(710d) Integration of Mathematical Knowledge Management for Improved Enterprise Decision-Making

Authors: 
Muñoz, E., Centro de Investigacion en Matematicas A.C.
Puigjaner, L., Universitat Politècnica de Catalunya
Espuña, A., Universitat Politècnica de Catalunya
Capon, E., Universitat Politecnica de Catalunya
Laínez, J. M., University at Buffalo



Nowadays, the application of analytical systems for decision-making has gained increased attention as a manner of gaining a competitive advantage to face globalization of markets and fierce competition. The basis of decision-making consists of formally representing the system to be analyzed in a model that emulates the important aspects of the studied system. Models adopted in enterprises are usually of high complexity. In addition, there is not a single valid model or model representation for each problem and the adoption of a model depends on both the decision-maker preferences and the specific problem features.

Recent trends in process industries are shifting the focus on the coordination of the decision making and the optimization of different decision levels. In fact, the border lines between the decision-making levels of the enterprise structure are often diffuse, and there are strong overlaps between planning in production, distribution or supply chain management and strategic planning. One first step toward such a coordination consists in sharing information, which is nowadays being achieved with modern IT tools. Semantic technologies seem to offer an appealing way to capture knowledge and integrate information, for supporting a smooth integration of information and mathematical modeling in a single framework.

This work proposes an ontological framework which includes the integration of knowledge models both for mathematical and enterprise domains. On the one hand, the Mathematical Knowledge Management model aims at translating the elements (i.e., decisions, parameters, constraints, performance indicators) of enterprise mathematical models to a semantic representation. On the other hand, the Enterprise Process Ontology Project represents the process tasks and supply chain domain and is based on the work of Munoz, et al (2012). An important advantage of this framework is that it facilitates the integration of different models as well as the straightforward incorporation of additional system/model aspects (e.g., constraints, performance indicators).

The “Ontological Math Representation” approach focuses in the semantic representation of the mathematical content of functions and equations. The mathematical expressions are represented as mathematical sets that are related among them by ontological properties. Thus, it handles the expression of functions, the quantification and the operators with qualifiers. The resulting relationships translate the mathematical expressions into the process explicit reality of the enterprise which is easier to understand by humans and machines.

In addition, the various variables/parameters are related to the enterprise objects by the connection and integrations with the process enterprise ontology. Specifically, this work presents supply chain and scheduling mathematical models which are merged when the respective equations are interpreted and related to the classes of the enterprise process ontology model. As a result, an integrated mathematical model is obtained and can be solved by exchanging xml files. Even more, in the classical hierarchical approach, this framework allows tracking the use of the elements of the different models and sharing the information obtained from their respective optimization, which may be performed separately.

The integration of mathematical models from different hierarchical levels (SC models and scheduling models) has been successfully done. This provides an additional degree of freedom for the enterprise modeling. So far the enterprise ontology relied on rigid analytical models which cannot be easily modified according to the new reality circumstances (constraints, variables). The new feature developed in this work opens the ability of modifying the analytical models from the ontological framework, providing a higher flexibility.

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