Ordering cost reduction in probabilistic inventory model with controllable lead time and a service level

The issues of lead time reduction and ordering cost reduction in inventory management have become a matter of great interest. We present and analyze a probabilistic inventory model under continuous review for the system with controllable lead time and optimal ordering cost caused by investment strategy subject to a service level constraint. We assume that the lead time demand has a mixture of normal distributions. Instead of having a stock-out term in the objective function, a service level constraint is added. Computational algorithm using the software Matlab 7.0 is developed to find the optimal solution. Numerical examples are also given to illustrate the results and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. By using our proposed model, we obtain a significant amount of savings, range from 5.42% to 5.93%. Finally, the effect of investment to reduce ordering cost is investigated. The numerical example shows that the model with varying order cost is better than the model with fixed ordering cost. One of the repercussions of this convergence is that if the ordering cost could be reduced effectively, then the total relevant cost per unit time could be automatically improved.