On Product Covering in Supply Chain Models: Natural Complete Problems for W[3] and W[4]

• Published in: Algorithmic Applications in Management pp. 400 - 410
• Main Authors: Chen, Jianer, Zhang, Fenghui
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Logistics; Mathematical programming; Operational research and scientific management; Operational research. Management science; Parameterized Problem; Polynomial Time Approximation Scheme; Supply Chain; Supply Chain Management; Theoretical computing; Vertex Cover; Lower bound; Hierarchy; Covering problem; Algorithmics; Coverage; Computational complexity; Discipline; Modeling; Hierarchized structure; Logistics; Mathematical programming
• ISBN: 3540262245; 9783540262244
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11496199_43

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.