This paper sets out to describe transform methods to control vendor‐managed inventory (VMI). It aims to examine the limits of modelling approaches within control‐theoretic models.
Modelling was achieved with the Simulink package using the equations developed by Disney and Towill for a two‐tier VMI system. Discrete and continuous models were considered together with two forms of production delays: a finite delay and the Forrester exponential delay. Standard control engineering analyses of these delay representations were compared to illustrate how the system response and stability depend on their formulation and to determine the permissible gains.
Response by a discrete or continuous model to step inputs in sales rates depends on the type of delay representation but the responses do not differ by more than 5 per cent if the same delay form is used in the models. The prime effect of using a finite delay is to deepen the stock‐out and increase the required order rate compared with the same response observed with the use of exponential forms of delay. Total time for recovery is similar with all models. It is shown that the continuous model with an exponential delay is always stable and when using a fixed delay the continuous model can be made stable.
The models presented here illustrate that the various forms of control‐theoretic models present similar results irrespective of technique used, provided that they have the same delay type. The range of gains for the required order rate can be computed for any VMI system, knowing that they can be designed to guarantee stable operation.
This work extends that of Disney and Towill to include different modelling representations. It allows operational gains to be safely chosen for stable operation.
