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Despite providing convenience and reducing the travel burden of patients, Video-Conferencing (VC) clinical visits have not enjoyed wide uptake by patients and care providers. It is desired that the medical problems addressed by VC visits can match a face-to-face encounter in scope and quality. Subsequently, VC visits with nurse assistance are emerging; however, the scalable and financially sustainable of such services are unclear. Therefore, we explore the implementability of VC visits with nursing services using a game-theoretic model, and investigate the impact of different pricing schemes (discriminative pricing based on patient characteristics vs. non-discriminative) on patients' care choices between VC and in-person visits. Our results shed light on the "artificial congestion" created by a profit-driven medical institution that hurts patient welfare, and subsequently identify the conditions where the interest of the social planner and the medical institution are aligned. Our results highlight that, compared to a uniform price of VC visits which seems fair, discriminative pricing can be more beneficial for patients and the medical institution alike. This heightens the importance of insurance coverage of telehealth-related services to promote the adoption of telehealth by patients and care providers, and ultimately, improving care access and patient outcomes. [ABSTRACT FROM AUTHOR]

The complexity of current electricity wholesale markets and the increased volatility of electricity prices because of the intermittent nature of renewable generation make independent power producers (IPPs) face significant challenges to submit offers. This challenge increases for those owning traditional coal-fired thermal generators and renewable generation. In this paper, an integrated stochastic optimal strategy is proposed for an IPP using the self-scheduling approach through its participation in both day-ahead and real-time markets (i.e., two-settlement electricity markets) as a price taker. In the proposed approach, the IPP submits an offer for all periods to the day-ahead market for which a multistage stochastic programming setting is explored for providing real-time market offers for each period as a recourse. This strategy has the advantage of achieving overall maximum profits for both markets in the given operational time horizon. Such a strategy is theoretically proved to be more profitable than alternative self-scheduling strategies as it takes advantage of the continuously realized scenario information of the renewable energy output and real-time prices over time. To improve computational efficiency, we explore polyhedral structures to derive strong valid inequalities, including convex hull descriptions for certain special cases, thus strengthening the formulation of our proposed model. Polynomial-time separation algorithms are then established for the derived exponential-sized inequalities to speed up the branch-and-cut process. Finally, both numerical and real case studies demonstrate the potential of the proposed strategy. Summary of Contribution: This paper develops innovative models and methods to study a family of practically important problems via the interactions of operations research and computing. Specifically, this paper provides in-depth analyses of innovative stochastic optimization modeling approaches and develops computationally efficient polyhedral results. The paper also verifies the effectiveness of proposed analyses via extensive computing experiments. [ABSTRACT FROM AUTHOR]

Reducing uplift payments has been a challenging problem for most wholesale markets in the U.S. The main difficulty comes from the discrete decision-making and non-linear objective function in the unit commitment (UC) problem. Recently, the convex hull pricing approach has shown promises to reduce the uplift payments, in which efficient algorithms are available when i) the convex hull description for each unit and ii) the convex envelope for the objective function are available. Following this framework, in this paper, we provide network-flow-based compact extended formulations for each UC considering ramping constraints, different initial statuses, and maximum start-up restrictions. Meanwhile, by using a piece-wise linear approximation of a quadratic cost curve in the objective function, we show that the corresponding piece-wise linear convex envelope converges to the quadratic envelope as the number of pieces increases in the convex hull pricing problem. The final computational experiments on a revised IEEE 118-bus system indicates the effectiveness of the proposed approach. The trade-off between the cost-saving and computational time improvement is also reported as a reference for further usage. [ABSTRACT FROM AUTHOR]

Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time. [ABSTRACT FROM AUTHOR]

With significant economic and environmental benefits, renewable energy is increasingly used to generate electricity. To hedge against the uncertainty due to the increasing penetration of renewable energy, an ancillary service market was introduced to maintain reliability and efficiency, in addition to day-ahead and real-time energy markets. To co-optimize these two markets, a unit commitment problem with regulation reserve (the most common ancillary service product) is solved for daily power system operations, leading to a large-scale and computationally challenging mixed-integer program. In this article, we analyze the polyhedral structure of the co-optimization model to speed up the solution process by deriving problem-specific strong valid inequalities. Convex hull results for certain special cases (i.e., two- and three-period cases) with rigorous proofs are provided, and strong valid inequalities covering multiple periods under the most general setting are derived. We also develop efficient polynomial-time separation algorithms for the inequalities that are in the exponential size. We further tighten the formulation by deriving an extended formulation for each generator in a higher-dimensional space. Finally, we conduct computational experiments to apply our derived inequalities as cutting planes in a branch-and-cut algorithm. Significant improvement from our inequalities over commercial solvers demonstrates the effectiveness of our approach, leading to practical usefulness to enhance the co-optimization of energy and ancillary service markets. [ABSTRACT FROM AUTHOR]

With the increasing penetration of intermittent renewable energy and fluctuating electricity loads, power system operators are facing significant challenges in maintaining system load balance and reliability. In addition to traditional energy markets that are designed to balance power generation and load, ancillary service markets have been recently introduced to help manage the considerable uncertainty by reserving certain generation capacities against unexpected events. In this paper, we develop a multistage stochastic optimization model for system operators to efficiently schedule power-generation assets to co-optimize power generation and regulation reserve service (a critical ancillary service product) under uncertainty. In addition, to improve the computational efficiency of the proposed multistage stochastic integer program, we explore its polyhedral structure by investigating physical characteristics of individual generators, the system-wide requirements that couple all of the generators, and the scenario tree structure for our proposed multistage model. We start with the single-generator polytope and provide convex hull descriptions for the two-period case under different parameter settings. We then provide several families of multiperiod strong valid inequalities linking different scenarios and covering decision variables that represent both power generation and regulation reserve amounts. We further extend our study by exploring the multigenerator polytope and derive strong valid inequalities linking different generators and covering multiple periods. To enhance computational performance, polynomial-time separation algorithms are developed for the exponential number of inequalities. Finally, we verify the effectiveness of our proposed strong valid inequalities by applying them as user cuts under the branch-and-cut scheme to solve multistage stochastic network-constrained power generation scheduling problems. [ABSTRACT FROM AUTHOR]

To increase market transparency, independent system operators (ISOs) have been working on minimizing uplift payments based on convex hull pricing theorems. Along this direction, in this paper, based on the analysis of specific generator features in the Midcontinent ISO (MISO) system, besides reviewing integral formulations for several special cases, we develop two integral formulations of a single generator that can capture these features. We then build a compact convex hull pricing formulation based on these integral formulations, which guarantees to obtain an exact convex hull price by solving a large-scale linear program. Meanwhile, to address the computational challenges caused by the large-scale MISO system, we propose innovative iterative algorithms with convergence properties, plus a complementary algorithm, to obtain an approximated convex hull price. The case studies on MISO instances with and without transmission constraints indicate that our algorithms lead to an exact convex hull price for all numerical studies and, the solutions can be obtained within 20 minutes. [ABSTRACT FROM AUTHOR]

As a consequence of industrial development, large quantities of hazardous materials are shipped everyday. Most related studies consider the risks as fixed weights on edges. However, the loads of the vehicles are important factors about the risks. Thus, considering the risks as fixed parameters cannot reflect actual practice. In addition, the vehicle routing models in previous studies simultaneously minimize the total transportation cost and the total risk. However, simply considering the total risk of a fleet as a whole cannot evaluate each vehicle's risk. Although the total risk is low, the risk of a specific vehicle may still be very high. In this paper, the actual load dependent risk is introduced, and a corresponding bi-objective vehicle routing model for hazardous materials transportation is developed, minimizing the maximum risk of vehicles and the total transportation cost simultaneously. An exact algorithm is developed based on the $\varepsilon $ -constraint method with several improvements. For large-scale problems, an approximation approach is proposed. Computational experiments on a series of instances are reported and several managerial insights are derived from the sensitivity analysis. [ABSTRACT FROM AUTHOR]

In this letter, we describe and develop edge-based and node-based formulations for combined-cycle units (CCUs) with different levels of accuracy in respect of the physical constraints of each turbine, from no requirement to partially and fully respecting all physical constraints, including min-up/-down time, capacity, and ramping constraints. We develop corresponding models for independent system operators (ISOs) and vertically integrated utilities (VIUs), respectively. These models demonstrate complexity in terms of the size of decision variables and show the tradeoff between accuracy and computational complexity. To the best of our knowledge, this letter provides one of the first models that can capture both configuration transition restrictions and all the physical constraints of each turbine within CCUs, for both ISOs and VIUs. [ABSTRACT FROM AUTHOR]

Recently, increasing penetration of renewable energy generation has created challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete decisions of each generation unit. Among all aspects to be considered, a unit commitment polytope is fundamental and embedded in the models at different stages of power system planning and operations. In this article, we focus on deriving polynomial-time algorithms for the unit commitment problems with a general convex cost function and piecewise linear cost function, respectively. We refine an time, where T represents the number of time periods, algorithm for the deterministic single-generator unit commitment problem with a general convex cost function and accordingly develop an extended formulation in a higher-dimensional space that can provide an integral solution, in which the physical meanings of the decision variables are described. This means the original problem can be solved as a convex program instead of a mixed-integer convex program. Furthermore, for the case in which the cost function is piecewise linear, by exploring the optimality conditions, we derive more efficient algorithms for both deterministic (i.e., time) and stochastic (i.e., time, where N represents the number of nodes in the stochastic scenario tree) single-generator unit commitment problems. We also develop the corresponding extended formulations for both deterministic and stochastic single-generator unit commitment problems that solve the original mixed-integer linear programs as linear programs. Similarly, physical meanings of the decision variables are explored to show the insights of the new modeling approach. [ABSTRACT FROM AUTHOR]

With fewer emissions, higher efficiency, and quicker response than traditional coal-fired thermal power plants, the combined-cycle units (CCUs), as gas-fired generators, have been increasingly adapted in the U.S. power system to enhance the smart grids operations. Meanwhile, due to the inherent uncertainties in the deregulated electricity market, e.g., intermittent renewable energy output, unexpected outages of generators and transmissions, and fluctuating electricity demands, the electricity price is volatile. As a result, this brings challenges for an independent power producer (served in the self-scheduling mode) owning CCUs to maximize the total profit when facing the significant price uncertainties. In this paper, a data-driven risk-averse stochastic self-scheduling approach is presented for the CCUs that participate in the real-time market. The proposed approach does not require the specific distribution of the uncertain real-time price. Instead, a confidence set for the unknown distribution is constructed based on the historical data. The conservatism of the proposed approach is adjustable based on the amount of available data. Finally, numerical studies show the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

In this article, we study a two-level lot-sizing problem with supplier selection (LSS), which is an NP-hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet-defining. We show numerically that incorporating these valid inequalities within a branch-and-cut framework leads to significant improvements in computation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 647-666, 2017 [ABSTRACT FROM AUTHOR]

Due to the sustainable nature and stimulus plans from government, renewable energy (such as wind and solar) has been increasingly used in power systems. However, the intermittency of renewable energy creates challenges for power systemoperators to keep the systems reliable and cost-effective. In addition, information about renewable energy is usually incomplete. Instead of knowing the true probability distribution of the renewable energy course, only a set of historical data samples can be collected from the true (while ambiguous) distribution. In this article, we study two risk-averse stochastic unit commitment models with incomplete information: the first model being a chance-constrained unit commitment model and the second one a two-stage stochastic unit commitment model with recourse. Based on historical data on renewable energy, we construct a confidence set for the probability distribution of the renewable energy and propose data-driven stochastic unit commitment models to hedge against the incomplete nature of the information. Our models also ensure that, with a high probability, a large portion of renewable energy is utilized. Furthermore, we develop solution approaches to solve the models based on deriving strong valid inequalities and Benders'decomposition algorithms. We show that the risk-averse behavior of both models decreases as more data samples are collected and eventually vanishes as the sample size goes to infinity. Finally, our case studies verify the effectiveness of our proposed models and solution approaches. [ABSTRACT FROM AUTHOR]

Considering recent development of deregulated energy markets and the intermittent nature of renewable energy generation, it is important for power system operators to ensure cost effectiveness while maintaining the system reliability. To achieve this goal, significant research progress has recently been made to develop stochastic optimization models and solution methods to improve reliability unit commitment run practice, which is used in the day-ahead market for ISOs/RTOs to ensure sufficient generation capacity available in real time to accommodate uncertainties. Most stochastic optimization approaches assume the renewable energy generation amounts follow certain distributions. However, in practice, the distributions are unknown and instead, a certain amount of historical data are available. In this research, we propose a data-driven risk-averse stochastic unit commitment model, where risk aversion stems from the worst-case probability distribution of the renewable energy generation amount, and develop the corresponding solution methods to solve the problem. Given a set of historical data, our proposed approach first constructs a confidence set for the distributions of the uncertain parameters using statistical inference and solves the corresponding risk-averse stochastic unit commitment problem. Then, we show that the conservativeness of the proposed stochastic program vanishes as the number of historical data increases to infinity. Finally, the computational results numerically show how the risk-averse stochastic unit commitment problem converges to the risk-neutral one, which indicates the value of data. [ABSTRACT FROM PUBLISHER]

As the number of combined-cycle units increases, efficient modeling approaches for these units play important roles for independent system operators (ISOs). Based on various combinations of combustion turbines (CTs) and steam turbines (STs), the combined-cycle unit could work at different configurations (modes) with different efficiencies. In this paper, we propose an edge-based formulation for the combined-cycle units in the unit commitment problem to improve the accuracy and effectiveness of current modeling approaches. Our formulation can 1) clearly describe the transition processes among different configurations so as to satisfy the ISO financial offer submission requirements and (2) capture physical constraints of each turbine, including the exact min-up/down time and time dependent startup cost, in the combined-cycle units so as to increase the operational flexibility while ensuring system feasibility. This model fits well with the current U.S. deregulated electricity market. The final numerical studies show that our approaches perform better than the current configuration-based modeling approach. [ABSTRACT FROM AUTHOR]

In this paper, we derive a strengthened MILP formulation for certain gas turbine unit commitment problems, in which the ramping rates are no smaller than the minimum generation amounts. This type of gas turbines can usually start-up faster and have a larger ramping rate, as compared to the traditional coal-fired power plants. Recently, the number of this type of gas turbines increases significantly due to affordable gas prices and their scheduling flexibilities to accommodate intermittent renewable energy generation. In this study, several new families of strong valid inequalities are developed to help reduce the computational time to solve these types of problems. Meanwhile, the validity and facet-defining proofs are provided for certain inequalities. Finally, numerical experiments on a modified IEEE 118-bus system and the power system data based on recent studies verify the effectiveness of applying our formulation to model and solve this type of gas turbine unit commitment problems, including reducing the computational time to obtain an optimal solution or obtaining a much smaller optimality gap, as compared to the default CPLEX, when the time limit is reached with no optimal solutions obtained. [ABSTRACT FROM AUTHOR]

This paper proposes an expected value and chance constrained stochastic optimization approach for the unit commitment problem with uncertain wind power output. In the model, the utilization of wind power can be adjusted by changing the utilization rate in the proposed expected value constraint. Meanwhile, the chance constraint is used to restrict the probability of load imbalance. Then a Sample Average Approximation (SAA) method is used to transform the objective function, the expected value constraint, and the chance constraint into sample average reformulations. Furthermore, a combined SAA framework that considers both the expected value and the chance constraints is proposed to construct statistical upper and lower bounds for the optimization problem. Finally, the performance of the proposed algorithm with different utilization rates and different risk levels is tested for a six-bus system. A revised IEEE 118-bus system is also studied to show the scalability of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

The electricity price volatility brings challenges to bidding strategies in the electricity markets. In this paper, we propose a minimax regret approach for a market participant to obtain an optimal bidding strategy and the corresponding self-scheduled generation plans. Motivated by recently proposed robust optimization approaches, our approach relies on the confidence intervals of price forecasts rather than point estimators. We reformulate the minimax regret model as a mixed-integer linear program (MILP), and solve it by the Benders' decomposition algorithm. Moreover, we design a bidding strategy based on the price forecast confidence intervals to generate the offer curve. Finally, we numerically test the minimax regret approach, in comparison with the robust optimization approach, on three types of thermal generators by using real electricity price data from PJM to verify the effectiveness of our proposed approach. [ABSTRACT FROM PUBLISHER]

Due to increasing penetration of intermittent renewable energy and introduction of demand response programs, uncertainties occur in both supply and demand sides in real time for the current power grid system. To address these uncertainties, most ISOs/RTOs perform reliability unit commitment runs after the day-ahead financial market to ensure sufficient generation capacity available in real time to accommodate uncertainties. Two-stage stochastic unit commitment and robust unit commitment formulations have been introduced and studied recently to provide day-ahead unit commitment decisions. However, both approaches have limitations: 1) computational challenges due to the large scenario size for the stochastic optimization approach and 2) conservativeness for the robust optimization approach. In this paper, we propose a novel unified stochastic and robust unit commitment model that takes advantage of both stochastic and robust optimization approaches, that is, this innovative model can achieve a low expected total cost while ensuring the system robustness. By introducing weights for the components for the stochastic and robust parts in the objective function, system operators can adjust the weights based on their preferences. Finally, a Benders' decomposition algorithm is developed to solve the model efficiently. The computational results indicate that this approach provides a more robust and computationally trackable framework as compared with the stochastic optimization approach and a more cost-effective unit commitment decision as compared with the robust optimization approach. [ABSTRACT FROM PUBLISHER]