Srinivas Bollapragada

A Simple Heuristic for Computing Nonstationary ( S, S ) Policies

Nonstationary inventory problems with set-up costs, proportional ordering costs, and stochastic demands occur in a large number of industrial, distribution, and service contexts. It is well known that nonstationary (s, S) policies are optimal for such problems. In this paper, we propose a simple, myopic heuristic for computing the policies. The heuristic involves approximating the future problem at each period by a stationary one and obtaining the solution to the corresponding stationary problem. We numerically compare our heuristic with an earlier myopic heuristic and the optimal dynamic programming solution procedure. Over all problems tested, the new heuristic averaged 1.7% error, compared with 2.0% error for the old procedure, and is on average 399 times as fast as the D.P. and 2062 as fast as the old heuristic. Moreover, our heuristic, owing to its myopic nature, requires the demand data only a few periods into the future, while the dynamic programming solution needs the demand data for the entire time horizon-which are typically not available in most practical situations.

Gaussian–minimum average correlation energy filters

Correlation filters with sharp delta-function correlation peaks [such as phase-only filters and minimum average correlation energy (MACE) filters] do not recognize images on which they are not trained. We show that the MACE filter cannot always recognize intermediate images of true class objects (e.g., aspect views or rotations midway between two training images). New Gaussian-MACE filters offer a solution to this problem.

Periodic review stochastic inventory problem with forecast updates: Worst-case bounds for the myopic solution

Abstract Muth first considered the linear cost periodic review inventory problem in which the mean demand in a period undergoes a non-observed random walk. Assuming the random walk variance and the within period demand variance to be known, and stationary, he showed that the Best Linear Unbiased Estimate (BLUE) for the mean is given by exponential smoothing and derived the formula for the optimal steady state smoothing constant in terms of the variances. We first show that the corresponding Bayesian analysis is useful under transient conditions, and converges to the Muth results under steady state. For the steady state solution, we prove that the myopic policy is near-optimal, using the concepts of P -myopic and D -myopic introduced in this paper, in the sense that the worst case bounds on policy errors in using it may be given analytically, and are small for reasonable values of parameters. As further validation, we use dynamic programming (DP) to compute optimal policies and compare them with myopic policies; policy errors are very small. By considering analogous results in recent literature, it is conjectured that additions of such factors as non-stationarity, lead-times, perishability, setup costs would produce near-myopic results.

Synthetic discriminant functions for recognition of images on the boundary of the convex hull of the training set

Abstract In designing synthetic discriminant function (SDF) filters, the usual choice for the correlation constraint is a real-valued constant for all training images of a given class. However, this choice of constraints results in a filter that recognizes all images in the convex hull of the training set, which is generally undesirable. The use of appropriate complex-valued constraints, though, produces an SDF filter which recognizes only images near the boundary of this convex hull and thus provides improved discrimination performance. This improvement in discrimination can be accomplished without degrading the generalization performance of the filter.

Role of the constraint values in synthetic discriminant function filter design

Several methods of designing Synthetic Discriminant Function (SDF) filters exist. All of these require that the correlation output take on specified values at origin. In this paper, we examine the role of these correlation plane constraints. We show that the conventional practice (of forcing the correlation outputs to a constant for all training images from a single class) leads to poor discrimination. We introduce a new method to improve the discrimination capabilities of SDF filters.

Pruning of training sets used for synthetic discriminant function (SDF) filter design by relaxing the correlation plane constraints

Conventional synthetic discriminant function (SDF) filter designs use all available training images by requiring that the designed SDF filter yield prespecified values at the origin of the correlation plane when various training images are used in the input. In this paper, we show that we can reduce the number of training images being used and improve the filter performance by relaxing the correlation plane constraints when threshold detection is employed in the output correlation plane.

Intraclass recognition with distortion-invariant filters

Correlation filters with sharp delta-function correlation peaks (such as phase only filters and minimum average correlation energy (MACE) filters) do not easily recognize images on which they were not trained. We show that the MACE filter cannot recognize intermediate images of true class objects (e. g. aspect views or rotations midway between two training images). New Gaussian-MACE filters offer a solution to this problem.