Optimum inventory and product quality control with deterministic and stochastic deterioration--An application of distributed parameters control systems

Inventory models with deterministic and stochastic deterioration rates are given. The first model, assuming deterministic deterioration rates, is a hyperbolic equation while the second one assuming a stochastic deterioration rate is reduced to a parabolic equation of the second order. Optimization of these in inventory models when costs are quadratic yields linear feedback replenishment policies. This short paper provides an analytic solution to both problems. The importance of such inventory models is to be found when the demand and value of stored products is also dependent on their quality.