We consider the supply planning for one level assembly system under uncertainty of lead times. The finished product need several components for the assembly operation. The lead times can be uncertain for different reasons such as machine breakdowns, transport delay, strike, etc. In literature, this type of problem was studied in the case of random lead times that follow continuous distributions as well as in the case of any discrete laws with known distribution. We consider the case of discrete distributions to be closer to the industrial reality because often in real life situations the lead time is expressed as the number of periods. Typically, this is an inventory control problem where the objective is to minimize the component holding and backlog costs for the finished product due to the uncertainty of lead times. Indeed, as the finished product is assembled by using several types of components, the assembly is stopped even if a single type of component is delayed. The other components are stored between their arrival and the arrival of the latest component. To reduce stock and backlog costs, we propose to pay the supplier more, if he/she agrees to decrease his lead time uncertainty. A model describing this choice is suggested.