Abstract: A computer program product is described for solving the traveling salesman problem in polynomial time. The probability distribution of the space of all paths is modeled in a configurational density distribution. A Hamiltonian is constructed specifying the costs, distance, or penalty associated with different legs of paths encompassed in the configurational density distribution. Starting at a maximum temperature where free energy dominates and the penalty function plays little role, the system is iteratively adapted to reduce the temperature in steps incrementally chosen to preserve the linear characteristic of the approximation, until a lower temperature state of reduced energy is reached in which a preferred set of paths can be identified from the configurational density distribution.

Abstract: In a planning model, a decision variable optimization process (200) generates a planning function (122) describing the planning model, the planning function (122) depending upon a set of decision variables (125). The planning function (122) is separated into independent planning functions, SPi, each of which depend upon different decision variables (125). Each of the independent planning functions, SPi, is independently optimized to obtain decisions for the different decision variables (125), and an outcome is presented that indicates the decisions. The planning function (122) further includes an embedded constraint function that introduces an embedded constraint to weaken the coupling between decision variables (125) in the planning model, thereby reducing an N-dimensional optimization problem into a lower order optimization problem.

Abstract: A computer-based method for characterizing relationships between a primary goal and an auxiliary goal in an enterprise planning model includes representing the primary goal by a primary objective function, the primary objective function being dependent upon a set of operational variables. The objective function is resolved to yield a plurality of sets of operational decisions. A plurality of auxiliary goal values associated with a plurality of primary goal values in response to said plurality of sets of operational decisions is presented in a data structure. The computer-based method allows the analysis of the costs and benefits of the auxiliary goal imposed upon the primary goal.

Abstract: A software method for strategic planning and optimization allows a user to model an enterprise to visualize an effect of an auxiliary goal, such as price image, on a primary goal of the enterprise. A primary goal of the enterprise is selected, and is represented by a primary objective function which, in turn, depends upon a set of operational variables. The auxiliary goal is represented by a constraint function that depends upon a subset of the operational variables. An effective objective function is constructed by combining the primary objective function and the constraint function, and the effective objective function is optimized to yield a set of operational decisions that optimize the primary objective function while concurrently satisfying the constraint function. The set of operational decisions are provided to a user, the operational decisions enabling the enterprise to achieve the primary goal and satisfy the auxiliary goal.

Abstract: A system and process for modeling attributes of a set of observed data. The system and process may include an initialization process providing for a likelihood function, a first order prior function; a calibration data set; a flexible interface module in which the likelihood function, the first order first order prior function, and the second order prior function are written in a programming language; a parameter bounding process in which parameters determined to be too large are interpolated or sequentially locked down; an outlier flagging process which identifies outliers using the gradient of the likelihood function; and an output process which reports information that may include outlier forces, confidence intervals, and other factors that are unique to this modeler and useful in refining the model.

Abstract: A computer program product is described for solving the traveling salesman problem in polynomial time. The probability distribution of the space of all paths is modeled in a configurational density distribution. A Hamiltonian is constructed specifying the costs, distance, or penalty associated with different legs of paths encompassed in the configurational density distribution. Starting at a maximum temperature where free energy dominates and the penalty function plays little role, the system is iteratively adapted to reduce the temperature in steps incrementally chosen to preserve the linear characteristic of the approximation, until a lower temperature state of reduced energy is reached in which a preferred set of paths can be identified from the configurational density distribution.

Abstract: A computer-based method for characterizing relationships between a primary goal and an auxiliary goal in an enterprise planning model includes representing the primary goal by a primary objective function, the primary objective function being dependent upon a set of operational variables. The objective function is resolved to yield a plurality of sets of operational decisions. A plurality of auxiliary goal values associated with a plurality of primary goal values in response to said plurality of sets of operational decisions is presented in a data structure. The computer-based method allows the analysis of the costs and benefits of the auxiliary goal imposed upon the primary goal.

Abstract: A demand control process (42) includes a price-image computation subprocess (44) and an optimization subprocess (46). The price-image computation subprocess (44) tunes a demand model to both price (76) and non-price (78) demand-parameters. Baseline and trial pricing scenarios (98, 114) are then compiled for a selected set (86) of products and operated upon by the demand model to forecast demand (110, 118) at the specified prices. Revenues (122) are calculated at the baseline pricing scenario (98) using the forecast demand (110), and the revenues (122) are used to calculate weights for compiling summary statistics over the set (86) of products. Price image is then calculated using the values forecast by the demand model so that the resulting price image is responsive to price and non-price demand parameters (76, 78).

Abstract: A software method for controlling the optimization of a planning model that uses historical sales data to predicts optimal prices and similar factors for meeting a number of business goals. Unlike previous systems that allow a user to model prices and other factors based on physical constraints, the present invention allows the optimization to occur against the background of one or more strategic objectives. Such objectives, such a price image, are not set by physical constraints but instead are imposed by the user with the notion that they will provide a strategic and ultimately an economic advantage. The system allows the analysis of the costs and benefits of such management imposed strategic objectives.

Abstract: A computer-implemented method and system for controlled optimization of enterprise planning models is provided. This is accomplished by first defining an auxiliary objective function, which depends on the same variables as the model, or a subset thereof. An effective objective function is then constructed from the primary objective function by subtracting the auxiliary objective function multiplied by a weighting factor. The effective objective function is then optimized for a whole range of weighting values, yielding a table that describes how the primary objective function varies according to different values of the weighting factor. Optimization of the effective objective function with a given value of the weighting factor results in a particular value for the auxiliary objective. Thus, this computed table essentially provides a relationship between different realized values of the primary objective, the auxiliary objective, and all the variables of the enterprise planning model.

Abstract: A method for incorporating psychological effects into a demand model for pricing. First the original demand model is modified to include a mechanism to convert actual prices into perceived prices, thus causing the demand model to predict higher demand for certain prices. The user specifies the function that converts from real prices to perceived prices. This modified demand function is then fitted to a sales history to yield the parameters appropriate to its particular form. Also, the demand model can be modified to account for promotional effects. The user defines a visibility model, which gives the relative increase in demand for an item caused by a promotion, and the cost of the promotion. The demand model is modified to include the effect of increased demand based on the visibility, and a profit model is modified to account for the added cost due to the added visibility. The profit model is then optimized with respect to both prices and promotions.

Abstract: A method for tuning a demand model in manner that is stable with respect to fluctuations in the sales history used for the tuning is provided. A market model is selected, which predicts how a subset of the parameters in the demand model depends upon information external to the sales history; this model may itself have a number of parameters. An effective figure-of-merit function is defined, consisting of a standard figure-of-merit function based upon the demand model and the sales history, plus a function that attains a minimum value when the parameters of the demand model are closest to the predictions of the market model. This effective figure-of-merit function is minimized with respect to the demand model and market model parameters. The resulting demand model parameters conform to the portions of the sales history data that show a strong trend, and conform to the external market information when the corresponding portions of the sales history data show noise.