Application of Stochastic Programming for Supply Chain Inventory Optimization under Uncertain Demand and Lead Time

Supply chain management deals with the management of information and material in a network of producers, retailers and customers. This task is rather complex since a high degree of uncertainty occurs in reality due to the fact that key factors such as product demands, stock availability, prices, facilities reliability, all have significant stochastic components. Stochastic programming is main representative approach to capture some aspects of the uncertainty due to the limited knowledge of the model input parameters. Although it has many contributions in supply chain management, they are mainly focused on the strategic decision level, where there is not enough concrete information about the features of uncertainties on which to base long-term decisions. Within a current research, it is supposed that the most of the uncertainty could be handled adequately using a stochastic modeling approach precisely at the tactical planning level, mostly employing stochastic values for customer demand, supplier lead times, production costs and/or price fluctuations. The paper illustrates the application of stochastic programming approach for inventory optimization under uncertain demand and lead time. The mathematical model is created and tested by using the algebraic modeling language AMPL, which uses the large-scale optimization solver CPLEX. The developed inventory model is tested, leading to the conclusion that stochastic programming provides superior planning decisions in comparison with deterministic equivalent. The effect of the scenario number on the model performance is evaluated. The conclusion is that the optimal number of scenario exists and it is not necessary to make the model work under all possible scenarios