Charles S. Beightler

Optimization in Tool Engineering Using Geometric Programming

Abstract This paper explores the use of geometric programming to solve tool engineering problems. The primary objective is to relate the technical factors involved in the cutting process to the economics of a particular tooling operation, and from this relationship determine the optimum speed and feed resulting in minimum cost per machined piece. Solution techniques are presented for non-linear objective criteria, subject to both linear and non-linear constraints. Computational procedures are illustrated through the solution of two typical examples.

Geometric Programming: A Technical State-of-the-Art Survey

Abstract This paper presents a detailed survey of the latest techniques for solving large geometric programs. Geometric programming is a very powerful method for solving a large class of nonlinear programming problems, but it has been severely restricted in practice due to the inability to handle even moderate sized problems; that is, those possessing more than a few degrees of difficulty. During the past two years, a number of significant break-throughs have taken place in regard to handling both large problems and the general signomial, or signed programs. Several new algorithms, some untested in practice, are presented and discussed in this paper.

A Discrete-Time Queuing Analysis of Conveyor-Serviced Production Stations

This paper analyzes production stations that operate in conjunction with conveyors. Two types of production stations are considered: 1 loading stations that load processed material to the conveyor, and 2 unloading stations that remove material from the conveyor. An operating policy, the sequential range policy, is proposed as a method for operating the production stations. An analysis of the sequential range policy is given. The system is considered as a discrete-time queuing process with a stationary Bernoulli arrival rate. In-process storage is treated as a Markov process discrete in time and discrete in space. The expected number of units in storage and the expected delay per unit produced are derived. Certain economic problems are considered.

Closed-Form Solutions to Certain Linear Allocation Problems

Abstract This article considers serial multistage systems with linear returns rn = an Dn+ bn sn and linear transitions sn-1 = AnDn+Bnsn . For certain cases, closed-form solutions are obtained which greatly reduce the computational effort required to obtain optimum solutions. An example problem is presented.

Management science models for evaluating regional government policies

This paper discusses the use of econometric models in evaluating alternative courses of action for public investment and governmental programs. Included are an extensive statewide and regional input-output analysis of the Texas economy, a simulation model to be used by government officials for fiscal policy-making and a model which simulates the demand for and use of water resources. These models provide a means whereby government planners and policy makers can plan and understand the consequences of investing limited resources in various public programs.

Analysis of Nonserial Multistaged Systems Using Compressio and Decomposition

Abstract This paper gives a derivation and description of an algorithm for solving nonserial multistage decision problems. This algorithm, together with the earlier branch absorption technique, decomposes the nonserial system into an equivalent serial system which can then be optimized by dynamic programming. The algorithm is illustrated with an example problem showing the compression of a feed-back loop.

Procedures for generating gamma variates with non-integer parameter sets

One of the most useful distributions in stochastic modeling is the two parameter gamma distribution. This paper presents a technique for generating random gamma variates from any two parameter gamma form with either integer or non-integer parameters. Only two techniques are presently available for generating gamma variates with a non-integer shape parameter, those being a variate averaging technique proposed by Naylor, et al. and a rejection scheme proposed by Johnk. The three generation schemes are compared with respect to (1) statistical goodness of fit, (2) computer running time and (3) random number calls. The authors scheme is shown to be statistically comparable with respect to goodness of fit, and generally superior relevant to computer running times and random number calls.