Multi-dimensional clearing functions for aggregate capacity modelling in multi-stage production systems

Nonlinear clearing functions have been proposed in the literature as metamodels to represent the behaviour of production resources that can be embedded in optimisation models for production planning. However, most clearing functions tested to date use a single-state variable to represent aggregate system workload over all products, which performs poorly when product mix affects system throughput. Clearing functions using multiple-state variables have shown promise, but require significant computational effort to fit the functions and to solve the resulting optimisation models. This paper examines the impact of aggregation in state variables on solution time and quality in multi-item multi-stage production systems with differing degrees of manufacturing flexibility. We propose multi-dimensional clearing functions using alternative aggregations of state variables, and evaluate their performance in computational experiments. We find that at low utilisation, aggregation of state variables has little effect on system performance; multi-dimensional clearing functions outperform single-dimensional ones in general; and increasing manufacturing flexibility allows the use of aggregate clearing functions with little loss of solution quality.