On the analysis of lead-time disturbances in production and inventory control models

Changes in the lead-time can lead to supply chain inefficiencies and risks. In this paper, we investigate the effects of lead-time disturbances on the system’s output responses of a production and inventory control model. In the adaption process of the control system for lead-time disturbance analysis, the resulting model becomes nonlinear. Hence nonlinear control theory in combination with simulation is used to analyse the impact of leadtime changes on the transient and steady state responses of order rate, inventory and work in process. Assuming constant customer demand, small perturbation theory is applied to linearise the model and to find the transfer functions relating the system’s outputs to the lead-time input. We find that the order rate, inventory and work in process transfer functions are input-dependent. In order words, the output responses depend on the input type, amplitude and direction of changes in the lead-time. When leadtime increases, the system has a relatively slow transient response and, as expected, work in process inventory levels increase and order rates are higher. However, step decreases in the lead-time can cause significant underdamped dynamics in the system. This work demonstrates that, although lead-time reduction is associated with service level improvement, increased flexibility and cost reductions, its implementation has to be carefully planned since a quick time compression may lead to undesirable oscillations in the supply chain system. In contrast, increased lead-times, associated say with a disturbance, yield slow recovery requiring adjustment of control parameters to increase resilience.