Trade-Offs

Last week I posted about constraints versus goals. This week I want to share a set of scenarios to help make things clearer. My goal through this exercise is to share how I interpret a problem statement. If you ask someone what they want their answer gives you some information. But asking someone about a series of alternatives tells you more. This is now my fourth week in a row trying to peel back the layers of this onion. Maybe someday reading the series backwards will seem coherent!

Suppose you are placing an order for grocery delivery. You want to have lasagna for dinner and have nothing on hand. So, you place your order. Your order is how you describe what you want. When you are checking out, you have the option to allow substitutes. If you cannot have what you wanted, what preferences would you need to tell your shopper? Let's go through three scenarios.

Scenario 1: I don’t want to cook

You place an order for a pre-made lasagna. If they have the specific one you selected on hand, great! Everything is simple.

But what if they turned out to be sold out of your choice? What should happen?

If you said substitution was ok, what sorts of alternatives are acceptable? Let’s go through some possibilities:

• Should your shopper pick another pre-made lasagna? If your shopper picked another pre-made lasagna that was $15 and the one you chose was $10, you would hope that this was the cheapest similar option. If you care about price, you might also hope that there are some guardrails so if the cheapest option was somehow $50 they would not buy that.

• What if there's a sale going on and exactly the brand you wanted to buy is available in a different variety for $2 cheaper? If your shopper saw both the option you selected and a different variety which was on sale, you might want them to switch to the cheaper option. Whether that is a good choice depends on if your shopper thought you saw the other option and turned it down, or not.

• What if there's another option that's twice as expensive for three times as much food? If your shopper saw that option, they would have to assess if you have a good use for the excess food or not.

• What if there's a package of pre-made stuffed pasta shells for the same price and the same amount of food? If your shopper picked the stuffed shells, you would hope that they decided it was very similar to lasagna given no other options. You would also hope they decided you would prefer the stuffed shells to being told “sorry, we’re out, please go to a different store.”

When you decide not to allow substitutions, you state that your requirement is to get exactly the thing you ordered or nothing at all. In the situation above most people would find at least one of my alternatives that they'd say yes to. Most people would also probably find at least one alternative they find unacceptable.

How could we convey these preferences to an algorithm to let it make the best choice for you?

• You could identify a specific food at a set price (i.e. no substitutions).

• You could submit preferences for a list of many food options, along with a tradeoff between those preferences and cost.

Given a reasonable grocery store and a decision maker, you could leave it open ended like most delivery websites. A human probably wouldn’t consider a $50 lasagna as a reasonable substitute for a $10 lasagna. And besides, most grocery stores do not sell $50 lasagnas. Relying on common sense is not a guarantee. But it can be a helpful shortcut in some cases.

Scenario 2: I order the ingredients

You place an order for lasagna noodles, meat, ricotta, mozzarella, and tomato sauce. If they have each of the items in exact brands and package sizes you selected, great! Everything is simple.

But what if they turned out to be sold out of some subset of your choice? What should happen?

If you said substitution was ok, what sorts of alternatives are acceptable? In the first scenario we talked about alternatives that were more or less expensive than your original choice, a better or worse cost per calorie, or just a different version of the underlying idea to eat lasagna. All of those same possibilities are options here for each ingredient.

But what if the store is completely out of every kind of lasagna noodle? In Scenario 1 we had the concept of substituting a single item. In this case, we have a slightly more complicated problem as we have to think about a set of decisions. Let’s go through some possibilities:

• Should the shopper buy you everything else and skip the noodle portion? If the shopper buys you everything else and skips the noodles, you end up with a choice on your hands. Do you place a second delivery order somewhere else, go to a different store yourself, or did you just waste a bunch of money and you have to make something else for dinner anyway? Taken one item at a time it makes sense to buy everything else, but in the context of our scenario, we may reach a different conclusion.

• Should they buy you everything else and then substitute the noodles for a pre-made lasagna as the "most similar option in the store to lasagna noodles." If the shopper bought you everything else and then a pre-made lasagna, it seems like it was a waste to buy everything else, or maybe it is even more wasteful to buy the pre-made lasagna since you could buy the noodles somewhere else. In this case it seems fairly clear that buying a substitute for the noodles plus all the other ingredients made you worse off. But just like above it is not necessarily clear one item at a time that they made a poor choice.

• Should they just scrap the entire list and replace it with the pre-made option? If the shopper bought you only the pre-made lasagna and nothing else, they have made a choice for you. This is a substitute of the overall, not one item at a time. Like in Scenario 1 you may agree or disagree that this is a substitute you would be happy with, but in either case the shopper made a decision that some people would agree with.

• They could also just cancel your whole order because lasagna without the noodles doesn't make a lot of sense. If the shopper realized you would be missing a key ingredient and got you nothing, that avoids some of the issues with substituting one item at a time. Like the rest of the examples in this scenario, an individual may or may not be happy with the choice.

When you decide to allow or not allow substitutions you are taking a risk of being in one or more of these situations. The right substitute is somewhat less clear here since achieving the presumed goal of “having lasagna for dinner” requires somewhat more liberty with the idea of a substitute than in Scenario 1. Instead of buying a half dozen ingredients, the closest substitute seems to be buying just 1 pre-made lasagna. But, that assumes the grocery store you ordered from is the only place you could get food, and most people have other options.

How could we convey these preferences to an algorithm to let it make the best choice for you?

• You could identify an all-or-nothing set of food (i.e. no substitutions or omissions).

• You could submit preferences for a set of food options including how each possible substitute or omission contributes.

Given a reasonable grocery store and a decision maker, you could leave it open ended like most delivery websites. A human probably wouldn’t consider a pre-made lasagna as a reasonable substitute for just the noodles. Relying on common sense is not a guarantee. But it can be a helpful shortcut in some cases.

Scenario 3: I have dietary restrictions

You place an order for gluten free lasagna noodles, vegan meat, non-dairy ricotta and mozzarella, and a brand of tomato sauce that meets your needs. If they have each of the items in exact brands and package sizes you selected, great! Everything is simple.

But what if they turned out to be sold out of some subset of your choice? What should happen?

If you said substitution was ok, what sorts of alternatives are acceptable? In Scenario 1 we talked about different versions of the same thing (pre-made lasagna or things that seem sort of equivalent to it). In Scenario 2 we talked about how some constraints could entirely change the right solution (I want to cook lasagna, but maybe I'd rather get something pre-made than resort to going to a second store).

Scenario 3 happens to be my life. After trying to allow substitutions a couple times, it became clear that would not work. Is normal ricotta a substitute for the vegan kind? It's cheaper for more, so in our discussions so far it could be "better." But I have a constraint that makes it an unacceptable alternative. And so if I want my groceries delivered, what should I do differently?

The short version is I plan things somewhat differently. I cannot rely on a human to make common sense decisions that align with my preferences. So, it rarely makes sense to order online, and often stockouts get in the way even if I go to the store myself. Instead, I acquire ingredients first, and plan dinner second. My problem statement is about how I can have the right set of food on hand over the course of my normal grocery shopping.

Conclusion

Hopefully this series of scenarios and discussions helps convey the different kinds of preferences that someone might have when they are making a decision. And further, how those preferences could change the problem statement entirely. Lastly, I hope you begin to see why I like studying “alternatives” as a tool for understanding the underlying problem.