and sample complexity results of the proposed methods. These algorithms and performance guarantees, developed for the single-bus network, are then extended to a general network setting for the uniform reserve case.