Mathematical Modeling of a Supply Chain with Uncertain Parameters

Decision making in supply chain network problems is fraught with numerous uncertainties. In this paper, we discuss and illustrate a four-layer supply chain network including suppliers, manufacturers, warehouses, and markets, which is designed to address the production and transportation of a single product. We present a robust optimization model that is useful in analyzing uncertainties associated with the primary input parameters including demand, supply, and cost parameters since it does not affect the complexity of the original deterministic model. The objective of the mathematical model is to obtain the optimal location of manufacturers and warehouses as well as the quantities of raw materials and final products, which result in the minimum total costs including the penalty costs.