On the inventory model with continuous and discrete lead time, backorders and lost sales

A well-established global supply chain system plays an important role in an enterprise's strategic management, and an effective just-in-time system is a critical success factor for a global supply chain system. The advantages and benefits of just-in-time are associated with controlling the lead time. In this paper, we propose an approach to overcome the drawback of traditional methods for improving the continuous and discrete lead time with mixture of backorders and lost sales, by which only a local optimal solution can be obtained. In addition, the proposed model allows decision-makers to add suitable constraints to their model in accordance with their actual business environments. Finally, in order to demonstrate the accuracy and effectiveness of the suggested model, a real-life case, some numerical examples and sensitivity analysis are also included.