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 this measure alone, the proposed method looks very attractive. However, as mentioned, we must evaluate all of the partial productivities and then calculate the combined productivity prior to passing final judgment. No information on raw material was given, thus it will be omitted from the calculations. Additionally, the cost of energy was given in the capital cost per hour. Thus, the only remaining partial productivity to evaluate is capital.
The increased capital hourly cost of the proposed method in conjunction with only a marginal increase in production rate makes the proposed method is only 48% as productive as the current method, from a capital perspective. Calculating the combined productivity yields:
Thus, the proposed method is 92% as productive as the current method. Thus, the proposed method is not justified and the firm should not purchase the automated work cell. The completed spreadsheet is shown in Figure 2-6.
Figure 2.6 Example 2.13, combined productivity calculation
This is the solution.
The last example demonstrates how to use the combined productivity comparison spreadsheet and highlights the importance of calculating the combined productivity before passing judgment on the proposed method. Another interesting benefit of the combined productivity comparison spreadsheet is that it can be a starting point or roadmap for identifying the type and quantity of improvements necessary to justify automation.
For example, one might ask, “If the proposed method is not justified (viz. Figure 2-6), what improvements would make it justifiable?” Obviously, if the work cell’s production rate would be increased substantially and/or capital cost decreased, the purchase of the work cell might be justified. Thus, by tweaking the values in the spreadsheet, target values for production rate and capital costs can be identified. These targets can then be presented to the suppliers of the work cell as required performance specifications. Consider the following example.
Example 2.14
Based on the results of Example 2.13, determine the following:
| a) | Minimum production rate of the proposed method to yield a 20% productivity improvement. Assume all other values are as before. |
| b) | Maximum capital cost per hour of the proposed method to yield a 20% productivity improvement. Assume all other values are as before. |
Solution
Both of these can be determined by two methods. The first is to solve directly by using algebra and rearranging the governing equations accordingly. The other method is a trial and error method that uses the spreadsheet to manually increment the variable in question until the desired result is achieved. For part (a) the result will be solved directly. Trial and error will be used to solve part (b).
Part (a)
The governing equations are
Ic = PC proposed/PC current
PC = PO/SPI
SPI = PI labor