Abstract: In traditional inventory model,lead time and setup cost are viewed as uncontrollable But,in practice,lead time can be shortened and set up cost can be reduced by added investment. During the short age,the supplier may of fer a price discount on the stock-outitem to compensate for the inconvenience of backorder and to prevent loss of orders. In practice,the mean and the standard variance of demand are a vailable,butitis hard to find its distribution. Under the assumption that backorder rate is dependent on inventory level and price discountin the period of shortage,this paper develops an EOQ model with controllable lead time and setup cost,in which the demand follows ageneral distribution The existence and uniqueness of optimal solution are proved and analgorithm searching for it is given. It is showed that order quantity,safety stock and inventory total cost can be generally reduced by shortening lead time and reducing set up cost. It is also showed that backordering parameter and probability of short age have a great impact on inventory total cost,so an enterprise should do its best to reduce probability of shortage,especially when backordering parameter is small.

Key words: lead time, setup cost, price discount, backordering rate, EOQ model