Total WIP and WIP mix for a CONWIP controlled job shop

A planning procedure to set the constant level of Work-In-Process (WIP) for each product type in a job shop operated under CONWIP control is developed. We model the job shop as a single chain multiple class closed queuing network. Given a specified product mix and a total WIP, a nonlinear program bounds the throughput of the network and optimizes the WIP mix. We identify the minimum total WIP that is guaranteed to yield throughput near the maximum possible for the specified product mix and set individual WIP levels by multiplying the optimal WIP mix proportions by the minimum total WIP. Numerical examples illustrate how these individual product WIP levels achieve the goal of high throughput consistent with the specified product mix.