I'm wondering if there is a good theoretical reason why nobody seems to use Marginal Analysis to optimize how much human talent is stocked in inventory. In all the classical treatments in textbooks, newspapers, donuts, bread etc have been analyzed using Marginal Analysis. It's always a widget that sells or doesn't sell within one inventory period.

Well, check this out: I know of specific firms where they contract with human talent, and sell that human talent to customers. Examples of talent for which there is a limited weekly supply (for example) and a definite demand, include former US presidents who give talks; tech support on the phone; management and technical consultants; astrology / entertainment. You might notice that a specific talented individual may be limited to a certain supply of hours they can provide in a given week. There is also some sort of demand for the talent to purchase their services.

How many hours would a smart firm want to stock, ie., purchase from such an individual, to book their time in advance? How many hours per week should the firm contract with the talent? This is the essential question.

Inputs to the calculation:

  • Marginal Loss (ML), the cost to the contracting firm when demand exceeds supply. For example the talent is contracted to be available for 5 hours in the week, and the customers continue to call to book time beyond those 5 hours.

  • Marginal Profit (MP), the selling price minus the contracted cost for when the talent actually gets purchased from the contracting firm.

Given ML and MP we now can compute P statistic = ML / (ML + MP). Now we can use probability distributions (discrete or continuous) to find the optimum "stocking" quantity for the talent. In this case it will be number of hours "on" that is contracted in one week for example.

Is Marginal Analysis suitable, or is it unsuitable for optimal stocking quantity of saleable human services? If not, why not?

Thanks for reading.

asked 12 Feb '13, 12:09

GeoffreyA's gravatar image

GeoffreyA
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I might have made a mistake in my ML and MP definitions. Let's not get too stuck on that mistake. I will correct them by saying that in the talent scenario, ML is the talent hours that costs the firm to contract as on-time, but which goes unsold due to insufficient demand. It is leftovers, like bread that goes unsold. MP is the hours (cf. bread) that actually gets sold by the firm during the time period for which it was purchased by the firm. In this case the firm enjoys a profit which equals price (of hours sold by the firm) minus cost (dollars the firm paid to the talent for each of those hours.)

(12 Feb '13, 12:25) GeoffreyA

On the surface, what you are describing is the classic "newsvendor" problem, only with multiple commodities. You could model the contractual arrangement with each individual (e.g., speakers) or group of commensurable individuals (e.g., level one tech support specialists) as a newsvendor problem. There are some difficulties, though. One is the issue of substitution: excess inventory for one individual/category may be useful to satisfy demand for another individual/category, but perhaps at a different revenue value (and possibly with a different cost -- I charge more for things I'd rather not do). Another is that, unlike newspapers, some individuals can provide multiple distinct services.

So those two wrinkles may account for a lack of inventory modeling of human assets. Another possibility is that it is in fact being done, but is not being published (or discussed) because it represents a proprietary method that provides competitive advantage to the user.

A third possibility (one that I think is a significant contributor) is that the people who manage human resources tend not to be the most quantitative by nature. I think that college HR majors rarely require any math beyond the general college requirement, and perhaps some statistics. When I taught quantitative modeling to MBA students, the HR concentrators (with one notable exception) tended not to dominate the top quantiles.

link

answered 12 Feb '13, 14:20

Paul%20Rubin's gravatar image

Paul Rubin ♦
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accept rate: 17%

Another possibility is that it is in fact being done, but is not being published (or discussed) because it represents a proprietary method that provides competitive advantage to the user. A third possibility (one that I think is a significant contributor) is that the people who manage human resources tend not to be the most quantitative by nature.

This is what I love to hear. The opportunity to do what I proposed, then, appears alive and well.

Thanks for these ideas.

(14 Feb '13, 20:24) GeoffreyA

Do you mean job evaluation?

link

answered 15 Feb '13, 09:09

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Slavko
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1

No I was thinking of optimizing the rates of the astrologists we had on contract for phone entertainment at the place I used to develop software. I think they did not know very well how to optimize the number of hours they contracted with the talent each week.

But thank you for this new information.

(15 Feb '13, 21:23) GeoffreyA
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Asked: 12 Feb '13, 12:09

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Last updated: 15 Feb '13, 21:23

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