> If you instruct a machine to optimize for the cheapest price; it will do that

if (x < y) { // } is a simple optimisation.

The classic "you optimise for what is or can be measured rather than what is important."

There are ways around this of course by setting minimum quality via an objective third party (MIL-STD's for example) but that process introduces a whole new can of worms.

That much should be clear, my (unfortunately) implicit question is: how can we instruct a machine to optimize for the very intangible things everybody seems to love so much about this chalk? What about the more subtle economic things (like signals of economic climate and value of quality).

I once worked for a guy once who claimed he could sole-source a peanut if he had to. Many of them boiled down to colluding with the supplier to find a set of properties that were unique to their particular peanuts; things like soil pH, average temperature of the area they were grown in, not too much rainfall, not too little rainfall. Most purchasers were neither educated sufficiently to question these kinds of specifications, nor were they particularly interested; they also wanted to find the path of least resistance through the process. We probably could have bought most anything we wanted. Later we had a DOE grant get audited and there was some nervousness on our parts about some of these shenanigans that might be found. The guy just chuckled and said nearly everyone has to play this game to some extent. His major complaint about our books was that our overhead costs were above average, and he helped us make a case to the Uni for lowering it. Didn't see that one coming.

For an item like chalk though, my employer now has an arrangement with one of the big office-supply companies who specialize in tolerating (and charging extra for) gov't nonsense. Lately it's been CDW-G, I think. They provide a walled garden of approved products (which don't include the kind of good quality chalk in question) and a semi-streamlined purchasing process. It works great for the purchasing dep't, I'm sure, but it sucks for end-users because it introduces the same kind of uncertainty that a purchasing organization is supposed to fix. For example, the prices quoted on the website are not the actual prices of the products, and the products have variable discounts; this and the latency inherent in dealing with the purchasing process makes budgeting and price-shopping difficult to impossible. In my very small dep't we usually have budget projections rounded to the nearest hundred even for small items like chalk/dry erase markers because doing otherwise is a waste of time. We spent a lot of time a few years ago, working around the purchasing system just trying to get decent chalk before fatigue eventually set in and we just gave up and installed whiteboards.

optimise by a score. score is calculated as a function of price and some quality metric. unfortunately this can get complex.

Regardless of what metric you choose, Arrow's Paradox will bite you. Single-objective optimization will always force you to ignore good alternatives.

I do not understand the reference to Arrow's Paradox in a discussion of procurement policy (almost certainly related to my lack of knowledge). Can you elaborate?

Sure --- there's a neat paper by Franssen (2006) that demonstrates the formal equivalence between optimization problems and the social policy problems Arrow was concerned with. Basically, Arrow says that some constituents will always lose out under any social policy. Franssen showed that you can swap out "composite cost metric" for social policy and "components of the cost metric" for constituents, and the same arguments apply.

It must be too early for me. I can not find the franssen citation. Title?

Here's the full citation. Turns out I misremembered the year (2005).

Franssen M (2005) Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design. Research in Engineering Design 16(1):42–56

Sure there is. Sadly you'll need humans for that part, though. You could get several humans who all get a sample of each supplyers chalk, and then ask them to rate the quality of each on one (or several) scales. The computer can then integrate this rating with the rest of its metrics.

I didn't mean to say that it wasn't possible, you probably don't need a subjective measure of quality. I think you could empirically discover some objective characteristics of good chalk that would do the trick. You could at least quickly reject the worst chalk which is too brittle and too hard. I meant to say that there was and is no way that is recognized sufficiently universally that enables one to specify a chalk with the desirable properties to a gov't purchasing agent such that s/he can buy the right stuff.

Specify bending strength, the chalk must not snap under specified force. Next define a writing pressure, angle and stroke speed and require fewer than x blank areas in the line. Require that the line width be within a specific tolerance, not too thick not too thin.

Maybe a spec like this doesn't exist now, but you could use the good chalk and write the spec based on how it did.

The trouble is that the places that sell chalk to universities don't rate chalk like this. Like I said in another post ITT, we derped around for a couple years before we just gave up and installed the damn whiteboards.