In this paper we address the general multi-period production/inventory problem with non-stationary stochastic demand and supplier lead-time under service level constraints. A replenishment cycle policy (R"S") is modeled, where R" is the nth replenishment cycle length and S" is the respective order-up-to-level. We propose a stochastic constraint programming approach for computing the optimal policy parameters. In order to do so, a dedicated global chance-constraint and the respective filtering algorithm that enforce the required service level are presented. Our numerical examples show that a stochastic supplier lead-time significantly affects policy parameters with respect to the case in which the lead-time is assumed to be deterministic or absent. (C) 2010 Elsevier B.V. All rights reserved.