Capacity-constrained Outsourcing to Two Contract Manufacturers with Diferent Improvement Capabilities

We investigate a supply chain arrangement where a manufacturing company outsources it sassmbly operations to two contract manufacturers. Each contract manufacturer is different in improvement capability : e.g., one is more capable than the other. This improvement capability is supposed to in-duce supply cost reduction that ultimately benefits the manufacturing company. Over time, the manufacturer has to decide how much it should outsource to each contract manufacturer and how much processde/assembled the semi-finished units should be when they re shipped back to the manufacturing company from the contract manufacturers. We employ the optimal control theory to answer the questions, and suggest numerical examples focused on the relationship among the optimal outsourcing amounts, contract manufacturer's improvement capabilities, and their capacity con-straints.