Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

R Markdown: Integrating A Reproducible Analysis Tool into Introductory Statistics

Nolan and Temple Lang argue that “the ability to express statistical computations is an es- sential skill.” A key related capacity is the ability to conduct and present data analysis in a way that another person can understand and replicate. The copy-and-paste workflow that is an artifact of antiquated user-interface design makes reproducibility of statistical analysis more difficult, especially as data become increasingly complex and statistical methods become increasingly sophisticated. R Markdown is a new technology that makes creating fully-reproducible statistical analysis simple and painless. It provides a solution suitable not only for cutting edge research, but also for use in an introductory statistics course. We present experiential and statistical evidence that R Markdown can be used effectively in introductory statistics courses, and discuss its role in the rapidly-changing world of statistical computation.

A COMPARISON OF MARKET CLEARING TOOLS IN ELECTRICITY SYSTEMS

To maintain a strict balance between demand and supply in the US power systems, the Independent System Operators (ISOs) schedule power plants and determine electricity prices using a market clearing model. This model determines for each time period and power plant, the times of startup, shutdown, the amount of power production, and the provisioning of spinning and non-spinning power generation reserves, etc. Such a deterministic optimization model takes as input the characteristics of all the generating units such as their power generation installed capacity, ramp rates, minimum up and down time requirements, and marginal costs for production, as well as the forecast of intermittent energy such as wind and solar, along with the minimum reserve requirement of the whole system. This reserve requirement is determined based on the likelihood of outages on the supply side and on the levels of error forecasts in demand and intermittent generation. With increased installed capacity of intermittent renewable energy, determining the appropriate level of reserve requirements has become harder. Stochastic market clearing models have been proposed as an alternative to deterministic market clearing models. Rather than using a fixed reserve targets as an input, stochastic market clearing models take different scenarios of wind power into consideration and determine reserves schedule as output. Using a scaled version of the power generation system of PJM, a regional transmission organization (RTO) that coordinates the movement of wholesale electricity in all or parts of 13 states and the District of Columbia, and wind scenarios generated from BPA (Bonneville Power Administration) data, this paper explores a comparison of the performance between a stochastic and deterministic model in market clearing. The two models are compared in their ability to contribute to the affordability, reliability and sustainability of the electricity system, measured in terms of total operational costs, load shedding and air emissions. The process of building the models and running for tests indicate that a fair comparison is difficult to obtain due to the multi-dimensional performance metrics considered here, and the difficulty in setting up the parameters of the models in a way that does not advantage or disadvantage one modeling framework. Along these lines, this study explores the effect that model assumptions such as reserve requirements, value of lost load (VOLL) and wind spillage costs have on the comparison of the performance of stochastic vs deterministic market clearing models.

Lessons from the 2015 earthquake(s) in Nepal: implication for rehabilitation.

PURPOSE: There has been an increase in the number of natural disasters in recent history, and the rate of disability is increasing among survivors. The most recent major natural disaster was the earthquake(s) that occurred in Nepal on 25 April 2015 and 12 May 2015. In total, more than 8500 people were killed and over 18,500 people were left injured. This article aims to demonstrate the role of rehabilitation professionals in post-disaster relief and beyond in Nepal. METHOD: This is an experiential account of physiotherapists present during the earthquake and participating in the post-disaster relief. RESULTS: Rehabilitation professionals played an important role in the acute phase post-disaster by providing essential services and equipment. However, discharge planning emerged as an important role for rehabilitation providers in the early days of post-disaster and signaled a relatively new and innovative function that facilitated the heavy imbalance between little supply and tremendous demand for care. In the coming years, rehabilitation will need to support local initiatives that focus on minimizing the long-term effects among people with a newly acquired disability. CONCLUSIONS: Rehabilitation serves an important role across the continuum in post-disaster relief from the initial stages to the months and years following an event. IMPLICATIONS FOR REHABILITATION: Driven by medical advances in acute field medicine, the relative proportion of casualties following natural disasters is decreasing, while relative rates of disability are rising among survivors. In post-disaster settings, the growing number of people with newly acquired disabilities will be added to the existing proportion of the population who lived with disabilities, creating a significant growth in the total number of people with disabilities (PWDs) in communities that are often ill prepared to provide necessary services. Rehabilitation interventions in the initial stages of emergency humanitarian response can minimize the long-term effects among people with newly acquired disabilities through early activation and prevention of secondary effects. Rehabilitation providers thus appear to have an important mediating effect on outcomes of disabilities in the early stages, but must also be strong partners with PWDs to advocate for social and political change in the long term.