Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies

Real-time Tactical and Strategic Sales Management for Intelligent Agents Guided By Economic Regimes

Many enterprises that participate in dynamic markets need to make product pricing and inventory resource utilization decisions in real-time. We describe a family of statistical models that address these needs by combining characterization of the economic environment with the ability to predict future economic conditions to make tactical (short-term) decisions, such as product pricing, and strategic (long-term) decisions, such as level of finished goods inventories. Our models characterize economic conditions, called economic regimes, in the form of recurrent statistical patterns that have clear qualitative interpretations. We show how these models can be used to predict prices, price trends, and the probability of receiving a customer order at a given price. These “regime†models are developed using statistical analysis of historical data, and are used in real-time to characterize observed market conditions and predict the evolution of market conditions over multiple time scales. We evaluate our models using a testbed derived from the Trading Agent Competition for Supply Chain Management (TAC SCM), a supply chain environment characterized by competitive procurement and sales markets, and dynamic pricing. We show how regime models can be used to inform both short-term pricing decisions and longterm resource allocation decisions. Results show that our method outperforms more traditional shortand long-term predictive modeling approaches.dynamic pricing;trading agent competition;agent-mediated electronic commerce;dynamic markets;economic regimes;enabling technologies;price forecasting;supply-chain

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Using Approximate Dynamic Programming to Solve the Stochastic Demand Military Inventory Routing Problem with Direct Delivery

A brigade combat team must resupply forward operating bases (FOBs) within its area of operations from a central location, mainly via ground convoy operations, in a way that closely resembles vendor managed inventory practices. Military logisticians routinely decide when and how much inventory to distribute to each FOB. Technology currently exists that makes utilizing cargo unmanned aerial vehicles (CUAVs) for resupply an attractive alternative due to the dangers of utilizing convoy operations. However, enemy actions, austere conditions, and inclement weather pose a significant risk to a CUAV\u27s ability to safely deliver supplies to a FOB. We develop a Markov decision process model that allows for multiple supply classes to examine the military inventory routing problem, explicitly accounting for the possible loss of CUAVs during resupply operations. The large size of the motivating problem instance renders exact dynamic programming techniques computationally intractable. To overcome this challenge, we employ approximate dynamic programming (ADP) techniques to obtain high-quality resupply policies. We employ an approximate policy iteration algorithmic strategy that utilizes least squares temporal differencing for policy evaluation. We construct a representative problem instance based on an austere combat environment in order to demonstrate the efficacy of our model formulation and solution methodology. Because our ADP algorithm has many tunable features, we perform a robust, designed computational experiment to determine the ADP policy with the best quality of solutions. Results indicate utilizing least squares temporal differences with a first-order basis function is insufficient to approximate the value function when stochastic demand and penalty functions are implemented

Sample-path solutions for simulation optimization problems and stochastic variational inequalities

inequality;simulation;optimization

Rational Decision-Making in Business Organizations

Lecture to the memory of Alfred Nobel, December 8, 1978decision making;