This paper studies the coupon subset collection problem with quotas, which is a variant of the classical coupon-collection problem. Specifically, the set of coupons is divided into distinct subsets, each of which is referred to as a class and each element of a class is referred to as a type. Coupons can be collected one by one by purchasing a coupon package. A coupon class is said to be acquired if the number of acquired types belonging to the class reaches a given threshold. This paper derives an explicit representation of the survival function of the number of purchases required to acquire a given number of different coupon classes. Several upper and lower bounds of the survival function that can be calculated with less computation time are also derived. Finally, this paper shows that coupon subset collection problems are closely related to some practical problems and the results derived in this paper are useful for solving these problems.

本文研究了带有配额的优惠券子集收集问题，它是经典优惠券收集问题的一种变体。具体地，优惠券的集合被分成不同的子集，每个子​​集被称为类别，并且类别中的每个元素被称为类型。购买优惠券包可以一张一张地领取优惠券。如果属于该类别的已获取类型的数量达到给定阈值，则认为已获取了优惠券类别。本文得出了获取给定数量的不同优惠券类别所需购买次数的生存函数的显式表示。还推导了可以用更少的计算时间来计算的生存函数的几个上限和下限。最后，