Inventory Management in Multi Echelon Supply Chain using Sample Average Approximation

Abstract

Inventory Management in Multi Echelon Supply Chain using Sample Average Approximation An optimization model of multiechelon supply chain is presented in this paper. The decisions to be made are the amount of beer to be ordered in every echelon of supply chain in each echelon over the time horizon of one year. Since demand of the end customer is stochastic and presented by means of scenarios, the problem is solved by using sample average approximation method. This method uses only a subset of the scenarios, randomly sampled according to the distribution over scenarios, to represent the full scenario space. An important theoretical justification for this method is that as the number of scenarios sampled increases, the solution to the approximate problem converges to an optimal solution in the expected sense. The computational results are presented for two cases. First target level is chosen as a decision variable and then order size is chosen as a decision variable of the problem. The target level strategy is based on making inventory for each echelon; in its turn order strategy is based on determination of optimal order quantity, which is independent from scenarios. However target level strategy provides high service at low cost, but it offers less reality under uncertain demand than order strategy. Practical experiments on finding the optimal SAA parameters are presented in the paper and as well as the analysis of their impact on solution quality.