A randomized concave programming method for choice network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular in assortment optimization and revenue management. The dynamic program for these models is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper we propose a new approach called SDCP to solving CDLP based on segments and their consideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound on the dynamic program but coincides with CDLP for the case of non-overlapping segments. If the number of elements in a consideration set for a segment is not very large (SDCP) can be applied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by (i) simulations, called the randomized concave programming (RCP) method, and (ii) by adding cuts to a recent compact formulation of the problem for a latent multinomial-choice model of demand (SBLP+). This latter approach turns out to be very effective, essentially obtaining CDLP value, and excellent revenue performance in simulations, even for overlapping segments. By formulating the problem as a separation problem, we give insight into why CDLP is easy for the MNL with non-overlapping considerations sets and why generalizations of MNL pose difficulties. We perform numerical simulations to determine the revenue performance of all the methods on reference data sets in the literature.assortment optimization, randomized algorithms, network revenue management.

Dynamic Capacity Control in Air Cargo Revenue Management

This book studies air cargo capacity control problems. The focus is on analyzing decision models with intuitive optimal decisions as well as on developing efficient heuristics and bounds. Three different models are studied: First, a model for steering the availability of cargo space on single legs. Second, a model that simultaneously optimizes the availability of both seats and cargo capacity. Third, a decision model that controls the availability of cargo capacity on a network of flights

Distributed Stochastic Market Clearing with High-Penetration Wind Power

Integrating renewable energy into the modern power grid requires risk-cognizant dispatch of resources to account for the stochastic availability of renewables. Toward this goal, day-ahead stochastic market clearing with high-penetration wind energy is pursued in this paper based on the DC optimal power flow (OPF). The objective is to minimize the social cost which consists of conventional generation costs, end-user disutility, as well as a risk measure of the system re-dispatching cost. Capitalizing on the conditional value-at-risk (CVaR), the novel model is able to mitigate the potentially high risk of the recourse actions to compensate wind forecast errors. The resulting convex optimization task is tackled via a distribution-free sample average based approximation to bypass the prohibitively complex high-dimensional integration. Furthermore, to cope with possibly large-scale dispatchable loads, a fast distributed solver is developed with guaranteed convergence using the alternating direction method of multipliers (ADMM). Numerical results tested on a modified benchmark system are reported to corroborate the merits of the novel framework and proposed approaches.Comment: To appear in IEEE Transactions on Power Systems; 12 pages and 9 figure

Dynamic Capacity Control in Air Cargo Revenue Management

This book studies air cargo capacity control problems. The focus is on analyzing decision models with intuitive optimal decisions as well as on developing efficient heuristics and bounds. Three different models are studied: First, a model for steering the availability of cargo space on single legs. Second, a model that simultaneously optimizes the availability of both seats and cargo capacity. Third, a decision model that controls the availability of cargo capacity on a network of flights

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small

Bidding Strategy for Networked Microgrids in the Day-Ahead Electricity Market

In recent years, microgrids have drawn increasing attention from both academic and industrial sectors due to their enormous potential benefits to the power systems. Microgrids are essentially highly-customized small-scale power systems. Microgrids’ islanding capability enables microgrids to conduct more flexible and energy-efficient operations. Microgrids have proved to be able to provide reliable and environmental-friendly electricity to quality-sensitive or off-grid consumers. In addition, during the grid-connected operation mode, microgrids can also provide support to the utility grid. World-widely continuous microgrid deployments indicate a paradigm shift from traditional centralized large-scale systems toward more distributed and customized small-scale systems. However, microgrids can cause as many problems as it solves. More efforts are needed to address these problems caused by microgrids integration. Considering there will be multiple microgrids in future power systems, the coordination problems between individual microgrids remain to be solved. Aiming at facilitating the promotion of microgrids, this thesis investigates the system-level modeling methods for coordination between multiple microgrids in the context of participating in the market. Firstly, this thesis reviews the background and recent development of microgrid coordination models. Problems of existing studies are identified. Motivated by these problems, the research objectives and structure of this thesis are presented. Secondly, this thesis examines and compares the most common frameworks for optimization under uncertainty. An improved unit commitment model considering uncertain sub-hour wind power ramp behaviors is presented to illustrate the reformulation and solution method of optimization models with uncertainty. Next, the price-maker bidding strategy for collaborative networked microgrids is presented. Multiple microgrids are coordinated as a single dispatchable entity and participate in the market as a price-maker. The market-clearing process is modeled using system residual supply/demand price-quota curves. Multiple uncertainty sources in the bidding model are mitigated with a hybrid stochastic-robust optimization framework. What’s more, this thesis further considers the privacy concerns of individual microgrids in the coordination process. Therefore a privacy-preserving solution method based on Dantzig-Wolfe decomposition is proposed to solve the bidding problem. Both computational and economic performances of the proposed model are compared with the performances of conventional centralized coordination framework. Lastly, this thesis provides suggestions on future research directions of coordination problems among multiple microgrids