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. Importance of This Paper The CONWIP control policy has been developed as an easily implementable alternative to pure pull policies for shop floor control. In contrast to pure pull policies, for which much research has concerned the appropriate number of production authorizations (kanbans) to place in circulation, CONWIP research on this decision has been scant. In addition, the development and analysis of this control policy has focused on flow lines or assembly systems. Many of the benefits of CONWIP should accrue in job shops as well; however, in order to implement it, one must determine the total amount of WIP allowed in the system, as well as the quantity for each product (the WIP mix). The designer of a pull policy for a job shop must also decide whether kanbans are shared among the products or whether individual WIP levels are fixed for each product. This issue is currently unresolved. We believe that the latter policy has more evidence to support it and that it is more consistent with the reasoning underlying the development of CONWIP control: that WIP levels are easy to control, while throughput (in particular, the production ratios for the different products) should be observed as an output variable. However, the allocation of a fixed total WIP to different products is a difficult combinatorial problem. Our procedure to determine the total WIP and WIP mix uses a shared kanban model for planning purposes. For a given product mix the procedure uses nonlinear and linear programs to bound the system throughput and suggest the total WIP and the WIP mix proportions. Individual product WIP levels are extracted from this solution. Numerical examples illustrate the tightness and robustness of the throughput bounds and show how the resulting WIP levels achieve high throughput consistent with the desired product mix.