In this study, we focus on a lot sizing problem with stochastic production and setup times and with limited inventory. In this problem, a single capacitated machine is used to produce several different items in each time period. Due to realization of stochastic times, companies may need to use overtime leading to additional costs considered as a part of the total operational cost. We model this problem as a stochastic programming where overtime values correspond to recourse decisions. Two solution approaches are developed. A first type of approach is based on tabu search algorithm where we employ a local search method specifically focusing on inventory bounds. A second type of solution approach is based on solving a stochastic programming model with a set of sample scenarios. We provide extensive computational results and confirm that the proposed procedures are effective to obtain very good solutions to be performed in real-life settings.