The assembly line worker assignment and balancing problem (ALWABP) is a hot and interesting topic. In an assembly line, persons with disabilities can be employed and work better due to the specialized work. In this paper, we investigate the ALWABP with heterogeneous workforce considering stochastic worker availability. The problem has been addressed in the previous literature. However, the workers are sometimes insufficient to meet all stations due to high level of workforce absenteeism and this situation has not been fully considered in the literature. Therefore, we propose an improved two-stage stochastic programming model allowing inadequate workers to minimize the weighted sum of cycle time and penalty cost caused by insufficient workers. The first stage is to assign fixed tasks to stations, and the assignment of flexible tasks and workers is regarded as the second-stage decision. Sample average approximation (SAA) is applied to solve the model within feasible time. Finally, we conduct computational experiments to test the model compared to the model with the assumption that the number of workers is adequate to meet the number of stations (AS model). We test two instances including 8 and 10 tasks respectively and different numbers of scenarios are also taken into account to demonstrate the improvement of our model.