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Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner's expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency deviation trajectories in a functional uncertainty set that encodes applicable legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem nonconvex. Methodology/results: By exploiting a total unimodularity property of the uncertainty set and an exact linear decision rule reformulation, we prove that this nonconvex robust optimization problem with functional uncertainties is equivalent to a tractable linear program. Through extensive numerical experiments using real-world data, we quantify the economic value of vehicle-to-grid and elucidate the financial incentives of vehicle owners, aggregators, equipment manufacturers, and regulators. Managerial implications: We find that the prevailing penalties for nondelivery of promised regulation power are too low to incentivize vehicle owners to honor the delivery guarantees given to grid operators. Funding: This work was supported by the Institut Vedecom. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0154. [ABSTRACT FROM AUTHOR]

Multimarket Multireservoir Hydro Scheduling Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. In their paper titled "A Planner-Trader Decomposition for Multimarket Hydro Scheduling" Schindler, Rujeerapaiboon, Kuhn, and Wiesemann propose a bi-layer stochastic programming framework that jointly optimizes the trading strategies on the spot and reserve markets. The model faithfully accounts for uncertainty in electricity prices, water inflows, and reserve activations, and it ensures that the hydropower producers can fulfill their market commitments under any circumstances. The model is numerically challenging due to the various sources of uncertainty that are revealed at different time scales and that affect the problem's objective function and constraints, and the authors propose a new planner-trader decomposition and an information restriction for its solution. A case study based on real data from Austria reveals significant benefits of simultaneously participating in the spot and the reserve markets. Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bilayer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner's problem) optimizes end-of-day reservoir filling levels over one year, whereas the inner layer (the trader's problem) selects optimal hourly market bids within each day. Using an information restriction whereby the planner prescribes the end-of-day reservoir targets one day in advance, we prove that the trader's problem simplifies from an infinite-dimensional stochastic program with 25 stages to a finite two-stage stochastic program with only two scenarios. Substituting this reformulation back into the outer layer and approximating the reservoir targets by affine decision rules allows us to simplify the planner's problem from an infinite-dimensional stochastic program with 365 stages to a two-stage stochastic program that can conveniently be solved via the sample average approximation. Numerical experiments based on a cascade in the Salzburg region of Austria demonstrate the effectiveness of the suggested framework. Funding: This research was supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 [Grant MOE-2019-T3-1-010], the National University of Singapore [Grant A-0009135-01-00], and the Swiss National Science Foundation [Grant BSCGI0_157733] as well as the Engineering and Physical Sciences Research Council [Grant EP/R045518/1]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2456. [ABSTRACT FROM AUTHOR]

In the era of modern business analytics, data-driven optimization has emerged as a popular modeling paradigm to transform data into decisions. By constructing an ambiguity set of the potential data-generating distributions and subsequently hedging against all member distributions within this ambiguity set, data-driven optimization effectively combats the ambiguity with which real-life data sets are plagued. Chen et al. (2022) study data-driven, chance-constrained programs in which a decision has to be feasible with high probability under every distribution within a Wasserstein ball centered at the empirical distribution. The authors show that the problem admits an exact deterministic reformulation as a mixed-integer conic program and demonstrate (in numerical experiments) that the reformulation compares favorably to several state-of-the-art data-driven optimization schemes. We provide an exact deterministic reformulation for data-driven, chance-constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ∞ -norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments. Funding: The authors gratefully acknowledge financial support from the Hong Kong Research Grants Council [Early Career Scheme CityU 21502820], the Swiss National Science Foundation [Grant BSCGI0_157733] as well as the Engineering and Physical Sciences Research Council [Grant EP/N020030/1]. [ABSTRACT FROM AUTHOR]

This article explores the significance of Bitcoin halving events within the cryptocurrency ecosystem and their impact on market dynamics. While the existing literature addresses the periods before and after Bitcoin halving, as well as financial bubbles, there is an absence of forecasting regarding Bitcoin price in the time after halving. To address this gap and provide predictions of Bitcoin price development, we conducted a rigorous analysis of past halving events in 2012, 2016, and 2020, focusing on Bitcoin price behaviour before and after each occurrence. What interests us is not only the change in the price level of Bitcoins (top and bottom), but also when this turn occurs. Through synthesizing data and trends from previous events, this article aims to uncover patterns and insights that illuminate the impact of Bitcoin halving on market dynamics and sustainability, movement of the price level, the peaks reached, and price troughs. Our approach involved employing methods such as RSI, MACD, and regression analysis. We looked for the relationship between the price of Bitcoin (top and bottom) and the number of days after the halving. We have uncovered a mathematical model, according to which the next peak will be reached 19 months (in November 2025) and the trough 31 months after Bitcoin halving 2024 (in November 2026). Looking towards the future, this study estimates predictions and expectations for the upcoming Bitcoin halving. These discoveries significantly enhance our understanding of Bitcoin's trajectory and its implications for the finance cryptocurrency market. By offering novel insights into cryptocurrency market dynamics, this study contributes to advancing knowledge in the field and provides valuable information for cryptocurrency markets, investors, and stakeholders. [ABSTRACT FROM AUTHOR]