Using Column Generation to Solve Extensions to the Markowitz Model

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such type of problems using a method similar to column generation. In this scheme, the original problem is restricted to a subset of the assets resulting in a master convex quadratic problem. Then the dual information of the master problem is used in a sub-problem to propose more assets to consider. We also consider other extensions to the Markowitz model to diversify the portfolio selection within the given intervals for active weights.Comment: 16 pages, 3 figures, 2 tables, 1 pseudocod

Optimal sales-mix and generation plan in a two-stage electricity market

A bi-level stochastic programming problem is used to model the optimal decision of a risk averse electricity producer, interacting in a two-stage market with cost minimizer competitors. His decision variables include the distribution of production (which plant of different technologies and variable costs to operate) and the sales-mix (how much generation to commit to bilateral contracts and spot market). To enhance computation times, the bi-level problem is transformed into a Mixed-Integer Linear Problem (MILP) by applying sophisticated linearization techniques. Electricity demand, Renewable Energy Sources (RES) generation and production costs are different sources of uncertainty. A copula method is used to generate scenarios under different correlations values (between RES generation and demand), to analyze the impact of correlation on the optimal solution. The model is tested through extensive numerical simulations based on data from the Spanish electricity market. The results show that correlation and risk aversion have a relevant impact on how sales-mix and generation plan decisions should combine optimally

A Model of Total Factor Productivity Built on Hayek’s View of Knowledge: What Really Went Wrong with Socialist Planned Economies?

Because Hayek’s view goes beyond the Walrasian framework, his descriptive arguments on socialist planned economies are prone to be misunderstood. This paper clarifies Hayek’s arguments by using them as a basis to construct a model of total factor productivity. The model shows that productivity depends substantially on the intelligence of ordinary workers. The model indicates that the essential reason for the reduced productivity of a socialist economy is that, even though human beings are imperfect and do not know everything about the universe, they are able to utilize their intelligence to innovate. Decentralized market economies are far more productive than socialist economies because they intrinsically can fully utilize human beings’ intelligence, but socialist planned economies cannot, in large part because of the imagined perfect central planning bureau that does not exist.Hayek; Market economy; Socialist planned economy; Total factor productivity; Innovation; Experience curve effect; China

Market based compensation, price informativeness and short-term trading

This paper shows that there is a natural trade-off when designing market based executive compensation. The benefit of market based pay is that the stock price aggregates speculators’ dispersed information and there-fore takes a picture of managerial performance before the long-term value of a firm materializes. The cost is that informed speculators’ willingness to trade depends on trading that is unrelated to any information about the firm. Ideally, the CEO should be shielded from shocks that are not informative about his actions. But since information trading is impossible without non- nformation trading (due to the ”no-trade” theorem), shocks to prices caused by the latter are an unavoidable cost of market based pay. This trade-off generates a number of insights about the impact of market conditions, e.g. liquidity and trading horizons, on optimal market based pay. A more liquid market leads to more market based pay while short-term trading makes it more costly to provide such incentives leading to lower CEO effort and worse firm performance on average. The model is consistent with recent evidence showing that market based CEO incentives vary with market conditions, e.g. bid-ask spreads, the probability of informed trading (PIN) or the dispersion of analysts’ forecasts. JEL Classification: G39, D86, D82Executive compensation, liquidity, Moral Hazard, stock price informativeness, trading

Reliability standards for the operation and planning of future electricity networks

Electricity networks, designed and operated in accordance with the historic deterministic standards, have broadly delivered secure and reliable supplies to customers. A key issue regarding their evolution is how the operation and planning standards should evolve to make efficient use of the existing assets while taking advantage of emerging, non-network (or non-wires) technologies. Deployment of the smart grid will require fundamental changes in the historical principles used for network security in order to ensure that integration of low-carbon generation is undertaken as efficiently as possible through the use of new information and communication technology (ICT), and new flexible network technologies that can maximize utilization of existing electricity infrastructure. These new technologies could reduce network redundancy in providing security of supply by enabling the application of a range of advanced, technically effective, and economically efficient corrective (or post-fault) actions that can release latent network capacity of the existing system. In this context, this paper demonstrates that historical deterministic practices and standards, mostly developed in the 1950s, should be reviewed in order to take full advantage of new emerging technologies and facilitate transition to a smart grid paradigm. This paper also demonstrates that a probabilistic approach to developing future efficient operating and design strategies enabled by new technologies, will appropriately balance network investment against non-network solutions while truly recognizing effects of adverse weather, common-mode failures, high-impact low-probability events, changing market prices for pre- and post-contingency actions, equipment malfunctioning, etc. This clearly requires explicit consideration of the likelihood of various outages (beyond those considered in deterministic studies) and quantification of their impacts on alternative network operation and investment decisions, which cannot be undertaken in a deterministic, “one size fits all” framework. In this context, we developed advanced optimization models aimed at determining operational and design network decisions based on both deterministic and probabilistic security principles. The proposed models can recognize network constraints/congestion and various operational measures (enabled by new technologies) composed of preventive and corrective control actions such as operation of special protection schemes, demand side response and generation reserve utilization and commitment, considering potential outages of network and generation facilities. The probabilistic model proposed can also provide targeted levels of reliability and limit exposure to severe low probability events (mainly driven by natural hazards) through the use of Conditional Value at Risk (CVaR) constraints, delivering robust and resilient supplies to consumers at the minimum cost. Through various case studies conducted on the Great Britain (GB) power network, we set out the key questions that need to be addressed in support of the change in network reliability paradigm, provide an overview of the key modelling approaches proposed for assessing the risk profile of operation of future networks, propose a framework for a fundamental review of the existing network security standards, and set out challenges for assessing the reliability and economics of the operation of future electricity network

Stochastic equilibrium models for generation capacity expansion

Capacity expansion models in the power sector were among the first applications of operations research to the industry. The models lost some of their appeal at the inception of restructuring even though they still offer a lot of possibilities and are in many respect irreplaceable provided they are adapted to the new environment. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then take up different questions raised by the new environment. Some are due to developments of the industry like demand side management: an optimization framework has difficulties accommodating them but the more general equilibrium paradigm offers additional possibilities. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context. Specifically we consider the use of plant specific discount rates that we derive by including stochastic discount rates in the equilibrium model. Linear discount factors only price systematic risk. We therefore complete the discussion by inserting different risk functions (for different agents) in order to account for additional unpriced idiosyncratic risk in investments. These different models can be cast in a single mathematical representation but they do not have the same mathematical properties. We illustrate the impact of these phenomena on a small but realistic example.capacity adequacy, risk functions, stochastic equilibrium models, stochastic discount factors

Review of trends and targets of complex systems for power system optimization

Optimization systems (OSs) allow operators of electrical power systems (PS) to optimally operate PSs and to also create optimal PS development plans. The inclusion of OSs in the PS is a big trend nowadays, and the demand for PS optimization tools and PS-OSs experts is growing. The aim of this review is to define the current dynamics and trends in PS optimization research and to present several papers that clearly and comprehensively describe PS OSs with characteristics corresponding to the identified current main trends in this research area. The current dynamics and trends of the research area were defined on the basis of the results of an analysis of the database of 255 PS-OS-presenting papers published from December 2015 to July 2019. Eleven main characteristics of the current PS OSs were identified. The results of the statistical analyses give four characteristics of PS OSs which are currently the most frequently presented in research papers: OSs for minimizing the price of electricity/OSs reducing PS operation costs, OSs for optimizing the operation of renewable energy sources, OSs for regulating the power consumption during the optimization process, and OSs for regulating the energy storage systems operation during the optimization process. Finally, individual identified characteristics of the current PS OSs are briefly described. In the analysis, all PS OSs presented in the observed time period were analyzed regardless of the part of the PS for which the operation was optimized by the PS OS, the voltage level of the optimized PS part, or the optimization goal of the PS OS.Web of Science135art. no. 107