\chapter{Cost Analysis}
One of the most essential tasks in engineering design is estimateing the
production cost of a new product.  Generally speaking the lowest cost design
will be successful in a free marketplace.  Understanding the elements that make
up the cost is essential.   Furthermore, cost estimatees are used 
\begin{enumerate}
\item to provide basis to estimatee the selling price of the new product
\item to distinguish between the different concepts based on material and
manufacturing processes
\item to provide information on the new product profit
\item to be used as basis for redesign certain elements to reduce the cost
\end{enumerate}


It is important to generate a rough cost estimatee as early as possible in the
design process then refine the cost estimate as soon as the embodiment phase  is
reached. As the design  is refined the cost estimatee is also refined until the
final product is produced.

Cost evaluation includes the estimateion of the cost of building a plant or installing a process within
a plant to produce a product or a line of products and the estimateion of the cost of manufacturing a
part based on particular sequence of manufacturing steps.  

\section{Costs Classifications}
Each company or organization develops there own bookkeeping method.  In the following the different
classification divisions of costs are presented.  It should be realized that cost estimateion within a
particular industrial or governmental organization will follow a highly specialized and standardized
procedures peculiar to the organization. 

\begin{enumerate}
\item Nonrecurring-Recurring:  There are two broad categories of costs:

\begin{enumerate}
\item Nonrecurring costs:  These are one-time costs, which usually called capital costs such as plant
building and  manufacturing equipment. 
\item Recurring costs:  These costs are direct functions of the manufacturing operations. 
\end{enumerate}

\item Fixed-Variable costs: Fixed costs are independent of the rate of production of goods; variable
costs change with the production rate.

\begin{enumerate}
\item Fixed Costs: includes

\begin{enumerate}
\item Investment costs
\begin{itemize}
\item Depreciation on capital investment
\item Interest on capital investment
\item Property taxes
\item Insurance
\end{itemize}
\item Overhead Costs: includes
\begin{itemize}
\item Technical service (Engineering)
\item Nontechnical service (Office personnel, security, etc.)
\item General supplies
\item Rental of equipment
\end{itemize}
\item Management expenses
\begin{itemize}
\item Share of corporate executive staff
\item Legal staff
\item Share of corporate research and development staff
\end{itemize}
\item Selling Expenses
\begin{itemize}
\item Sales force
\item Delivery and warehouse costs
\item Technical service staff
\end{itemize}
\end{enumerate}
\item Variable Costs:
\begin{enumerate}
\item Materials
\item Direct labor 
\item Maintainance cost
\item Power and utilities
\item Quality-control staff
\item Royalty payments
\item Packaging and storage cost
\item Scrap losses and spoilage
\end{enumerate}

\end{enumerate}
\item Direct-Indirect: A cost is called direct cost when it can be direclt assigned to a particular
cost center, product line or part.  Indirect costs cannot be directly assigned to a product but must
be spread over the entire factory.
\begin{enumerate}
\item Direct costs: include
\begin{enumerate}
\item Material: Include the expenses of all materials that are purchased for a product, including the
expense of  wast caused by scrap and spoilage.
\item Purchased Parts: Components that are purchased from vendors and not fabricated in-house. 
\item Labor Cost: Wages and benifits to the workforce needed to manufacture and assemble the product. 
This includes the employees' salaries as well as all fring benfits, includeing medical insurance,
retirments funds and vacation times.
\item Tooling Cost: All fixtures, molds and other parts specifically manufactured or purchased for
production of the product.
\end{enumerate}
\item Indirect Costs: includes
\begin{enumerate}
\item Overhead: Cost for adminstartion, engineering, secretarial work, cleaning, utilities, leases of
buildings, insurance, equipment and other costs that occure day to day. 
\item Selling expenses: 
\end{enumerate}
\end{enumerate}
\end{enumerate}
 
\section{Cost estimatee Methods}
The cost estimateing procedure depends on the source of the components in the product.  There are three
possible options for obtaining the components:
\begin{enumerate}
\item Purchased finished components from a vendor
\item Have a vendor produce components designed in-house
\item Manufacture components in-house
\end{enumerate}
There are strong incentives to buy existing components from vendors.  If the quantity to be purchased
is large enough, most vendors will work with the product design and modify existing components to meet
the needs of the new product.  If existing components or modified components are not available off the
shelf, then they must be produced in which case a decision must be made as to whether they should be
produced by a vendor or made in-house.  This buy-make decision is based on the cost of the component
involved as well as the capitalization of equipment and the investment in manufacuring personnel.

When manufacturing an element, the methods used to develop cost evaluation fall into three categories:
\begin{enumerate}
\item Methods Engineering (Industrial Engineering Approach): The separate elements of work are
identified in detail and summed into total cost per part. Machined components are manufactured by
removing portions of the material not wanted.  Thus the costs for machining are primarly dependednt on
the cost and shape of the stock material, the amount and shape of the material that needs to be
removed and how accuratley it must be removed.
 An example for the production of a simple
fitting from a steel forging is shown here.  

\begin{table}[ht]
\begin{tabular}{ccccc}
Operations&Material&Labor&Overhead&Total\\ \hline
Steel forging&37.00&&&37.00\\
Set-up on milling machine&&0.2&0.8&1.00\\
Mill edges&&0.65&2.6&3.25\\
Set-up on drill press&&0.35&1.56&1.91\\
Drill 8 holes&&0.9&4.05&4.95\\
Clean and paint&&0.3&0.9&1.2\\
Total&37.00&2.40&9.91&49.31\\ \hline
\end{tabular}
\end{table}

\item Analogy: Future costs of a project or design are based on past costs of a similar project or
design with due allowance for cost escalation and size difference.  The method therefore requires a
backlog of experience or published cost data.

\item Satistical Approach: Techniques such as regression analysis are used to establish relations
between system cost and initial parameters of the system: weight, speed, power, etc. 
For example, the cost of developing a turbofan aircraft might be given by
\[C=0.13937 x_{1}^{0.7435}  x_{2}^{0.0775}\]
where C is in millions of dollars, $x_{1}$ is the maximum engin thrust, in pounds, and $x_{2}$ is the
number of engines produced.  
\end{enumerate}

\section{Labor Costs}
 The most accurate method of determining labor cost is to setup a manning table
and find the actual number of people required to run the process line.  Be sure to account for standby
personnel.  Cost of operating labor include fring benfits.  As an order of magnitude estimatee of labor
costs
\[\frac{\mbox{Operating man-hour}}{\mbox{Tons of product}}=K\frac{\mbox{no. of process
steps}}{\mbox{(tons/day)}^{0.76}}\]
where\\
 K=23 for a batch operation\\
 K=17 for avergae labor requirements\\
 K=10 for automated process\\
 \section{Product Pricing}
 Pricing can be defined as the technique of arriving at a selling price for a product or service that
 will Interest the cutomer while returning the greatest prrofit.  Different methods are available to assist in
 arriving at the optimum price for a product. One of these method is known as the {\bf Break-Even
 Chart}.  
 
 
 
 
\subsection{Break-Even Chart} 
Break-even chart is designed to show graphically profit and loss on the selling price
 and manufacturing cost of the product.  The manufacturing cost of a product includes
 \begin{enumerate}
 \item Material: Credit should be accounted for recycled scrap and by products.
 \item Purchased parts
 \item Labor
 \item Tooling
 \item Overhead
 \end{enumerate}
 Material, purchased parts and labor are variable costs that depends on the number of goods produced
 while tooling and overhead are fixed costs regrdless of the number of goods produced. The fact that
 the variable costs depend on the rate or volume of production while fixed costs do not, leads to the
 idea of a break even point.   The detrimnation of the production lot size to exceed the break even
 point and produce a profit is an important consideration.  To draw a break even point chart follow
 the following steps
 \begin{enumerate}
 \item Determine the varaiabel costs per product: Variable costs depends on the number of products and include
 \begin{enumerate}
 \item Material
 \item purchased parts
 \item Labor
 \end{enumerate}
 \item Determine the fixed cost: Fixed cost do not depend on the volume or the number of ptroducts
 \item Draw on the chart The total cost as a function of the number of products. The total cost = Fixed cost + Variable cost
 \item Determine a sale price of the product.  Draw the sales as a function of the number of products
 \item The iterscetion of Sales line with total price is the break-even point
 \end{enumerate}
 \begin{figure}[ht]
 \vspace{2.5in}
 \caption{Break-even chart}
 \end{figure}
 \subsection{Linear Programming}
 Linear programming is a tool that is used to represent a situation in which some optimum goal is sought such
 as maximize profit and minimize cost.  Mathematically it involves finding a solution to a system of
 simultaneous linear equations and linear inequalities which is optimized in linear form. 
 



