Synchronization in the Single-Manufacturer Multi-Buyer Integrated Inventory Supply Chain: Derived Without Derivatives

The significant advances in information and communication technologies and the growing focus on E-business and modern supply chain management have pushed firms towards closer collaboration and more efficient integration of the supply chain functions. In this paper, we consider two known integrated supply chain inventory models. In the first model the vendor ships a batch for each buyer immediately after the completion of batch production, whereas in the second model, the buyer receives the batch only after the previous batch is consumed by demand. We derived the closed form solutions for both models using a simple algebraic approach that can be easily applied without differential calculus. The proposed solution is illustrated by a numerical example.