Analysis of the robustness of a single-tier pipeline inventory model

This paper examines the conditions necessary to specify a robust element of a supply chain using control theory and proposes a new robustness criterion clearly separating robustness from resilience. Algebraic analysis, using the Mikhailov criterion to determine robustness, yields simple criteria for an automatic pipeline with variable inventory and order-based production control system (APVIOBPCS) model. Models implemented with either exponential delays or finite delays are found to be completely robust. A new robustness measurement criterion is defined and applied to a case study of RAM manufacture. Results show that the continuous model of an APVIOBPCS system with an exponential delay has a wider allowable range of process delay time than other models and the range of permissible delay is sufficient to cope with a substantial increase in process delay time while retaining adequate performance and stability. Use of nonlinear inventory generally reduces the robustness range. The techniques used here can also determine the effects of other parameters on robustness.