Adaptive optimal model and algorithm for distributed inventory allocation based on Steiner tree

This paper promotes an adaptive optimal model and algorithm for the distributed inventory system which includes one plant, m candidate distribution centers and time-varying customers. The inventory control policy (Q,s) is used in the distributed inventory system. First of all, we adopt theory of the weighted graph to build a mathematical model, which can convert general optimal mathematical model of the distributed inventory allocation to the weighted graph optimal model. Secondly, an adaptive optimal algorithm based on Steiner tree theory is presented to solve the mathematical model above. Finally, the results of numerical simulation show that the model and algorithm are effective. We discuss the sensitivity of potential cost reduction to the changes of inventory key parameters, such as demand of customers and the distribution center inventory capacity.