Accuracy of Numerical Solution to Dynamic Programming Models

Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.Research Methods/ Statistical Methods,

Using a multifrontal sparse solver in a high performance, finite element code

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation.

Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function. This nonparametric technique has been employed in a number of empirical studies including the state-price density estimation pioneered by Aït-Sahalia and Lo (1998). However, the widespread usefulness of multivariate kernel regression has been limited by the difficulty in computing a data-driven bandwidth. In this paper, we present a Bayesian approach to bandwidth selection for multivariate kernel regression. A Markov chain Monte Carlo algorithm is presented to sample the bandwidth vector and other parameters in a multivariate kernel regression model. A Monte Carlo study shows that the proposed bandwidth selector is more accurate than the rule-of-thumb bandwidth selector known as the normal reference rule according to Scott (1992) and Bowman and Azzalini (1997). The proposed bandwidth selection algorithm is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow-Debreu securities. When applying the proposed method to the S&P 500 index options and the DAX index options, we find that for short-maturity options, the proposed Bayesian bandwidth selector produces an obviously different state-price density from the one produced by using a subjective bandwidth selector discussed in Aït-Sahalia and Lo (1998).Black-Scholes formula, Likelihood, Markov chain Monte Carlo, Posterior density.

Managerial Compensation in Midwestern Cooperatives: Results from a Follow-up Study

Results are presented from a follow-up survey of managerial compensation practices in local farm supply and marketing cooperatives in Minnesota, North Dakota, and Wisconsin. In contrast to findings from the original survey, total compensation levels, bonuses, and changes in compensation are all found to be positively and significantly associated with local net margin and not closely related to sales and sales growth.Agribusiness,

CHANGES IN RETAIL FOOD DELIVERY: SIGNALS FOR PRODUCERS, PROCESSORS AND DISTRIBUTORS

This paper contains two chapters related to changes in retail food delivery and sales. The first discusses trends in consumer demographics and lifestyles and how these continue to drive changes in the way food is prepared and delivered to consumers. Retail stores are responding with new formats: providing more ready to eat foods; more convenient store layouts; lower prices and better service in niche markets across the country. Their demands send signals up the food chain to processors and producers that alter their production and inventory decisions. Electronic information technology speeds these changes and leads to more efficient operation with, allegedly, better service for consumers. The second chapter discusses how advances in information technology affect not only the internal business operations in food firms throughout the food supply chain but also how the product flows and how businesses link their processes together. The reengineering of the food supply chain by way of an industry-wide initiative called "efficient consumer response" (ECR) is explained and analyzed for its motivations and implementation, thus far. The many facets of ECR such as product replenishment and promotion are discussed. Lessons learned from ECR include that it is possible to accommodate the coexistence of firms of various sizes and types, and that the role of trade associations in facilitating industry-wide changes is vital and impressive.Agribusiness, Industrial Organization,

THE SUPERMARKET INDUSTRY AT THE START OF THE 21st CENTURY: KEY FINDINGS FROM THE 2000 SUPERMARKET PANEL

The 2000 Supermarket Panel gathered data on store characteristics, management practices, and operating performance from a representative, nation-wide sample of supermarkets. The Panel is unique because the unit of analysis is the individual store, and the same stores will be surveyed over time. Linking information on management practices and store and market characteristics with measures for key performance measures provides useful information for both strategic and tactical decisions. Descriptive findings are presented for stores groups by ownership group size and format. Results from a multivariate analysis of relationships between store performance and key performance drivers also are presented.Agribusiness,

The dynamism of salt crust patterns on playas

Playas are common in arid environments and can be major sources of mineral dust that can influence global climate. These landforms typically form crusts that limit evaporation and dust emission, modify surface erosivity and erodibility, and can lead to over prediction or under prediction of (1) dust-emission potential and (2) water and heat fluxes in energy balance modeling. Through terrestrial laser scanning measurements of part of the Makgadikgadi Pans of Botswana (a Southern Hemisphere playa that emits significant amounts of dust), we show that over weeks, months, and a year, the shapes of these surfaces change considerably (ridge thrusting of >30 mm/week) and can switch among continuous, ridged, and degraded patterns. Ridged pattern development changes the measured aerodynamic roughness of the surface (as much as 3 mm/week). The dynamic nature of these crusted surfaces must be accounted for in dust entrainment and moisture balance formulae to improve regional and global climate models

Polarization Signals of Common Spacecraft Materials

This is the final report documenting the results of the polarization testing of near-planar objects with various reflectance properties. The purpose of this investigation was to determine the portion of the reflected signal which is polarized for materials commonly used in space applications. Tests were conducted on several samples, with surface characteristics ranging from highly reflective to relatively dark. The measurements were obtained by suspending the test object in a beam of collimated light. The amount of light falling on the sample was controlled by a circular aperture placed in the light field. The polarized reflectance at various phase angles was then measured. A nonlinear least squares fitting program was used for analysis. For the specular test objects, the reflected signals were measured in one degree increments near the specular point. Otherwise, measurements were taken every five degrees in phase angle. Generally, the more diffuse surfaces had lower polarized reflectances than their more specular counterparts. The reflected signals for the more diffuse surfaces were spread over a larger phase angle range, while the signals from the more specular samples were reflected almost entirely within five degrees of angular deviation from the specular point. The method used to test all the surfaces is presented. The results of this study will be used to support the NASA Orbital Debris Optical Signature Tests. These tests are intended to help better understand the reflectance properties of materials often used in space applications. This data will then be used to improve the capabilities for identification and tracking of space debris