Assortment Optimization For Conference Goodies With Indifferent Attendees

Conferences such as FUN with Algorithms routinely buy goodies (e.g., t-shirts, coffee mugs, etc) for their attendees. Often, said goodies come in different types, varying by color or design, and organizers need to decide how many goodies of each type to buy. We study the problem of buying optimal amounts of each type under a simple model of preferences by the attendees: they are indifferent to the types but want to be able to choose between more than one type of goodies at the time of their arrival. The indifference of attendees suggests that the optimal policy is to buy roughly equal amounts for every goodie type. Despite how intuitive this conjecture sounds, we show that this simple model of assortment optimization is quite rich, and even though we make progress towards proving the conjecture (e.g., we succeed when the number of goodie types is 2 or 3), the general case with K types remains open. We also present asymptotic results and computer simulations, and finally, to motivate further progress, we offer a reward of $100usd for a full proof.