Decision-making for supply chains with transportation and production units

The paper concerns a supply chain system, that consists of three interconnected sub-systems (stages): a set of raw material warehouses, a set of production units and a set of product warehouses. The purpose of the decision-making for such a system is the allocation of a raw material among parallel production units and the determination of the transportation plans for the raw material and the product to minimize the total cost. In the paper, two versions of the decision-making problem are formulated. In the first one, all decisions are made jointly. The second simplified version consists in a consecutive determination of optimal allocation of the raw material and both transportation plans. The problem formulation for both cases are given. The equivalence condition of both versions for the simple case is presented. The numerical example completes the paper.