Note that none of the values in the spreadsheet for the current method changes. Also, all the partial productivity inputs for the proposed method stay the same. Therefore, the following values are given:
Ic = 1.20
PC current = 1.64 parts/$
SPI = $83/hr.
Setting up the equations:
1.20 = PC proposed/1.64 parts/$.
Rearranging yields
PC proposed = (1.20)(1.64 parts/$) = 1.968 parts/$.
But PC proposed is determined from the equation
PC proposed = (PO/SPI) proposed.
Dropping “proposed” and entering the correct values gives
1.968 parts/$ = PO/$83/hr.
Thus, the minimum production rate is
PO = (1.968 parts/$)($83/hr) = 163.34 parts/hr.
The result is confirmed in the spreadsheet shown in Figure 2-7.
Figure 2-7 Example 2.14, part (a) solution
Part (b)
For this solution, trial and error will be used with the spreadsheet. Start by decrementing capital cost/hr in $10/hr increments. As productivity approaches desired value, decrease the increment until the final number is arrived at, which is approximately $45.50/hr. The result is shown in Figure 2-8.
Figure 2-8 Example 2-14, part (b) solution
This is the solution.
The previous example demonstrates how the spreadsheet variables can be tweaked to identify how the proposed method could be enhanced to make it a more attractive option from a productivity standpoint. Other variables could also be adjusted including reducing or eliminating the operator altogether and looking for material savings with the proposed method. Thus, the spreadsheet can be used as a roadmap to identifying other improvements the proposed method may have to offer.
When a combined productivity analysis indicates that the proposed method is justified, there is still one measure we should consider. That measure is production volume. Its impact on choosing alternatives is discussed in the next section.
2.6 The Impact of Production Volume on Alternatives
Thus far we have assumed that product volume—both current and future—of the process under consideration for automation is sufficient to support an automation investment. In general, when product volumes are low, manual methods are more cost effective. A manufacturing firm does not want to invest significant funds in the manufacture of a product that will no longer be produced in 6 months to year, or for which the annual volume is not great enough. Although predicting future volume, called forecasting, is a risky venture, it is an essential part of doing business. Product forecasts are typically available from marketing or upper management. The risky nature of production volume forecasting is one reason a manufacturing firm needs to see a quick payback of the automation investment. Thus, one must ascertain whether there is sufficient production volume to justify the investment in the automation. This can be accomplished by considering current and proposed methods’ fixed and variable manufacturing costs and performing a production volume breakeven point analysis.
A product’s manufacturing cost can be broken into two categories, fixed costs and variable costs. Fixed costs are costs that are independent of the quantity of product; i.e., they are incurred whether one part or one million parts are produced. These typically include building rent or mortgage costs, property taxes, equipment costs, and equipment maintenance, to name a few. Fixed costs are most conveniently expressed on an annual basis.
Variable costs, on the other hand, are dependent on the quantity of product. The higher the production, the more the cost incurred. Variable costs include direct labor, raw material costs, and energy costs to operate the equipment. Utilizing these concepts the total annual cost of a product can be represented by the following equation:
CT = CF + QCV,
where
| C T | = | total cost incurred on an annual basis ($/yr) |
| C F | = | fixed cost of product on an annual basis ($/yr) |
| Q | = | quantity of parts produced per year (parts/yr) |
| C V | = | variable cost per part ($/part). |
This formula’s use is demonstrated in the following example.
Example 2.15
Referring to the manual manufacturing method and information in Example 2.13, and given that the annual cost of maintenance for the machine is $8000 and the raw material cost is $1.25 per part, calculate total annual cost of producing 100,000 parts per year
Solution
The given information from the problem statement and taken from Example 2.13 is as follows:
PO = 100 parts/hr (production rate)
PI labor = $36/hr (2 operators at $18/hr)
PI capital = $25/hr
Q = 100,000 parts/yr
CF maint = $8000
raw material cost = $1.25/part.
The first step is to identify the variable costs, which include the labor wage rate, the machine’s capital cost, and the raw material cost. The labor and machine capital costs must be converted to units of $/part. This is accomplished by dividing the hourly cost by the production rate as follows:
CV labor = PI labor/PO = ($36/hr)/(100 parts/hr) = $0.36/part
CV capital = PI capital/PO = ($25/hr)/(100 parts/hr) = $0.25/part.
Next determine the total variable costs by summing each of the individual variable costs:
CV = CV labor + CV capital + CV material
= $0.36/part + $0.25/part + $1.25/part = $1.86/part.
The fixed cost is simply the annual maintenance costs:
CF = $8000/yr.
Solving for the total annual cost to make the product yields
CT