This paper provides an exension of the optimal control problem of multi-item inventory model with deteriorating items using the negative value of natural logarithm of deterioration and spoilage function, depending on the alternative quadratic exponential form. The solution of optimal control problem of this model can be carried out using the pontryagin principle. The controlled system of non-linear differential equations will be solved numerically. Different functions of the demand rates are used to study the effect demand retes on the optimal inventory levels,optimal productiion rates and then measure the optimal value of objective function.