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 + PI cap + PI mat + PI energy.
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
