An exploratory study of disaggregated clearing functions for production systems with multiple products

Clearing functions (CFs) have shown considerable promise for representing production capacity in production planning models due to their ability to capture the non-linear relationships between throughput, order releases and lead times. Most CFs developed to date use the total work in progress of all products, in units of processing time, as the state variable. In this paper, we investigate CFs for multi-product systems where the overall throughput of the system is affected by the product mix. We show that the aggregate work in process (WIP) variable used in the previous CF literature may lead to inaccurate estimates of expected throughput for individual products. To address this issue, we explore the use of multi-dimensional CFs (MDCFs) that use an extended definition of resource state based on the disaggregated WIP levels for individual products. Several new functional forms for MDCFs are postulated for single machine multi-product systems and their ability to represent system behaviour is assessed using simulation experiments. Results reveal that MDCFs are better able to predict system performance in the presence of mix-dependent capacity losses. We also discuss the extension of the MDCF approach to multi-stage production systems.