Optimal decision for fashion supply chains with service level constraint and controllable lead time

We study a two-echelon supply chain inventory model with controllable lead time and service level constraint in fashion supply chains, in which we assume that the unit cost of compressing lead time follows exponential distribution. Under these conditions we investigate the optimal ordering quantity and production quantity in the fashion supply chain by minimizing the joint total cost. Simultaneously, we work out the boundaries of ordering quantity and production quantity, which simplify the computation. Furthermore, numerical examples are presented to test the feasibility of the model. The results show that assuming the unit cost of compressing lead time in accordance with exponential distribution is realistic. It also notices that the optimal order and production decision for fashion supply chains are constrained obviously by the service level and safety factors. What is more, the holding cost rate of both the service level and safety factors has a certain influence on it. And by further analyzing on some references in the last part, we have done some extensions and found some interesting results.