Determining inventory levels in a CONWIP controlled job shop

We extend the concept of CONWIP control to a job shop setting, in which multiple products with distinct routings compete for the same set of resources. The problem is to determine the fixed overall WIP level and its allocation to product types (WIP mix) to meet a uniformly high customer service requirement for each product type. We formulate an optimization problem for an open queuing network model in which customer orders pull completed products from the system. Then, assuming heavy demand, we derive a throughput target for each product type in a closed queuing network and provide a simple heuristic to find a minimum total WIP and WIP mix that will achieve an operating throughput close to this target. In numerical examples, the WIP mix suggested by this approach achieves the customer service requirement with a relatively low total WIP.