Coupon Subset Collection Problem with Quotas

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.