  We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to
ideals in normal semigroup rings. In the case of monomial ideals, we also
relate the roots of the Bernstein-Sato polynomial to the jumping coefficients
of the corresponding multiplier ideals. In order to prove the latter result, we
obtain a new combinatorial description for the multiplier ideals of a monomial
ideal in a normal semigroup ring.
