Abstract: Extending the work in 2D/3D graphical databases, the present invention discuss constraints in high dimensional spaces, its efficient storage; relational algebra. The relational algebra includes queries like finding polytopes disjoint or intersecting with the given polytope; or finding a subset or superset of the polytope. This invention also presents methods to generate new information equivalent constraints set from existing constraints sets, presents new kinds of joins and a rich relational algebra of the constraints. Different methods such as distortion, rotation and shape scaling transformations are employed to obtain the information equivalent different sets of constraints. Also, this invention discusses queries to obtain the information equivalent constraints set of the given constraints set along with a new query language, when the data is in memory.

Abstract: Extending the work in 2D/3D graphical databases, the present invention discuss constraints in high dimensional spaces, its efficient storage; relational algebra. The relational algebra includes queries like finding polytopes disjoint or intersecting with the given polytope; or finding a subset or superset of the polytope. This invention also presents methods to generate new information equivalent constraints set from existing constraints sets, presents new kinds of joins and a rich relational algebra of the constraints. Different methods such as distortion, rotation and shape scaling transformations are employed to obtain the information equivalent different sets of constraints. Also, this invention discusses queries to obtain the information equivalent constraints set of the given constraints set along with a new query language, when the data is in memory.

Abstract: This invention relates to inventory optimization under uncertainty wherein uncertainty is represented in a constraint based framework derived from basic economic principles. This approach offers the ability to use information theoretic concepts to quantify the amount of information used in the optimization. The invention extends the state-of-art to include optimal inventory optimization when relevant supply chain variables are correlated. It can be used in other contexts also.

Abstract: In this research, we propose to extend the robust optimization technique and target it for problems encountered in supply chain management. Our method represents uncertainty as polyhedral uncertainty sets made of simple linear constraints derivable from macroscopic economic data. We avoid the probability distribution estimation of stochastic programming. The constraints in our approach are intuitive and meaningful. This representation of uncertainty is applied to capacity planning and inventory optimization problems in supply chains. The representation of uncertainty is the unique feature that drives this research. It has led us to explore different problems in capacity/inventory planning under this new paradigm. A decision support system package has been developed, which can conveniently interface to manufacturing/firm data warehouses, inferring and analyzing constraints from historical data, analyzing performance (worst case/best case), and optimizing plans.

Abstract: Modern decision support methods handle uncertainty or hypothesis about operating conditions, using one of two techniques viz. probabilistic formulation and constraints based method, which is the subject of the present invention. A large number of applications use linear constraints to specify uncertainty. These linear constraints are the set of linear inequalities, which are used to define the demand/supply in the area of supply chains. The set of linear inequalities forms a polytope, the volume of which represents the information content. The present invention deals with the application of computational geometrical methods to find the set theoretic relationship—subset, intersection and disjointness among the polytopes and then present a visualization technique to represent these relationships among polytopes. This invention proposes a decision support system and method to visualize the relationship among the polytopes to help with decision support.