Optimization of stochastic, (Q, R) inventory system in multi-product, multi-echelon, distributive supply chain

The key idea of the paper is the development of a probabilistic model for optimum inventory policy for a three-product, four-echelon, distributive system. The mathematical model is built based on integer policy of ordering in the deterministic part with continuous review inventory policy. It is found to be a non-linear multi-variable constrained optimization problem. For illustration purpose, demand is taken as stationery random one and lead time is normally distributed. A MATLAB program is generated to derive the solution based on exhaustive search method. Optimum lot sizes, safety stocks, reorder points, and service levels for each product at each stage are found out in accordance with continuous review inventory system. Further inventory turnover ratio computed is found to be reasonable and bubble plot of chosen service levels of different products with annual sales, profit margin, variability in demand, and lead time is obtained with expected characteristics. The proposed model along with the applied method of solving can find the best possible order quantity and ROP of a stochastic inventory system efficiently.