Building Linear Programming Models from Structural Model Components

Model management research investigates the formulation, analysis and interpretation of models. This paper focuses on the formulation aspects of modeling so that the task can be supported by decision support systems (DSS) environments. Given the knowledge intensive nature of the formulation process, the development of a modeling tool requires explicating the knowledge pertaining to modeling. This involves comprehending not only the static knowledge about model components (e.g. decision variables, coefficients, associated indices and constants), but also the process knowledge required to construct models from model pieces. The proposed top-down approach configures equations by exploiting the structural modeling knowledge inherent in equation components. The possible representation of equations at various abstraction levels is introduced, the aim being to uncover the structural model components together with the process knowledge required for their appropriate configuration. As part of developing this conceptual model, the role of semantic and syntactic information in model building is investigated. The paper proposes an approach where the formulation semantics are captured as a simple 'action-resource' view which composes models by identifying and piecing together the equation components. The process of equation construction is illustrated with examples from the linear programming (LP) modeling domain. The proposed top-down approach is contrasted with a bottom-up method.