\chapter{Cost Analysis}
One of the most essential tasks in engineering design involves estimating the
production cost of a new product.  Generally speaking, the lowest cost design
will be the most successful in a free marketplace.  Understanding the elements that make
up the cost is essential.   Furthermore, cost estimates are used: 
\begin{enumerate}
\item to provide a basis for estimating 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 a basis for redesigning 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, and then to refine the cost estimate as soon as the embodiment phase is
reached. As the design is refined, the cost estimate is also refined until the
final product is produced.

Cost evaluation includes the estimation of the cost of building a plant, or the cost of installing a process within
a plant to produce a product or a line of products. It also involves the estimation of the cost of manufacturing a
part based on a particular sequence of manufacturing steps. 

In design, it becomes important to find techniques that help reduce 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 knowledge 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 the 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 factors that tend to increase costs are:
\begin{enumerate}
\item Incomplete product design specifications.
\item Redesign due to failures.
\item Supplier delinquency.
\item Management and/or personnel changes.
\item Relocation of facilities.
\item Unmet deadlines.
\item The product becomes too complex.
\item Technology and/or processes are not developed as well as they were thought to be.
\item Inadequate customer involvement.
\item Disregarding the needs.
\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 minute test).
\end{enumerate}
 

\section{Costs Classifications}
Each company or organization develops its own bookkeeping methods.  In the following, the different
classification divisions of costs are presented.  It should be realized that cost estimation within a
particular industrial or governmental organization will follow a highly specialized and standardized
procedure, particular 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 are 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 include:

\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 include:
\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 Maintenance 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 a direct cost when it can be directly 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: Includes the expenses of all materials that are purchased for a product, including the
expense of waste caused by scrap and spoilage.
\item Purchased Parts: Components that are purchased from vendors and not fabricated in-house. 
\item Labor Cost: Wages and benefits to the workforce needed to manufacture and assemble the product. 
This includes the employees' salaries as well as all fringe benefits, including medical insurance,
retirements 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 include:
\begin{enumerate}
\item Overhead: Cost for administration, engineering, secretarial work, cleaning, utilities, leases of
buildings, insurance, equipment and other costs that occur 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 Purchasing finished components from a vendor.
\item Have a vendor produce components designed in-house.
\item Manufacturing 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 include:
\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\\
Compatible and fits in production line& Inexperience with making process\\
Part is proprietary&Existence and availability of suppliers\\
Wish to avoid dependency on supplier&Maintain existing supplier\\
Part fragility requiring high packing&Higher reliability and quality\\
Transportation 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 this case, a decision must be made regarding 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 on the capitalization of equipment and the investment in manufacturing 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 that are not wanted.  Thus, the costs for machining are primarily dependent on
the cost and shape of the stock material, the amount and shape of the material that needs to be
removed and how accurately 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 designs 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 Statistical Approach: Techniques such as regression analysis are used to establish relations
between system costs 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 engine 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 to find the actual number of people required to run the process line.  Be sure to account for standby
personnel.  Cost of operating labor includes fringe benefits.  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 average labor requirements\\
 K=10 for an automated process\\
 
 \section{Product Pricing}
 Pricing can be defined as the technique used for arriving at a selling price for a product or service that
 will interest the customer, while simultaneously returning the greatest profit.  Different methods are available to assist in
 arriving at the optimum price for a product. One of these methods is known as the {\bf Break-Even
 Chart}.  
 
 
 
 
\subsection{Break-Even Chart} 
The break-even chart is designed to show, graphically, the profits and losses on the selling price
 and manufacturing costs of the product.  The manufacturing costs of a product include:
 \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 depend on the number of goods produced
 while tooling. Overhead are fixed costs, regardless 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 determination of the production lot size needed 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 variable costs per product: Variable costs depend 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 does not depend on the volume or the number of products.
 \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 intersection of the sales line with the total price is the break-even point.
 \end{enumerate}
 
 
 \def \epsfsize#1#2{0.7#1}
 \begin{figure}
 \epsffile{../figures/10-1.eps}
 \caption{Break-even chart}
 \end{figure}
 
 \subsection{Linear Programming}
 Linear programming is a tool that is used to represent a situation in which an optimum goal is sought, such
 as to 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 illustrative
 example is listed here for demonstration of this technique.  
 
 A manufacturer of desk staplers and other stationary items produces two different stapler models.  One is
 manual in operation, retails at \$12.50 and returns \$2.00 to profit. The other is automatic and sells for
 \$31.25,  returning \$5.00 to profit.  The manufacturer is concerned with how to utilize his production
 facilities in order to maximize profits.  One constraint placed upon the maximizing of profits 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; thus, varying quantities of manual and automatic staplers may be produced on the same day.  Also,
 assume that the present demand is such that the company can sell as many as it can produce.  There are certain production
 restraints.  Most of the major components are prepared on separate assembly lines, prior to moving to the final
 assembly area.  There is a 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 duties of employees, fabrication and assembly requires 18 man-minutes for each manual model and 54
 man-minutes for each automatic stapler.  The plant employs 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:
 \[ 18 Q_{M}+ 54 Q_{A} \leq 21,600\]
 The 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, and 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 summarizes 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 yields graphs \ref{fg1} and \ref{fg2}.
  
  \def \epsfsize#1#2{0.7#1}
  \begin{figure}
  \epsffile{../figures/10-2.eps}
  \caption{Constraints equation without profit}
  \label{fg1}
  \end{figure}
  
  
  \def \epsfsize#1#2{0.7#1}
  \begin{figure}
  \epsffile{../figures/10-3.eps}
  \caption{Constraints equation with profit}
  \label{fg2}
  \end{figure}
  
  
 
 Linear programming is used to find the iso-profit line that is farthest away, yet 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. The linear programming
 approach can be used to determine the optimum number of goods, then that number may be used on the break-even chart to
 determine the selling price.  The actual setting of a price resides at the heart of business practice, but describing it
 briefly is not easy.  A key issue in establishing a price involves the reaction of the competition and the customer.  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 discounts, premiums, extras, trade-ins, volume discounts
 and trade-in allowances are often used.
 
\section{Problems}
\subsection{Team Activities}

The objective of this exercise is to use C++ programming to write a program that can find
the cost of different alternatives for your design project in Introduction to Mechanical
Engineering.  Manufacturing cost is an important factor in evaluating the different
alternatives.  Some alternatives will be eliminated because of their high manufacturing cost.

{\bf Outline}

In engineering design projects, students are expected to build a device by the end of a limited
time period.  With a limited amount of money, students need to figure out the manufacturing costs of different designs
before they actually start building these devices. A manufacturing cost is a key determinant of the
economic success of a product.  When computing the manufacturing cost, one can divide the cost into two broad
categories (a) Fixed cost and (b) Variable cost. 
 Fixed costs are those that are incurred regardless of
the number of products that are manufactured, while variable costs depend on the amount
 of goods that are produced.  In student design projects, students are not expected to buy major
 tools nor rent warehouses for production, hence the fixed costs and variable costs in this case
 may use the following components:
 
 \begin{enumerate}
 \item {\bf Fixed Cost}
 \begin{enumerate}
 \item {\bf Tooling Cost} Tooling cost can include buying or renting.  Renting
 depends on the charge per unit time, regardless of the number of units produced.  Buying in
 this case will be for this project only, and it will be assumed that it is paid for in full (i.e. no interest
 and no depreciation).
 \item {\bf Setup Cost} This is the cost required to prepare equipment for a production, and it is
 fixed regardless of the number of units produced.
 \end{enumerate}
 \item {\bf Variable Cost}
 \begin{enumerate}
 \item {\bf Material Cost} See Table \ref{mat} for reference.
 \item {\bf Processing Cost} Varies with the type of manufacturing equipment used, and includes
 charges for both machine time and labor.
 \end{enumerate}
 \end{enumerate}
 
 {\bf Programming Requirements}
 The program should be readable all items from the terminal and sorted into "ready" and
 "need-manufacturing" items.  The information should be fed by the user.  Ready items need prices
 from the vendor, while items that need manufacturing require the following calculation:
 \begin{enumerate}
 \item User inputs the following information:
 
 \begin{enumerate}
 
 \item user inputs the mass of the material (see provided table)
 \item user inputs the total number of units of this type
 \item user inputs the the setup cost
 \item user inputs the tooling cost
 \item user inputs the processing cost
 \end{enumerate}
 
 \item  The computer calculates the manufacturing cost for each element.
 \end{enumerate}
 
 The output should be in the following format:
 \begin{table}[ht]
 \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline
 Component& Martial& Ready& Part Number&Vendor&Fixed Cost&Variable
 cost& Total Cost\\ \hline
 
 
 &&&&&&&\\ \hline
  &&&&&&&\\ \hline
  
  \end{tabular}
  \caption{Table Title: Concept number 1, attach a figure}
  \end{table}

 
 
\begin{figure}[ht]
\vspace{8 in}
\caption{Material cost}
\label{mat}
\end{figure}

\end{enumerate}

\subsection{Individual activities}
\begin{enumerate}

\item Name three different cost classifications, and state the differences among
them.
\item What are the three cost estimate methods and what is the difference
between them?  What method is more appropriate for your design project and
why?
\item What is the break-even chart?
\item Using the break-even method, find break-even points if:

\begin{enumerate}
\item the fixed cost is \$12,000.
\item the variable cost is \$17.95 per unit.
\item the sale price is \$29.50 per unit.
\end{enumerate}

\item What would be the break-even in the previous question 
if the fixed cost is the same but the variable cost becomes \$29.50 and the
selling price becomes \$37.50?

\item The following data are for a company that produces black-and-white and color TV sets: 

\begin{itemize}
\item Black-and-white sets retail for \$198 and  contribute \$15 to profit.
\item Color sets retail for \$499.95 and contribute \$45 for profit. 
\item The color cathode-ray tube is limited in production capacity to 50 tubes, while all
other components have no limits.
\item Chassis assembly requires 6 man-hours for each black-and white set and 18 man-hours
for each color set.  The plant employs 225 workers for an eight-hour shift to perform
chassis assembly operations.
\item A black-and-white set spends 1 man-hour on the assembly line, a color set 1.6
man-hours.  There are 30 men on a single eight-hour shift assigned to assembly.
\item Final inspection requires 0.5 man-hour for a black-and white set and 2.0 man-hours
for color.  The plant employs 20 full time inspectors and one part time for 2 hours per
day.
\end{itemize}

\begin{enumerate}
\item Write a linear programming model. 
\item What is the optimum number of black-and-white and color sets.
\item Calculate the maximum profit. 
\item The linear programming and break-even are used to find the selling price
for both the black-and-white and color, based on (10,000 fixed cost for both black-and-white and
color) with a variable cost of \$160 for the black-and white and \$330 for the color.
Find out how many days it will require until the company starts making a profit for the color and the
black-and white. Use \$198 and \$500 as selling prices for the black-and-white and the
color respectively. 
\end{enumerate}

\end{enumerate}
 



