An extensive research and development activity to reduce the cost of manufacturing photovoltaic solar arrays by a factor of approximately one hundred is discussed. Proposed and actual manufacturing process descriptions were compared to manufacturing costs. An overview of this methodology is presented

Chamberlain, R. G.

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MACIEA Assessment of Low-Cost Manufacturing Process Sequences*
Robert G. Chamberlain
Operations Research Group
Systems Analysis Section
Jet Propulsion Laboratory
California Institute of Technology
4800 Oak Grove Drive
Pasadena, CA 91103 USA
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Abstract
The Low-Cost Solar Array Project, sponsored by the U.S. Department
of Energy, is managing an extensive research and development activity to
reduce the cost of manufacturing photovoltaic solar arrays by a factor of
approximately one hundred. This management objective implies the need for
a capability to relate proposed and actual manufacturing process descrip-
tions to manufacturing costs.
The Solar Array Manufacturing Industry Costing Standards (SAMICS)
methodology was developed to meet this need. An overview of this method-
ology is presented. Since the solar array manufacturing industry is
expected to increase in capacity by several orders of magnitude when the
price is reduced to a competitive level, it would be inappropriate to
assume that indirect costs will be the same multiple of direct costs as
is presently observed in the industry. Furthermore, identification of
some other industry as "similar" would be highly questionable. Conse-
quently, SAMICS contains a "factory construction and staffing algorithm,"
which infers indirect requirements from the specified direct requirements
and implicitly builds a hypothetical, dedicated factory for performing
the specified manufacturing processes.
SAMICS has been implemented by a computer program (SAMIS III). It
has been applied to the assessment of Low-Cost Solar Array Project pro-
gress, and it has been used as a tool in the selection of research and
development priorities.
*Prepared by the Jet Propulsion Laboratory, California Institute of
Technology for the U.S. Department of Energy by agreement with the
National Aeronautics and Space Administration.
Key words: Cost Estimation, Manufacturing, Mathematical Models,
Photovoltaics, SAMICS
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OBJECTIVES
The objective of the U.S. Solar Photovoltaic Conversion. (PV) Program
is to establish the direct conversion of solar energy to electricity (that
is, photovottaicb) as a technologically and economically viable option for
the generation of energy.
The U.S. Depnrtment of Energy is sponsoring the Low-Cost Solar Array
(LSA) Project at the Jet Propulsion Laboratory as a part of the PV Program
to initiate a major effort toward the development of low-cost : polar arrays.
The LSA Project objective is to manage the research and development, being
carried out by over 80 companies and universities under JPL contracts,
needed to reduce the costs of manufacturing by approximately a factor of
one hundred (from about $50 per peak watt in 1975 to $0.50 — expressed in
1975 dollars — per peak watt by 1986).
The Solar Array Manufacturing Industry Costing Standards (SAMICS)
were developed to provide the LSA Project with an accurate means of a:asess-
ing the costs of purportedly low-cost manufacturing processes and process
sequences proposed by its actual and prospective contractors in a fair,
consistent fashion. As the price of solar arrays is brought down by a
factor of a hundred, the size of the industry is expected to increase by
several orders of magnitude, and the technology used is expected to evolve
from being labor-intensive to being capital-intensive. T'-Sus, to meet its
objectives, the SAMICS methodology must be very versatile.
SAMICS OVERVIEW
A complete description of the SAMICS methodology is contained in
reference [2]. The reader is directed to that document for a more complete
bibliography as well as for detailed exposition of the derivations and
algorithms of SAMICS.
2
The cost of manufacturing a product depends more on the manufacturing
processes used than on the functional — or even the physical — description
of the product. Consequently, any accurate estimate of manufacturing
costs must start with detailed descriptions of the economically important
characteristics of those processes.
Indirect costs — those that result from operating a company to
support the performance of the manufacturing processes — are also very
important, and usually account for 30% to 70% of the final product price.
Comparison of competing processes to perform the same function requires
that indirect costs be estimated in the same way for all processes to
ensure that it is indeed the processes, and not the indirect cost
assumptions, that are compared.
SAMICS requires that the direct requirements (floor space and other
facilities, machine operating and servicing personnel, utilities and
plant services, and materials and supplies) of each manufacturing process
step be specified. New process steps are placed in the context of
complete manufacturing sequences.
The annual production of the industry is specified as input, then
a hypothetical industry containing those complete manufacturing sequences
is created and its operation is simulated.
Industry Simulation
The hypothetical industry is constructed as a sequence of companies
in a geneAal zed tAee (or nee tAiexed ne&o)tk) structure, with plant
capacities consistent with the annual industry production and all process
yields taken into account. Thus, alternative industry structures can be
3
readily compared in terms of their effects on product cost. The industry
simulation is composed of a sequence of company simulations.
Company Simulation
Companies are constructed to contain the specified processes in a
generalized tree structure, therefy providing a great deal of flexibility
in defining the manufacturing sequences. Within each company, the annual
direct process requirements for all processes in that company are collected
in order to allow for economies of scale in the construction and staffing
of the standardized hypothetical factory.
The procedure for building and staffing the standardized hypothetical
factory depends upon the observation that the indirect requirements of a
company (facilities, supervisors, air conditioning, etc.) depend on the
direct requirements (floor space, welders, process power requirements, etc.)
and on construction and staffing traditions, but not on any other charac-
teristics of the processes. A major part of SAMICS is a collection of
indirect nequiument he.Cazfon6hip6 that express those traditions as
standardized submodels:
Ni = E j f ij (Tj )
where
Ni = Indirect requirement for expense item i,
T  = Total requirement for expense item j,
fij = Standardized submodel for the amount of item i required
indirectly to support an amount T  of item j.
The functions fij (Tj ) are expressed as piece wise continuous power
functions, which permits a great deal of flexibility. Since these
4
functions represent construction and staffing traditions, they depend upon
the economic environment — the functions currently in the SAMICS data base
represent the U.S. electronics manufacturing industry, and will probably
be changed as the differences between solar array manufacturing and
electronics manufacturing, if any, gradually become apparent.
The total requirement for any expense item is simply the sum of the
direct and indirect requirements:
T. = D^ + N.
where
D^ = Direct requirement for expense item j.
Since the D  are known and the fi3 are standardized submodels, the
indirect and total requirements vectors can be determined by recursive
solution* of these two equations. It may be noted that the analytical
problem is similar to that for which Leontief introduced input-output
matrices [3-6].
After all of the quantities in a company have been determined, the
associated prices (which are allowed to depend upon annual quantities
purchased) can be determined. Of course, since some of the things pur-
chased by a company may be manufactured by other companies in the modeled
industry, their prices must be determined first, by starting the price
calculations at the raw materials end of the industry. Conversely, since
companies are sized to produce the specified annual industry production
quantity, the quantity calculations had to start at the finished goods
The author intends to present several algorithms for obtaining solutions
at the XXIV International Meeting of The Institute of Management Sciences
in Honolulu, Hawaii, in June 1979.
5
end. Calculation of quantities throughout the industry before calculation
of prices allows those price calculations to incorporate economies of
scale, and is a very important characteristic of SAMICS.
Required Revenue Cond iticn
Normative product prices are determined by specifying a required rate
of return on equity, treating profit (defined as the retuAn on equity)
as a cost, and applying the required revenue condition:
The nonnative product price Aha2e be chozen bo that the present vatu.e o6
att revenues .cis exactty equal to the presenx vague o6 a t costs.
The SAMICS Stna.nciat model os the SiAm is based on the required
revenue condition. If it is assumed that the company is operating in a
.6teady-btate condition (that is, producing the same quantity every year,
and replacing equipment that wears out with identical — but new — equip-
ment), then revenues must equal costs each year, not just in present value,
even in the presence of inflation, provided that a cost term to account
for the amortization of one-time costs is added. Thus,
Revenues = Product Price * Quantity + Byproduct Income
and
Costs = The sum of the following expenses:
• Annual purchased products expense,
• Annual cost of all expense itemq,
• Annual cost of replacing capital goods,
• Annual return on equity (profit),
• Annual interest on debt,
6
• Annual insurance premiums,
`	 u Annual ad vatmem (property) taxes,
^^ 1 e Annual income taxes,
• Annual miscellaneous expenses,
• Annual amortization of one-time costs,
t
• Annual value-added tax (not applicable -- yet — in the U.S.;
not now incorporated in SAMICS),
• Other annual expenses not now applicable in the U.S. that
may be required for application of SAMICS in other countries.
Details of the submodels for each of these cost terms are given in
reference [ 2]. Aside from differences in numerical values of parameters,
the only cost term whose submodel may vary from country to country is
the _ncome tax:
TAX = tax (Taxable Income) - Tax Credits
with
Taxable Income = Revenues - Deductible Expenses
IMPLEMENTATION
SAMIS Computer Program
The generation of indirect requirements, even if the non-linearities
that produce economies of scale were not allowed, is a formidable computa-
tional task. Allowing for non-linear price versus quantity functions and
for differential inflation make the computational burden even worse.
Consequently, a computer program, SAMIS III, has been prepared to facili-
tate application of SAMICS. SAMIS III is currently available on an
international time-sharing service (NCSS, Inc.); contact Mr. Paul J.
Firnett at JPL for details.
7
IPEG Manual Approximation
By making very stringent simplifying assumptions with regard to
indirect requirements, it is possible to obtain a price equation [1] that
can be used* without a computer:
Price = (0.49*EQPT + 97*SQFT + 2.1*DLAB + 1.3*MATS + 1.3*UTIL)/Quantity
where
EQPT = Cost of all the equipment,
SQFT = Floor space required by the equipment,
DLAB = Annual cost of all direct labor,
MATS = Annual cost of all direct materials and supplies,
UTIL = Annual cost of all direct utilities.
Under appropriate conditions, the above equation gives results
within about 5% to 10% of the SAMIS computer program results. It is
anticipated that econometric calibration of the coefficients will make
an equation of this form very useful for sensitivity studies.
VALIDATION
Validation of the SAMICS methodology has been sought gonstantly
throughout its development.
The methodology and numerical results have been given extensive
exposure, albeit primarily among the LSA Project contractors. Since those
contractors have often made their own estimates, and since they can be
expected to be financially affected by the numerical results produced by
*
Warning: The coefficients in this equation depend upon particular
assumed values of a variety of financial parameters. See [1] for
further information..
8
SAMICS, the fact that SAMICS is gaining wide acceptance is very encourag-
ing. These contractors have made numerous detailed suggestions — mostly
with regard to prices in the expense item data file; by and large, these
suggestions have been accepted.
A major validation study [7] recently compared the results of SAMIS
computations against the results of applying conventional manual methods
to conceptual point designs, on a very detailed level. Price estimates
were within about 5% over a 1000 to 1 size range.
Users of the methodology are urged to apply their experience,
engineering judgment, and common sense to all details of results, and to
pass along any discrepancies found.
SAMICS results have not yet been compared with costs observed in
existing manufacturing plants. Such comparisons may be obtained within
the next couple of years.
ASSESSMENT OF PROCESS SEQUENCES
SAMICS was developed primarily to facilitate comparison of alterna-
tive manufacturing processes. Analysis of 24 variations on manufacturing
process sequences in the summer of 1978 gave the results sr,,wn in Table 1;
the prices of all sequences were within the range $7-11/Wpk.
Proposed process "improvements" can be (and have been) similarly
compared, with the interesting observation that anticipated savings are
not strongly correlated with development risk.
Due to the extreme versatility that had to be built into SAMICS in
order to meet its objectives, a wide variety of other questions can also
be addressed.
9
3i
Table 1. Comparisons of Current Process Options
Preferred
	
Savings	 Not Preferred
r---
Superstrate $2.14/Wpk Substrate
Silk screen printing of $0.83/Wpk Plating of metal pattern
metal pattern
$0.33%Wpk Back, then front
Simultaneous front and back
junction formation $0.10/Wpk Front, then back
Texturization etch $0.17/Wpk Damge removal etch
Different Economic Environments
Since prices of all expense items are supplied to SAMICS as data,
it is possible to investigate the implications of differences in price
structures (such as labor costs versus capital costs) on prices of pro-
ducts from particular process sequences, and to obtain preferred process
sequences for particular environments. The effects of local factory
construction and staffing traditions (such as working conditions and
building designs) can also be investigated.
Changing Economic Conditions
Changes in industry structure and size, and long-run (but not
short-run) company growth can be studied, as can the effects of differ-
ential inflation rates and of changes in interest rates, company fiscal
structure (debt-to-equity ratio), and rates of return on equity.
10
Although SAMICS is designed to accept the %ate od 4exuAn on equity
as an input and to produce pniee as output, the same relationships, once
obtained, can be interpreted as if the input/output roles were reversed.
Government Policies
The effects of some governmental policies, particularly those that
affect tax laws, can be assessed. Policies that affect economic parameters
(such as loan guarantees which affect interest rates) can also be addressed.
REFERENCES
1. R. W. Aster and R. G. Chamberlain, Interim Price Estimation Guidelines:
A Precursor and an Adjunct to SAMIS III, JPL Document* 5101-33, Jet
Propulsion Laboratory, Pasadena, Calif. (1977).
2. R. G. Chamberlain, A Normative Price for a Manufactured Product: The
SAMICS Methodology (2 Volumes), JPL Document* 5101-93, Jet Propulsion
Laboratory, (1979). Presented at November 1978 ORSA/TIMS Meeting in
Los Angeles, Calif.
3. W. Leontief, "Quantitative Input-Output Relations in the Economic
System of the United States," in The Review o6 Economies and
Statistics XVIII, pp. 105-125, Aug. 1936.
4. W. Leontief, The S.thu.c-tuAe o6 the American Economy, 1919-1939,
Revised Edition, New York: Oxford, 1951.
5. W. Leontief, Input-Output Economics, New York: Oxford, 1966.
6. W. Leontief, et al., Studies in the StAuctune ob the Amehican
Economy, New York: Oxford, 1953.
7. Theodore Barry & Associates, Phase III SAMICS Support Study Final
Report (Volume I: SAMIS III Computer Program Validation),
DOE/JPL-955123-79/1, *
 Los Angeles, Calif. (1979).
*
JPL internal documents, available from the Jet Propulsion Laboratory,
California Institute of Technology, 4800 Oak Grove Dr., Pasadena,
Calif. 91103, U.S.A.
11


Assessment of low-cost manufacturing process sequences

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