A mathematically reduced approach to predictive control of perishable inventory systems

  • Joanna Orzechowska

    Student thesis: Doctoral ThesisDoctor of Philosophy


    The design and optimisation of inventory replenishment systems has already been exhaustively studied by the operational research community. Many classical mathematical methods and simulation techniques have been developed and introduced in the literature. However, what can be observed is the fact that in a real case scenario the lead-time, deterioration of goods and demand for product are likely to be time-varying and uncertain, which traditionally have not necessarily been reflected in the model formulations. Therefore, in response to the dynamical nature of inventory systems, the potential of algorithms based on control theory to reduce the undesirable influences of system uncertainties on inventory level stability, have been investigated /proposed. Consequently, the mapping of the inventory problem into the control theory domain, for cost-benefit inventory trade-off achievement has been realised. Although, the application of control theory in inventory optimisation appears to be beneficial, there are certain reasons why the approach has gained yet little attention among the operational research community. One reason is that it cannot be adopted easily by researchers who are unfamiliar with control theory and another is due to a communication gap which exists between the control theory and operational research communities. Prompted by these observations, the thesis presents a novel, systematic mathematical approach for finding the optimal order quantities. The proposed approach has been mathematically demonstrated to be equivalent in study-sate to model-based predictive control, which is one of the more well-established productive control techniques with industrial application today. The mathematically reduced approach attempts to bridge the identified gap to fulfil the lacking dual perceptions of both communities. It enables the straightforward benefits afforded by predictive control without the necessity to become familiarised with principles of control theory. The method is shown to be applicable for both perishable and non-perishable inventory. Although the novel technique was inspired by MPC and noticing the MPC patterns in the mathematical description, the resulting proposal is no longer MPC. It is in fact a minimum variance approach, or dear beat controller, with an incorporated Smith predictor. Therefore using the adjective ‘predictive’ in the title of the thesis refers to both, the inspiration of MPC and the predictive nature of the minimum variance controller to accommodate lead time, being incorporated within an inherent Smith predictor. The developed approach is considered to be transferable to other applications, where similar model formulations may be applicable.
    Date of Award2014
    Original languageEnglish
    Awarding Institution
    • Coventry University
    • Łódź University of Technology
    SupervisorKeith Burnham (Supervisor), Dobrila Petrovic (Supervisor) & Andrzej Bartoszewicz (Supervisor)


    • Inventories
    • Mathematical models

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