Periodic review policy in the production management of a single-item inventory with deterioration

In the dynamic field of inventory management, effective control of perishable goods presents a significant challenge. Additionally, most organizations are greatly concerned about the bullwhip effect, which is further exacerbated in the case of perishable goods. This paper considers an effective control theoretic analysis of the periodic review strategy for perishable production-inventory systems. In contrast to the earlier approaches, which are mainly based on heuristics and static optimization, discrete Pontryagin's maximum principle of dynamic optimization is applied for the analytical solution of the problem. In the proposed model, the time-variant deteriorating stock is replenished with delay from its manufacturing unit in order to fulfil unknown stock-dependent time-varying demand. Handling loss in the saturating integrator is considered, but handling time is neglected. The inventory model is framed as a linear quadratic regulator to reduce the risk of the bullwhip effect. The other benefit is to get the optimal solution analytically. The supply of goods from its manufacturing unit also helps minimize the bullwhip effect. The optimal production and optimal growth of the inventory are calculated based on some specific choice of the parametric functions involved in the process, and they are represented graphically. The problem of periodic blood supply to the Blood bank through blood donation camps is studied as a practical application of the proposed inventory model. Finally, the proposed model works well for real-world scenarios under sensitivity analysis with a proper choice of parameters.