Order release planning with clearing functions: A queueing‐theoretical analysis of the clearing function concept

We consider the problem of planning future order releases in hierarchical production planning and control systems. An established research direction is the clearing function concept: the planned material flow through a production unit is modelled by inventory balance equations for WIP and final products, and the consequences of the stochastic properties of the material flow are modelled by clearing functions, which is the functional relationship between the level of WIP and the maximum output of a work centre in a period. Using a transient M/M/1 model, our paper shows that the usual definition of a nonlinear clearing function suffers from substantial shortcomings concerning both the definition of the function and empirical estimation of its parameters. We propose an alternative transient clearing function and derive a procedure for its parameterization.