What approaches can be used in measuring productivity?
The category of this question is quite important; "productivity" means somewhat different things in business versus economics.
Whereas economists might be interested in the overall efficiency of an entire economy, treating "productivity" as a macroeconomic concept (such as "total factor productivity"), businesses are generally concerned with their own productivity as a firm: How efficiently are expensive inputs being used to produce revenue-generating outputs?
A few different approaches can be taken for answering that basic question.
The simplest way is to divide the amount produced by the amount consumed, which can be done for each input separately. We can speak of labor productivity, how many units of goods are produced per worker hour, and capital productivity, how many units of goods are produced per machine hour. You can also assess each of these in financial terms: How many units of good are produced per dollar spent on labor versus capital. We can compare both total productivity and marginal productivity, where total is simply output divided by input, while marginal is the amount of output that would be generated if we added one more unit of input. If we are spending optimally, the marginal productivity of each dollar spent on each input should be the same; if they are not the same, we may be overspending on one input versus another.
Probably the most useful measure of productivity for business purposes is value added, which considers the total revenue generated by selling products in each period, minus the total expenditure paid to produce those same products. Adjustments need to be made to ensure the right things are being compared; if you are depleting inventory from past purchases, you need to either include those purchases or exclude those sales.
You can also calculated value added another way, by adding up all the places that net revenue ends up going: Profit, dividends, retained earnings, depreciation, labor expenditure (sometimes called "labor cost"; this is actually economically erroneous but I've even seen economists make the mistake), interest, and taxes---essentially, all forms of profit plus all expenditures that weren't for inputs other than labor.
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