An optimal control of inventory-production system with gamma distributed deterioration

The study is concerned with the optimal control of an inventory-production system with time-varying demand and deterioration items assuming that the deterioration rate follows the Gamma distribution. The Pontryagin maximum principle is applied here to derive the optimality conditions from the dynamic of the inventory- production level.The simulation and sensitivity analysis results of the inventory system are illustrated for a set of Gamma distributed parametric values.The numerical solution of the inventory-production system with different demand functions are presented extensively