On product covering in 3-tier supply chain models: Natural complete problems for W[3] and W[4]

The field of supply chain management has been growing at a rapid pace in recent years, both as a research area and as a practical discipline. In this paper, we study the computational complexity of product covering problems in 3-tier supply chain models, and present natural complete problems for the classes W[3] and W[4] in parameterized complexity theory. This seems the first group of natural complete problems for higher levels in the parameterized intractability hierarchy (i.e., the W-hierarchy), and the first precise complexity characterizations of certain optimization problems in the research of supply chain management. Our results also derive strong computational lower bounds and inapproximability for these optimization problems.