Buddy L. Myers

Flexible manufacturing systems evaluation: An alternative approach

The purpose of this article is to integrate the von Neumann-Morgenstern theory of utility functions and the mean-variance approach of portfolio analysis within the computational framework of selecting a production technology to replace an existing one. A stochastic, static one-period problem is formulated, and a measure that takes into account both the capital costs of implementing the new technology and the random monetary value of its output is identified to solve the problem. The properties of this measure are discussed particularly with reference to the optimal selection decision. An example is described to illustrate the methodology.

Quality and inventory issues within the newsboy problem

Abstract Most inventory models assume that the production lot size does not contain any defectives. Clearly, this assumption does not reflect the reality of most manufacturing systems. The number of defects in a production lot depends on the manufacturing technology implemented by the firm. In this paper we study the decision of a firm seeking to replace its existing manufacturing technology with an improved one. Furthermore, we study the effect the quality of the technology has on the optimal production lot size. In this paper, we formulate a two-stage stochastic programming problem. In the second stage, the optimal production lot size is derived for a given manufacturing technology and a given demand forecast. This derivation is provided under the framework of the one-period inventory problem while maintaining a minimal service level. In the first stage, and using the optimal production lot size of the second stage problem, an optimal manufacturing technology that minimizes the total expected cost to the firm is implemented. An algorithm to find an optimal solution is presented. A numerical example illustrates the results.

The bivariate beta distribution: comparison of Monte Carlo generators and evaluation of parameter estimates

The bivariate and multivariate beta distributions may provide appropriate stochastic models for a number of processes, particularly those involving random proportions. Researchers may therefore find it necessary to estimate the parameters of such distributions or generate Monte Carlo samples with known parameter values. Two possible generating techniques for beta bivariates are presented and compared in this paper. Estimating equations for the three parameters of the bivariate beta distribution are presented. These use the method of moments, the only tractable estimating technique, and an analysis of their properties is also presented. This paper focuses on the bivariate beta distribution, but a user of a higher-dimensioned beta model will be able to make use of the discussion herein to provide assistance in determining many of the properties of such a model.

Classical error pairs and the Bayesian prior

SummaryWe have attempted to show the way in which Bayesian and classical approaches are both similar and divergent. The vehicle for discussion, primarily, involved considerations of cost consequences, planning horizons and numbers of alternatives. In turn, these variables were related to the statistical problem continuum, with classical and Bayesian approaches at opposite ends of the scale. By relating problem variables to this continuum, the question of which approach is most appropriate in a particular situation can be more readily resolved.

A Monte Carlo approach for the solution of the simple quadratic and cubic self-avoiding random walk

A procedure for virtually memory-free Monte-Carlo simulation of the self-avoiding random walk (SAW) in a two-dimensional network and in a simple cubic lattice has been developed. It is highly efficient in yielding values of the intrachain meansquare end-to-end distance n > for chains up to n = 1000 and n = 400 steps, for the two and three-dimensional cases respectively. The number N of walks per each chain of n steps involved n = 500 to N = 3000.Accessing a medium-sized computer via a portable terminal, it was possible to obtain values for n up to 21, with N up to 1000, in minutes, and to obtain values for n up to 400 and 1000 with N up to 300 in approximately an hour of computing time.The principal finding is that for n > = anγ, the value of the exponent remains stable at approximately 6/5, consistent with the results of prior work involving complete enumeration for n up to 16 and n up to 10 in the two-dimensional and three-dimensional cases. No comparative data are available for higher levels of n because of the time constraints of memory-dependent computer programs.

A logic system for the choice of risk levels in hypothesis testing

We have examined current, traditional practice of establishing risk levels, favoring use of small α and implicitly accepting correspondingly larger β errors. There are both loses and gains associated with this approach. In particular, small a minimizes the probability of erroneously rejecting Ho, but it also increases the chances that a new model, representing a real improvement, may be discarded. There is no overwhelming logic that one type of error is always more important than the other, since relative costs vary with the conditions surrounding the research investigation.

Strategy in research design and hypothesis testing

The efficiency of a research design may be measured in terms of the degree to which knowledge is enhanced within given resource constraints. Thus, two different types of research design, even though they contain the same number of expected observations, may differ considerably in the amount of information provided. An example is the number N of 32 observations obtained with an analysis of variance witheither 2 factors, 2 levels per factor and a replication of 8or 4 factors, 4 levels per factor and a replication of 2. We analyze and compare the relative efficiencies of regression and variance analysis models and their implications to research strategy development. Three major considerations are evaluated: (1) short versus long time horizon (interval until effects of a decision are realized), (2) small versus large cost of erroneous rejection of the Null Hypothesis and (3) gross versus refined stage of development of the research study. A set of general guidelines towards improved designs is developed.