Continuous-time dynamic modelling of variable lead times

Dynamic modelling of production–inventory systems usually involves lead time models since this is one of the most important aspects of these systems. Many different models are possible and this paper presents an overview and some ideas for how the models may be interpreted. Three different approaches to continuous-time dynamic modelling of variable lead times based on Control Theory are discussed. Two of the models can easily be incorporated into linear models based on the Laplace transform. The models are shown to be three instances of a generic delay model, which by careful selection of two parameters can be adapted to a wide variety of systems. Also the relation between waiting line theory concepts and the generic delay model is analysed, establishing an interpretation of the models as generating the concept of expected dynamic behaviour.