First, calculate capital recovery factor:
| f cr | = | r(1 + r)n/[(1 + r)n − 1] |
| = | 0.15(1 + 0.15)4/[(1 + 0.15)4 − 1) | |
| = | (0.15)(1.749)/(1.749 − 1) = 0.26235/0.749 = 0.3503. |
Next, calculate the estimated hourly rate of the work cell (Ca):
Ca = CIfcr/ha = ($150,000)(0.3503)/2080 hr = $25.26/hr.
Calculate factory overhead rate:
rfoh = ($2,300,000/yr)/($6,500,000/yr) = 35.4%.
Finally, calculate the hourly capital cost:
Cc = Ca(1 + rfoh ) = ($25.26/hr)(1 + 0.354) = $34.20/hr.
Thus, the estimated capital cost for operating the new automated work cell is $34.20/hr.
2.5 Comparing Alternatives with Productivity Calculations
Section 2.2 demonstrated the basic procedure for calculating the productivity of a process. Sections 2.3 and 2.4 demonstrated how to quantify the output and inputs of a process for use in the productivity calculations. This section is devoted to developing a methodology of performing the actual comparison of the alternatives. This essentially involves organizing the data in a logical, comprehensive manner in which the alternatives can be directly compared. The author has found that this is easily accomplished by organizing the data in a spreadsheet as shown in Figure 2-5.
Figure 2-5 Combined productivity comparison spreadsheet
The spreadsheet, aptly titled “Combined Productivity Comparison,” organizes the productivity data in rows and columns. The column headings are shown at the top in boldface print. The first column lists the description of the measure, the second is the variable used for the measure, and the third column displays the units. The next two columns, “Current Method” and “Proposed Method,” hold the data and calculation results for each method. The close proximity of these two columns enables swift comparison of the two options. The sixth column is reserved for formulas or comments (where certain cells hold formulas for performing the calculations). In the first row is entered the production rate for each method. This rate is determined through calculations dependent on the type of manufacturing system, as was discussed in Section 2.3.1. The next 12 rows are separated into groups corresponding to the partial productivity measures discussed in Section 2.2. The organization of the rows culminates with several combined productivity measures, the group at the bottom of the spreadsheet.
Note that each of the five productivity measure groups contains a new measure, not previously discussed: productivity index. The productivity index is a clear and concise method for comparing partial and combined productivity measures of the two options. Observe that for the so-called current method, each productivity index row contains a value of 1.0. This is because current method is used as a baseline against which the proposed method will be compared. The productivity index for the new method is determined by dividing the proposed method’s productivity (partial or combined) by the current method’s productivity. For example, the formula for the combined productivity index (Ic) is given by the equation
Ic = (PC) proposed/(PC) current
where
Ic = combined productivity index
(PC) proposed = combined productivity of the proposed method (parts/$)
(PC) current = combined productivity of the current method (parts/$).
Thus, if the proposed method has a productivity index greater than 1, it can be said that it is more productive than the current method. Conversely, a productivity measure of less than 1 indicates the proposed method is less productive than the current measure. Recall that for showing productivity improvement a combined productivity index greater than 1.0 is the key to justifying an investment in automation.
One should always look at combined productivity when comparing two methods. Consideration of only a partial productivity measure can often result in misleading results. However, if partial productivity measures are the same for the two methods being compared, they can be omitted from the calculations. But, odds are that there will always be more than one partial productivity measure to consider.
The following examples demonstrate the use of the spreadsheet.
Example 2.13
A manufacturing firm uses a manual machine for production. Production rate is 100 parts/hr. This current method utilizes two operators at a labor wage rate of $18/hr. The manual machine’s capital cost (including cost of electricity) of operation is $25/hr. This firm is considering replacing the manual machine with a programmable automation work cell. The new cell requires only one operator, but has a capital cost (including cost of electricity) of $65/hr. The production rate of the machine is 125 parts/hour. Perform a combined productivity analysis to determine if the firm should purchase the automated work cell.
Solution
The governing equations are listed in the spreadsheet shown in Figure 2-5. Entering production rate and calculating the labor partial productivity yields:
Eliminating the operator and increasing the production rate results in the proposed method that is 250% as productive as the current method from a labor perspective. Considering
