Production Planning (PP) plays an important role in modern manufacturing enterprises. With more and more restrictions imposed by various labour laws, PP decisions should be made not only based on industrial constraints, such as production capacity and inventory level, but also with respect to social constraints, such as limited use of overtime. Under such conditions, we propose a dynamic programming based approach for solving a class of PP problems with explicit consideration of social constraints. The problem considered in this paper is defined based on a real-life problem proposed by an international automobile industry. The objective is to find a feasible and flexible PP with respect to both industrial and social constraints. In the studied assembly system, PP decisions are made based on the sales forecast, the available production capacity and the current inventory level and with respect to the limited use of non-working days, overtimes and third shifts.