Companies are attempting to find ways to improve their flexibility and responsiveness and in turn Competitiveness by changing their operations strategy, methods and technologies that include the implementation of supply chain management (SCM) paradigm and information technology (IT). IT has a tremendous influence on achieving an effective SCM. This study derives a new mathematical model aimed to consider virtual design of information system for effective supply chain management. An attempt is made in this article to identify different subsystems and other constituents of five main subsystems - Strategic Planning of IT, Virtual Enterprise, E-Commerce, IT Infrastructure and Knowledge and IT Management system of total information system in SCM.Graph theoretical models, variable permanent adjacency matrix models, and permanent functions of these systems based on graph theory-matrix algebra-permanent function methodology are developed .Analytical tests for structural analysis of information system are derived to select optimum constituents in each of these five systems of information system in SCM.Coefficient of similarity and dissimilarity are useful aid to take right decisions between alternative solutions. Permanent function is a unique representation and to be used by SCM solution providers for coding, evaluation, comparison, ranking, and optimum selection. Structural models are useful for basic understanding of complete information system, leading to right decisions for business strategies. Step by step procedure is developed to assist SCM solution providers to implement the proposed method in a right way. Usefulness of the present methodology is also illustrated.

Key words: Information System (IS) in SCM, Structural modeling, DigraphApproach, Permanent function.