Managing Production and Transportation in a Class of Non-Balanced Supply Networks

The paper deals with a supply network that consists of three interconnected subsystems: raw material warehouses, production units and product warehouses. The allocation of a raw material among parallel production units and the determination of transportation plans for a product and a raw material that minimize the total cost connected with the production and the transportation, are the purpose of the decision-making for such a system. For a special case of non-balanced supply networks, where all production units can produce the same amount of the product from a unit of the raw material, a solution algorithm is presented. It is based on a special decomposition of the problem which allows to determine the solution consecutively for the increasing number of production units involved in the manufacture, starting from the case with only one production unit. A sufficient condition for the optimal solution is proved, and the properties of the algorithm are presented.