Let T={1,...,n} be a set of tasks. Each task i has associated a non negative processing time p_i and a deadline d_i. A feasible schedule of the tasks consists of a permutation of n elements pi, such that \sum_i=1^k p_(pi(i)) <= d_(pi(i)) for all k=1,...n.

Does there exists a pseudo-polynomial time algorithm for computing the total number of feasible schedules?

A pseudo-polynomial time algorithm is an algorithm whose running time is bounded by a polynomial on the size of the input, given that the input is written in unary notation (2=II, 3 =III). (e.g., the size of a number n in unary notation is O(n), and not O(log(n)).

This is an open question from an article published in 2009 at Operations Research Letters.

no sense whatsoever$\endgroup$1more comment