Manufacturer-retailer integrated inventory model with controllable lead time and service level constraint under the effect of learning-forgetting in setup cost

The present study aims to establish a manufacturer-retailer integrated inventory model to jointly compute the optimal values of order quantity, lead time, reorder point, and number of shipments considering the effect of learning-forgetting phenomenon on the setup cost. The fabrication process of the manufacturer is not perfect; therefore, a certain level of product quality can be obtained for an additional cost. Service level constraint is incorporated into the inventory model to evade the backorder, which has negative impact on the company reputation. The lead time is also reduced by crashing cost. The proposed inventory model is illustrated through an example according to which centralized decision is preferred over the decentralized one. In addition, the analysis reveals that players should make a compromise concerning their profit if they wish to enhance the service level and product quality. The profit of the centralized system increases under the effect of learning-forgetting on the setup cost.