Soumyadip Ghosh

Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves

Consider a marketplace operated by a buyer who wishes to procure large quantities of several heterogeneous products. Suppliers submit price curves for each of the commodities indicating the price charged as a function of the supplied quantity. The total amount paid to a supplier is the sum of the prices charged for the individual commodities. It is assumed that the submitted supply curves are piecewise linear as they often are in practice. The bid evaluation problem faced by the procurer is to determine how much of each commodity to buy from each of the suppliers so as to minimize the total purchase price. In addition to meeting the demand, the buyer may impose additional business requirements that restrict which contracts suppliers may be awarded. These requirements may result in interdependencies between the commodities which lead to suboptimal results if the commodities are traded in independent auctions rather than simultaneously. Even without the additional business constraints the bid evaluation problem is NP-hard. The main contribution of our study is a flexible column generation based heuristics that provides near-optimal solutions to the procurer’s bid evaluation problem. Our method scales very well due to the Branch-and-Price technology it is built on. We employ sophisticated rounding and local improvement heuristics to obtain quality solutions. We also developed a test data generator that produces realistic problems and allows control over the difficulty level of the problems using parameters.

Chessboard Distributions and Random Vectors with Specified Marginals and Covariance Matrix

There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models.Moti vated by this need, several authors have explored the generation of random vectors with specified marginals, together with a specified covariance matrix, through the use of a transformation of a multivariate normal random vector (the NORTA method).A covariance matrix is said to be feasible for a given set of marginal distributions if a random vector exists with these characteristics. We develop a computational approach for establishing whether a given covariance matrix is feasible for a given set of marginals. The approach is used to rigorously establish that there are sets of marginals with feasible covariance matrix that the NORTA method cannot match. In such cases, we show how to modify the initialization phase of NORTA so that it will exactly match the marginals, and approximately match the desired covariance matrix.An important feature of our analysis is that we show that for almost any covariance matrix (in a certain precise sense), our computational procedure either explicitly provides a construction of a random vector with the required properties, or establishes that no such random vector exists.

Integration of demand response and renewable resources for power generation management

A single-period optimal dispatching problem is considered for a network of energy utilities connected via multiple transmission lines, where we seek to find the lowest operationalcost dispatching of various energy sources to satisfy demand. Our model includes traditional thermal resources and renewable energy resources available generation capabilities within the grid. A key novel addition is the consideration of demand reduction as a virtual generation source that can be dispatched quickly to hedge against the risk of unforeseen shortfall in supply. Demand reduction is dispatched in response to incentive signals sent to consumers. The control options of our optimization model consist of the dispatching order and dispatching amount of the thermal generators together with the rebate signals sent to end-users at each node of the network under a simple demand response policy. Numerical experiments based on our analysis of representative data are presented to illustrate the effectiveness of demand response as a hedging option.

Simulating distribution of emergency relief supplies for disaster response operations

In the event of disasters such as hurricanes, earthquakes and terrorism, emergency relief supplies need be distributed to disaster victims in timely manner to protect the health and lives of the victims. We develop a modeling framework for disaster response where the supply chain of relief supplies and distribution operations are simulated, and analytics for the optimal transportation of relief supplies to various POD (Points of Distribution) are tested. Our simulation model of disaster response includes modeling the supply chain of relief supplies, distribution operations at PODs, dynamics of demand, and progression of disaster. Our analytics optimize the dispatch of relief supplies to PODs and cross-leveling among PODs. Their effectiveness is estimated by the simulation model. The model can evaluate a wide range of disaster scenarios, assess existing disaster response plans and policies, and identify better approaches for government agencies and first responders to prepare for and respond to disasters.

Fully decentralized AC optimal power flow algorithms

Motivated by the increasing complexity in the control of distribution level electric power systems especially in a smart grid environment, we propose fully decentralized algorithms to solve alternating current (AC) optimal power flow (OPF) problems. The key feature of the proposed algorithms is a complete decentralization of computation down to nodal level. In this way, no central or sub-area controller is needed, and the OPF problem is solved by individual nodes, which only have local knowledge of the system. Preliminary results show promising performance of the fully decentralized algorithms.

Incentive Design for Lowest Cost Aggregate Energy Demand Reduction

We design an optimal incentive mechanism offered to energy customers at multiple network levels, e.g., distribution and feeder networks, with the aim of determining the lowest-cost aggregate energy demand reduction. Our model minimizes a utilitys total cost for this mode of virtual demand generation, i.e., demand reduction, to achieve improvements in both total systemic costs and load reduction over existing mechanisms. We assume the utility can predict with reasonable accuracy the average load reduction response of end-users with respect to rebates by observing and learning from their past behavior. Within a single period formulation, we propose a heuristic policy that segments the customers according to their likelihood of reducing load. Within a multi-period formulation, we observe that customers who are more willing to reduce their aggregate demand over the entire horizon, rather than simply shifting their load to off-peak periods, tend to receive higher incentives, and vice versa.

A two-stage non-linear program for optimal electrical grid power balance under uncertainty

We propose a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Each stage models dispatching and transmission decisions that are made on subsequent time periods. Certain generation decisions are made only in the first stage and the second stage realizes the actual renewable generation, where the uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using extra, high marginal-cost power sources that can be tapped in short order. We propose two outer approximation algorithms to solve this nonconvex optimization problem to optimality. We show that under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. Numerical experiments for a variety of parameter settings were carried out to indicate the efficiency and usability of this method of large practical instances.

Chapter 5 Multivariate Input Processes

Abstract Representing uncertainty in a simulation study is referred to as input modeling, and is often characterized as selecting probability distributions to represent the input processes. This is a simple task when the input processes can be represented as sequences of independent random variables with identical distributions. However, dependent and multivariate input processes occur naturally in many service, communications, and manufacturing systems. This chapter focuses on the development of multivariate input models which incorporate the interactions and interdependencies among the inputs for the stochastic simulation of such systems.

Power generation management under time-varying power and demand conditions

A multi-period optimal power dispatching problem is considered for a network of energy utilities connected via multiple transmission lines, where the goal is to find the lowest operational-cost dispatching of diverse generation sources to satisfy demand over a time horizon comprised of multiple periods, and consisting of varying power and demand conditions. Our model captures various interactions among the time-varying periods including which generators should be allocated, when they should be brought into use, and the operational costs associated with each. An efficient algorithm is derived that exploits the structure inherent in this multi-period economic dispatch problem. The control options of our optimization model consist of the dispatching order and dispatching amount of available power generators. Our solutions are shown to be globally optimal under conditions that often arise in practice. Numerical experiments based on these solutions and analysis are presented to illustrate our findings.

A Framework for the Analysis of Probabilistic Demand Response Schemes

We describe the class of probabilistic demand response (PDR) schemes, which are particularly suited for dynamic load management in the residential sector. Our main contribution is a new methodology for implementing and analyzing these schemes based on an operational objective function that balances the total cost of meeting demand, which includes the costs of supply generation, and spinning reserves, with the total revenue from the met demand and the gain from storage/deferment. We derive structural results for the design of PDR schemes in terms of sufficient conditions that yield a well-posed joint optimization problem for the two decision variables: the planned supply generation level and the real-time PDR signal magnitude. These results are used to evaluate the suitability of various proposed PDR schemes in single-period and multiple-period contexts. Finally, using simulations, we illustrate the application and effectiveness of the proposed methodology for a collection of thermostatically-controlled residential loads.