\chapter{Cost Analysis}
One of the most essential tasks in engineering design is estimating the
production cost of a new product.  Genrally speaking the lowest cost design
will be successful in a free marketplace.  Undesrtanding the elements that make
up the cost is essential.   Furthermore, cost estimates are used 
\begin{enumerate}
\item to provide basis to estimate 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 redsign certain elements to reduce the cost
\end{enumerate}


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

Cost evaluation includes the estimation 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 estimation of the cost of manufacturing a
part based on particular sequence of manufacturing steps. 

In design it become important to find techniques that help reducing the cost.  
Some of the cost reduction techniques that can be used are:

\begin{enumerate}
\item Introduce new processes.
\item Take advantage of the increase in knoweldge that is increased as experience increases and with the
standardization of parts, materials and methods.
\item  Employ a steady production rate, when feasible.
\item Utilize all production capacity.
\item Have product specific factories or production lines.
\item Improve methods and processes to eliminate rework and reduce work in process and inventory.
\end{enumerate}

Also, it become important to avoid factors that tend to increase the cost while in the design process.  
Some factros that tend to increase costs are:
\begin{enumerate}
\item Incomplete product design specification.
\item Redesign due to failures.
\item Supplier delinquency.
\item Management and/or personnel changes
\item Relocation of facilities.
\item Unmet deadlines.
\item Product becomes too complex.
\item Technology and/or processes not as developed as thought
\item Inadequate customer involvement.
\item Disregarding the need.
\item Not subjecting a new product idea to competitive evaluation.
\item Not demonstrating that a new design can function properly under realistic conditions.
\item Designing without considering manufacturing processes
\item Not continually improving and optimizing the product
\item Relying on inspection (Last minut test)
\end{enumerate}
 

\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 estimation within a
particular industrial or governemental orgnization will follow a highly specialized and standardized
procedures peculiar to the organization. 

\begin{enumerate}
\item Nonrecurring-Recurring:  There are two broad catagories 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 independednt 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 Intrest 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 reserach 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 Estimate Methods}
The cost estimating 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.  Cost is only one factor that
determines whether a product or a component of a product will be made in-house or brought from an outside
supplier.  Some of the reasons for each decision are:
\begin{table}
\begin{tabular}{ll}
Reason to make& reason to Buy\\
Cheaper to make&Cheaper to buy\\
Company has experience making it & Production facilities are unavailable\\
Idle production capacity available&Avoid fluctuating or  seasonal demand\\
Compatibile and fit in production line& Inexperience with making process\\
Part is proprietary&Existance and availability of suppliers\\
Wish to avoid dependency on supplier&Maintain existing supplier\\
Part fragility requiring high packing&Higher reliability and quality\\
Tranportation costs are high&\\
\end{tabular}
\end{table}




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 catagories:
\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\\ \hlinr
\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 estimate 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 intrest 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. An illiustrative
 example is listed here for demonstartion of this technique.  
 
 A manufacturer of desk staplers and other stationary items produces two different stapler models.  One is
 manual in operation retails at \$12.5 and returns \$2.00 to profit, the other is automatic and sells for
 \$31.25  returning \$5.00 to profit.  The manufacturer is concerend with how to utilize his production
 facilities inorder to maximuize profits.  One constraint placed upon the maximizing of profit can be written
 as follows
 \[P=2Q_{M}+5Q_{A}\]
 where P is profit function\\
 $Q_{M}$ is the quantity of manual staplers, and\\
 $Q_{A}$ is the quantity of automatic staplers.\\
 
 Assume the manufacturing Operation is such that labor skills and plant facilities are completely
 interchangeable and so varying quantities of manual and automatic staplers may be produced on the same day.  Also
 assume that present demand is such that the compnay can sell as many as it can produce.  There are certian production
 restrains.  Most of the major components are prepared on seeparate assembly lines perior to movement to the final
 assembly area.  There is sufficient inventory of components for both staplers to satisfy daily production with the
 exception of solenoids for the automatic model, which has a daily production capacity of 200.  This constraint may be
 written as 
 \[ Q_{A} \leq 200\]
 Among other dutiees of employees, fabrication and assembly require 18 man-minute for each manual model and 54
 man-minutes for each automatic stapler.  The plant employ 45 men for this task on an eight-hour shift.  SInce there
 is only one shift, the capacity is $8 \times 45 \times 60$ or 21,600 man-minutes per day.  This may be defined
 mathematically by
 \[ 18 Q_{M}+ 54 Q_{A} \leq 21,600\]
 Final adjustment in the manual stapler requires 3 man-minutes on the assembly line, whereas the automatic model
 requires 5.4 man-minutes.  This phase requires 6 men, the daily capacity is $8 \times 6 \times 60$ or 2,880
 man-minutes.  This constraint is expressed as 
 \[3 Q_{M} + 5.4 Q_{A} \leq 2880\]
 
 Final inspection for workability requires 1 man-minute for manual models and 1.5 man-minutes for the automatic model. 
 There are 4 half-time inspectors assigned to this task, the inspection capacity is $8 \times 2 \times 60$ or 960
 man-minutes.  The inspection constraint is
 \[ Q_{M} + 1.5 Q_{A} \leq 960\]
 
The following table summries the given information
\begin{table}
\begin{tabular}{lll}
&Manual&Automatic\\
selling price & 31.25&12.5\\
profit &\$2 &\$5\\
Constraints&&power supply 200 per day\\
Labor& 18 man-minutes&54 man-minutes\\
Adjustment &3 man-minutes&5.4 man-minutes\\
Inspection &1 man-minute&1.5 man-minutes\\
\end{tabular}
\end{table}
The constraints equations are

\[ P=2Q_{M}+5Q_{A}\]
 \[ Q_{A} \leq 200\]
 \[ 18 Q_{M}+ 54 Q_{A} \leq 21,600\]
 \[3 Q_{M} + 5.4 Q_{A} \leq 2880\]
  \[ Q_{M} + 1.5 Q_{A} \leq 960\]
  
  Plotting these equations  yeilds graphs \ref{fg1} and \ref{fg2}
  \begin{figure}[h]
  \vspace{4in}
  \cpation{Constriants equation without profit}
  \end{figure}
  \begin{figure{[ht]
  \vspace{4in}
  \cpation{Constriants equation with profit}
  \end{figure}
  
  
 
 The linear programm is used to find the iso-profit line that is farthest away and still contains at least one point
 that is technically feasible.
 
 A combination of the break-even and linear programming can be used to set a price for a product.  Linear programming
 approcah can be used to determine the optimum number of goods then that number is used on the break even chart to
 determine the selling price.  The actual setting of price is at the heart of buisness practice, but describing it
 briefly is not easy.  A key issue in establishing a price is the reaction of the competition and the cutomer.  When
 competition is fierce, the sales force may push hard for price reductions, claiming they can make-up the lost revenues
 by increasing the volume.  Special offers such as promotional discouts, primiums, extras, trade-ins, volume discounts
 and trade-in allowances are often used.
 
 
 



