Integrated production and transportation in a class of supply networks – deterministic and uncertain cases

A class of supply networks, which consist of warehouses of a raw material and of a product as well as of production units which manufacture a product from a raw material, is investigated. A joint problem of a raw material allocation among production units and transportation of both a raw material and a product is considered. The corresponding optimization problem is formulated with the total cost comprising a non-linear sub-cost of production. Two versions are considered: deterministic and uncertain for a selected case. For the former one, exact and approximate algorithms are presented and then compared via computational experiment. The uncertain version with interval parameters in the models of production units is discussed, and a special case is considered when it is enough to apply a solution algorithm for the deterministic counterpart to solve the problem.