Managing operations of a system using non-linear modeling techniques
A computer-implemented method for managing operations of a system includes deriving a nonlinear modeling function from a nonlinear response function, defining an allowed range for output values of the nonlinear modeling function, determining a range of a first set of input values of the nonlinear modeling function based on the allowed range of the output values, deriving a nonlinear probability function from the nonlinear response function, receiving the first set of input values, calculating the output values by processing each input value in the first set of input values through the nonlinear modeling function, determining, using the probability function, a relative probability of performing a first future system operation for each input value of the first set of input values and displaying, for each input value in the first set of input values, the corresponding output value and the corresponding probability.
1. A computer-implemented method for managing operations of a system, the method comprising:
deriving a nonlinear modeling function from a nonlinear response function, wherein the nonlinear modeling function models an affinity between multiple variables, wherein the multiple variables define one or more characteristics of the operations of the system, and wherein the nonlinear modeling function approximates one or more operations of the system;
defining an allowed range for output values of the nonlinear modeling function;
determining a range of a first set of input values of the nonlinear modeling function based on the allowed range of the output values, wherein a boundary of the range of the first set of input values is an optimal input value, wherein the optimal input value can be processed through the nonlinear modeling function to produce an optimal output value;
deriving a nonlinear probability function from the nonlinear response function;
receiving the first set of input values;
calculating the output values by processing each input value in the first set of input values through the nonlinear modeling function;
determining, using the probability function, a relative probability of performing a first future system operation for each input value of the first set of input values, wherein, for each input value of the first set of input values, the relative probability shows a probability of performing the first future system operation for the corresponding input value relative to a probability of performing the first future system operation for the optimal input value; and
displaying, for each input value in the first set of input values, the corresponding output value and the corresponding probability.
2. The computer-implemented method of claim 1 , wherein techniques of unobserved component models are used in the nonlinear modeling function in order to provide a serial correlation between events that have a close chronological relationship.
3. The computer-implemented method of claim 1 , further comprising:
collecting a historical data set from the operations of the system; and
loading the historical data set into a database;
wherein deriving the nonlinear modeling function comprises using the historical data set.
4. The computer-implemented method of claim 3 , wherein loading the historical data set further comprises aggregating and clustering the historical data set.
5. The computer-implemented method of claim 1 , wherein processing the first set of input values comprises replacing a first variable of the nonlinear modeling function with each value in the first set of input values and wherein each output value is calculated using an input value in the first set of input values.
6. The computer-implemented method of claim 5 ,
wherein calculating the output values further comprises processing a second set of input values through the nonlinear modeling function; and
wherein processing the second set of input values comprises replacing a second variable of the nonlinear modeling function with each value in the second set of input values; and
wherein each output value is calculated using an input value in the second set of input values.
7. The computer-implemented method of claim 1 , wherein the range of the first set of input values is determined based on one or more of the following: movement rules, linear constraints based on business rules, and nonlinear constraints based on portfolio level rules.
8. The computer-implemented method of claim 1 , further comprising:
deriving a linear modeling function from a linear utility function; and
calculating output values of the linear modeling function by processing the first set of input values through the linear modeling function;
wherein displaying the corresponding output value and the corresponding probability further comprises displaying, for each input value of the first set of input values, the corresponding output value of the linear modeling function.
9. The computer-implemented method of claim 1 , wherein calculating the output values comprises performing an approximation, the method further comprising:
modifying the nonlinear modeling function when the calculated output values do not correspond to a degree of the nonlinear modeling function.
10. The computer-implemented method of claim 1 , further comprising:
determining a number of future system operations performed based on the relative probability of performing the first future system operation and the output of a segmentation model based on customer relationship management attributes.
11. The computer-implemented method of claim 5 , wherein the nonlinear modeling function is
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wherein r client (t) is the first variable, wherein r comp (t) is given a constant value, and wherein β is sensitivity of the output values to a change in r client (t).
12. The computer-implemented method of claim 1 , wherein the probability function is
Exp(β i ( X i (DDS)− X i (Opt)),
wherein, when calculating the output values, X i (DDS) is replaced by each input value in the first set of input values, and wherein X i (Opt) is replaced by the optimal input value, and wherein β is the sensitivity of X i .
13. The computer-implemented method of claim 1 , further comprising:
deriving a multinomial logit function from the nonlinear response function; and
processing the input values through the multinomial logit function in order to determine a relative probability of a second future system operation.
14. A computer system for managing the operations of a system, the computer system comprising:
a database configured to store a historical data set;
a processor; and
a graphical user interface;
wherein the processor is configured to execute instructions that cause the computer system to perform the following operations:
derive a nonlinear modeling function from a nonlinear response function, wherein the nonlinear modeling function models an affinity between multiple variables, wherein the multiple variables define one or more characteristics of the operations of the system, and wherein the nonlinear modeling function approximates one or more operations of the system;
define an allowed range for output values of the nonlinear modeling function;
determine a range of a first set of input values of the nonlinear modeling function based on the allowed range of the output values, wherein a boundary of the range of the first set of input values is an optimal input value, wherein the optimal input value can be processed through the nonlinear modeling function to produce an optimal output value;
derive a nonlinear probability function from the nonlinear response function;
receive the first set of input values;
calculate the output values by processing each input value in the first set of input values through the nonlinear modeling function, wherein the nonlinear modeling function approximates one or more operations of the system; and
determine, using the probability function, a relative probability of performing a first future system operation for each input value of the first set of input values, wherein, for each input value of the first set of input values, the relative probability shows a probability of performing the first future system operation for the corresponding input value relative to a probability of performing the first future system operation for the optimal input value;
wherein the graphical user interface is configured to display, for each input value in the first set of input values, the corresponding output value and the corresponding probability.
15. The computer system of claim 14 wherein techniques of unobserved component models are used in the nonlinear modeling function in order to provide a serial correlation between events that have a close chronological relationship.
16. The computer system of claim 14 wherein the processor is further configured to execute instructions that cause the computer system to perform the following operations:
collect a historical data set from the operations of the system; and
load the historical data set into a database;
wherein the operations of deriving the nonlinear modeling function comprises using the historical data set.
17. The computer system of claim 14 wherein the operations of processing the first set of input values comprises operations of replacing a first variable of the nonlinear modeling function with each value in the first set of input values and wherein each output value is calculated using an input value in the first set of input values.
18. The computer system of claim 14 wherein the processor is further configured to execute instructions that cause the computer system to perform the following operations:
derive a linear modeling function from a linear utility function; and
calculate output values of the linear modeling function by processing the first set of input values through the linear modeling function;
wherein the graphical user interface is configured to display, for each input value of the first set of input values, the corresponding output value of the linear modeling function.
19. The computer system of claim 14 wherein the processor is further configured to execute instructions that cause the computer system to perform the following operation:
determining a number of future system operations performed based on the relative probability of performing the first future system operation and the output of a segmentation model based on customer relationship management attributes.
20. A computer program product comprising computer-readable instructions embodied on a non-transitory computer-readable medium, which, when loaded and executed on a computer system, cause the computer system to perform the following operations:
derive a nonlinear modeling function from a nonlinear response function, wherein the nonlinear modeling function models an affinity between multiple variables, wherein the multiple variables define one or more characteristics of the operations of the system, and wherein the nonlinear modeling function approximates one or more operations of the system;
define an allowed range for output values of the nonlinear modeling function;
determine a range of a first set of input values of the nonlinear modeling function based on the allowed range of the output values, wherein a boundary of the range of the first set of input values is an optimal input value, wherein the optimal input value can be processed through the nonlinear modeling function to produce an optimal output value;
derive a nonlinear probability function from the nonlinear response function;
receive the first set of input values;
calculate the output values by processing each input value in the first set of input values through the nonlinear modeling function, wherein the nonlinear modeling function approximates one or more operations of the system;
determine, using the probability function, a relative probability of performing a first future system operation for each input value of the first set of input values, wherein, for each input value of the first set of input values, the relative probability shows a probability of performing the first future system operation for the corresponding input value relative to a probability of performing the first future system operation for the optimal input value; and
display, for each input value in the first set of input values, the corresponding output value and the corresponding probability.