Table Of ContentCost Analysis and Estimating
Willis R. Greer, Jr. Daniel A. Nussbaum
Editors
Cost Analysis
and Estimating
8
Tools and Techniques
With 48 Figures
Springer Science+Business Media, LLC
Willis R. Greer, Jr.
College of Business Administration
University of Iowa
Iowa City, IA 52242
USA
Daniel A. Nussbaum
Naval Center for Cost Analysis
Washington, D.C. 20350-1100
USA
Library of Congress Cataloging-in-Publication Data
Greer, WiIIis R.
Cost analysis and estimating : tools and techniques / Willis R.
Greer. Jr., Daniel Nussbaum.
p. cm.
1. Costs, Industrial-Estimates. 2. Manufacturing processes
-Costs-Estimates. 3. Manufactures-Costs-Estimates.
1. Nussbaum, Daniel, 1943- II. Title.
TS167.G74 1990
658.15'52-dc20 90-9783
Printed on acid-free paper.
©1990 Springer Science+Business Media New York
Originally published by Springer-Verlag New York, Inc. in 1990
Softcover reprint of the hardcover Ist edition 1990
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Camera-ready text prepared by the authors.
987654321
ISBN 978-1-4612-6976-2 ISBN 978-1-4612-0995-9 (eBook)
DOI 10.1007/978-1-4612-0995-9
FOREWORD
Changes in production processes reflect the technological advances permeat
ing our products and services. U. S. industry is modernizing and automating. In
parallel, direct labor is fading as the primary cost driver while engineering and
technology related cost elements loom ever larger. Traditional, labor-based ap
proaches to estimating costs are losing their relevance. Old methods require aug
mentation with new estimating tools and techniques that capture the emerging
environment. This volume represents one of many responses to this challenge
by the cost analysis profession.
The Institute of Cost Analysis (lCA) is dedicated to improving the effective
ness of cost and price analysis and enhancing the professional competence of its
members. We encourage and promote exchange of research findings and appli
cations between the academic community and cost professionals in industry and
government. The 1990 National Meeting in Los Angeles, jointly spo~sored by
ICA and the National Estimating Society (NES), provides such a forum. Presen
tations will focus on new and improved tools and techniques of cost analysis.
This volume is the second in a series. The first was produced in conjunction
with the 1989 National Meeting of ICA/NES in Washington, D.C. The articles
in this volume, all refereed, were selected from about 100 submitted for presen
tation at the Los Angeles meeting.
On behalf of the cost professionals who will benefit from this volume, I want
to thank those who brought it to us. Professor Willis R. Greer, Jr. and Dr. Daniel
A. Nussbaum, the editors, dealt ably with an extremely tight schedule and
gained commendable cooperation from the authors. Once again, we thank Pro
fessor Thomas R. Gulledge who conceived the idea for the series and worked
with the editors and authors to perpetuate it.
Stephen J. Balut
President
Institute of Cost Analysis
PREFACE
The articles which appear in this volume could have been published in a vari
ety of high quality, scholarly journals. Among them would have been operations
research, information systems, economics, and defense systems journals.
However, these authors chose to make these manuscripts available to us rather
than the more conventional literature for laudable purpose. They recognized that
the readers of this volume, the attendees of the ICA/NES Conference, and oth
ers, would benefit by having their work assembled in one convenient reference
manual. Accordingly, the reader is treated to a broad cross section of work with
a single focus; to improve our ability to estimate and analyze the cost of defense.
We, the editors, and the readers are deeply indebted to the authors, whose self
less contributions made this volume possible.
We are also deeply indebted to the following individuals, who served as refer
ees for th~ complex task of reviewing manuscripts, some of which have been
published here and others not.
Steve Balut Bruce Miller
Avijit Banerjee R. P. Mohanty
Peter Beck Doug Moses
Dan C. Boger Richard Nelson
Steve Book Michael Peters
J. D. Camm Dan Sheldon
Sidhartha R. Das Mike Sovereign
Ed Deane Philip Tsung
Brian Flynn Karen Tyson
Thurman Gardner Rsit Unal
Thomas R. Gulledge V. Valdmanis
John Honig H.D. Vinod
Roland Kankey Ted Wallenius
David Lamm James Weathersbee
Schuyler C. Lawrence J . C. Westland
Bin-Shan Lin Norman K. Womer
Lewis A. Litteral
CONTENTS
Foreword.............................................................................. v
Preface ................................................................................ VII
I. Cost Estimating and Changing Technology
Reestimating the Cost of Production in a Fuzzy Technological
Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
H.D. Vinod and Parantap Basu
Estimating and Explaining the Cost of High-Technology
Systems....................................................................... 30
O. Douglas Moses
II. Lot Sizing and Cost Control
Allocated Cost Structures to Control Equipment Usage
"Bottlenecks"............................................................... 67
J. Christopher Westland
The Effects of Different Production Rate Measures and Cost
Structures on Rate Adjustment Models................................. 82
Dan C. Boger and Shu S. Liao
Production Lot Sizing in a Class of Batch Process Flow
Shops ......................................................................... 99
Avijit Banerjee and Somkiat Eiamkanchanalai
Ill. Schedule Estimating
Schedule Estimating Relationships for Air-Launched
Missiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 15
Bruce Harmon and Lisa Ward
IV. Uncertainty in Cost Estimating
A General Analytic Approach to System Cost Uncertainty
Analysis.... . ... .... ...... . . .... . ....... .... ..... ....... .......... . . ......... . 161
P,aul R. Garvey
The Incorporation of Uncertainty into Investment Evaluations..... 182
William Resnick
x
V. Quality Control Techniques
Economic Design of Fraction Defective Control Charts:
Simplification of the Multiple Assignable Causes Situation........ 203
Michael~H. Peters
VI. Warranties and Repair Parts Costing
An Active Decision Support System for Warranty Cost
Estimation. . .. . . .. . .. . .. . . . . . .. . . . . . . . . . . . . . . .. . .. . . . .. . . . . . . . .. . . . . . . . . . . . . . . 221
Bin-Shan Lin
Parametric CERs for Replenishment Repair Parts.................... 245
Richard A. Katz
VII. Test and Evaluation Issues
Maintaining the Capital Stock at DoD Test and Evaluation
Sites ........................................................................... 283
Daniel B. Levine and K. M. Olver
I. Cost Estimating and
Changing Technology
REESTIMATING THE COST OF PRODUCTION
IN A FUZZY TECHNOLOGICAL ENVIRONMENT
BY
H. D. VINOD and PARANTAP BASU
Economics Dept, Fordham University, New York, 10458
ABSTRACT
Most profit maximizing firms are aware that the boundary of
the feasible set of technological opportunities is fuzzy. The
neoclassical theory of the firm assumes that the boundary of
the feasible set of technological opportunities is well-defined.
We use a spheroidal neighborhood of a neoclassical profit
maximizing equilibrium as a suitable approximation of a
fuzzy input demand correspondence. Using trigonometric
functions this spheroidal neighborhood is parameterized and
a fuzzy cost function is generated. We use Nerlove's (1963)
famous electric utility data to estimate a generalized Leontief
cost function, with and without inclusion of a fuzz factor.
The concept of fuzz used here seems to be in accord wi th
Popper's (1973) notion of "plastic control" and Simon's
notion of "bounded rationality". For concreteness we plot a
fuzzy isoquant for Nerlove's data. We also report numerical
estimates of scale elasticity, marginal cost, Hessian matrix,
etc .
.L. Introduction
The traditional neoclassical theory of the firm generally
accepts that firms maximize their objective function in a
precisely defined technological environment. It is usually
assumed that the producer kriows without any vagueness the
boundary of his feasible set of technological opportunities.
Technological uncertainty is treated in terms of the
producer's rational expectations about the objective
probability distribution of the random shock driving the
technology. Actually, all producing agents cannot be
expected to be well versed in probability theory when they
make their production and sales decisions. It is now
recognized in the literature that the observed behavior of
agents can be imprecise or fuzzy. The fundamental premise
of fuzzy set theory arises from a value-loaded description of
the environment. According to the Paretian notion, tech-
4
nological alternatives are either "efficient," meaning that
they are on. the boundary of the feasible set, or "inefficient,"
which means that they are inside the production possibility
set. In practice, a company manager is likely to perceive
varying degrees of technological efficiency (e .g., very
efficient, Jess efficient, not so efficient etc.). In this context,
an application of fuzzy set theory is potentially useful.
In the literature, this issue has been slowly becoming
prominent. Lester (1947) drew attention to the inadequacy
of marginalism to deal with this kind of situation and argued
that the equilibrium is a vague zone rather than a well
defined point. Hirshleifer and Riley (1979, 1981) recognize
that this type of fuzzy uncertainty about an agent's
environment may have possible implications for his decision.
There are several attempts to formalize the fuzzy nature of a
producer's behavior (see, Blin et al.(1974), Chang (1977),
Ponsard (1982), Taranu (1977)). Chen and Yu (1988) derive
some useful properties of the fuzzy production corres
pondence and show how the deterministic analysis of
production generalizes in a fuzzy environment. Following
Savage's focal decision theory, McCain (1987) introduces a
notion of fuzzy confidence interval and applies it to price
theory. There may be other attempts to formalize theore
tically a fuzzy production environment in the vast literature
on the subject. The measurement of fuzz in technology is
important because it has definite implications for the
estimation of a firm's cost function.
In this paper, we suggest a new methodology for estimating
cost and input demand functions in a technological environ
ment with fuzz. We approximate an input correspondence
with fuzz in terms of an ellipsoidal neighborhood around a
standard neoclassical profit maximizing equilibrium. Using
trigonometric functions we first obtain a parametric form for
the input correspondence. In the next step, we derive a
firm's cost function using these parametric forms. Applying
the duality theory, we illustrate that this cost function with
fuzz can be used to generate a fuzz technology of empirical
interest. Using Nerlove's (1963) famous electric utility data,
we finally estimate a generalized Leontief cost function
incorporating the fuzz factor. As one might expect, it turns
out that the neoclassical non-fuzzy (we call it crisp)
equilibrium is a special case of our cost function. Statistical
tests are conducted to verify the observed importance of the
proposed fuzz in the technology.
The paper is organized as follows. In Section 2, we review
