  Price of anarchy, the performance ratio, which could characterize the loss of
efficiency of the distributed supply chain management compared with the
integrated supply chain management is discussed by utilizing newsvendor problem
in single period which is well-known. In particular, some of remarkable
distributed policies are handled, the performance ratios in each case which
have been investigated in the previous works are analyzed theoretically and the
tighter upper bound of price of anarchy and the lower bound are presented.
Furthermore our approach is developed based on a generalized framework and a
geometric interpretation of price of anarchy is appeared via the literature of
convex optimization.
