Two-echelon inventory model with service level constraint and controllable lead time sensitive to order quantity

Two-echelon inventory problem with service level constraint and unknown distribution function was analyzed when controllable lead time was sensitive to order quantity. First the basic model of this problem was established and based on relevant analyses the original problem could be changed by Minimax method. Then the optimal order quantity and production quantity influenced by service level constraint were analyzed and range of optimal order quantity and production quantity were given. According to this range, an effective method and tactics were put forward to solve the changed problem. In case analysis, the optimal two-echelon inventory can be obtained and it was analyzed how service level constraint and safety factor influence the optimal two-echelon inventory. The case results show that with the service level constraint and safety factor, the optimal two-echelon inventory is constrained by the higher constraint between service level constraint and safety factor.