Optimal Control of a Production Inventory System with Generalized Pareto Distributed Deterioration Items

This study is concerned with the optimal control of inventory-production system subject to generalized Pareto distributed deterioration items. We formulated the model as a linear optimal control problem. This study deals with continuous review policy to solve the optimal control model. We obtained an explicit solution using Pontryagin maximum principle. We derive explicit optimal policies for the inventory model. It is then numerical illustrated with sidered as the sinusoidal function of time then it does not show the convergence of the optimal level. Whenever, if we take the inventory goal level is fixed the help different demand patterns examples. Whenever the goal inventory level is con then it shows the convergence of the optimal inventory towards inventory goal level. The solution of the second-order differential equation is represented and shows the state of optimal inventory level is increasing but converges initially for the certain period of time. In this case, we found the optimal production level with time shows the slight variations with changing the shape of the demand functions. It is observed that the optimal production rates are not very sensitive to changes in the demand functions in case of generalized Pareto distribution.