Optimal Control of a Two-Item Inventory System with Different Types of Item Deterioration

The present paper provides a new approach to study the problem of optimal control of a two-item inventory system with different types of deterioration. The total cost, which includes the sum of the holding costs of inventory levels, the holding costs of one item due to the presence of the other and the production costs, is minimized. The optimal solution is obtained based on Pontryagin's principle. The system is modeled by a system of non-linear differential equations and its solution is discussed numerically. It is also used for illustrating the system performance as function of the monetary and non-monetary input parameters.