参会者无偏好情形下的会议周边商品组合优化
Assortment Optimization For Conference Goodies With Indifferent Attendees
AI总结：
该研究针对会议周边采购的组合优化问题，在参会者对类型无偏好但需多类型可选的模型下，验证了2、3类时等量采购的猜想，给出渐近结果与模拟，悬赏求解K类一般情形。
摘要：
诸如FUN with Algorithms（算法之趣）之类的会议通常会为参会者购置周边商品（例如T恤、马克杯等）。这类周边往往有不同类型，在颜色或设计上存在差异，组织者需要决定每种类型的周边应采购多少。我们在一种简单的参会者偏好模型下研究各类型最优采购量的问题：参会者对周边类型本身无偏好，但希望在抵达时能在不止一种类型的周边中进行选择。参会者的无偏好特性意味着，最优策略是为每种周边类型采购大致相等的数量。尽管这一猜想听起来十分直观，但我们证明这种简单的组合优化问题结构相当丰富：虽然我们在证明该猜想的方向上取得了进展（例如在周边类型数为2或3的情况下证明成立），但K种类型的一般情形仍悬而未决。我们还给出了渐近结果和计算机模拟，最后，为推动进一步研究，我们为完整证明提供100美元的奖励。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
