Generating an optimized pricing plan

1. A computer-implemented method of generating an optimized pricing plan, comprising:

accessing, by a computer, a hierarchy comprising a sequence of levels, each level comprising an objective function and a set of objective function constraints, wherein each objective function represents a primary objective or one or more secondary objectives;

assigning, by the computer, a first fixed to a first item and a second fixed price to a second item according to one of the set of objective function constraints;

preventing, by the computer, a rule violation resulting from the first and second fixed prices by de-linking the first and second items within a plurality of items;

determining, by the computer, a mathematical programming model representing a pricing plan problem for an item group comprising the plurality of items, the mathematical programming model comprising a set of initial constraints;

repeating, by the computer, for each level of the sequence of levels, until a last level is reached:

adding the set of objective function constraints to the set of initial constraints;

optimizing the mathematical programming model to yield an optimized boundary for the objective function;

generating an optimized constraint from the optimized boundary; and

adding the optimized constraint to the set of objective function constraints of the next level of the sequence of levels;

optimizing, by the computer, an objective function of the last level of the sequence of levels subject to the set of objective function constraints to yield an optimized result, the set of objective function constraints comprising the optimized constraint generated from the optimized boundary of a previous level;

generating, by the computer, an optimized pricing plan in accordance with the optimized result, the optimized pricing plan associating an optimized price with each item of the item group;

determining by the computer, a number of price changes for ones of the plurality of items in accordance with the optimized pricing plan;

determining, by the computer, when the number of price changes for the ones of the plurality of items exceeds a predetermined number of price changes;

assigning a priority to the prices of the ones of the plurality of items that (1) have larger price changes, (2) are image items used to track competitors, or (3) have more stable prices; and

changing the prices of the ones of plurality of items that have the highest priority.

2. The method of claim 1 , wherein:

the mathematical programming model comprises a non-linear programming model; and

optimizing the objective function of the last level comprises optimizing the objective function using a non-linear programming technique.

3. The method of claim 1 , further comprising:

splitting a category of items into a plurality of item groups, each item group comprising a set of items related by one or more item constraints; and

selecting one of the plurality of item groups for which to generate the optimized pricing plan.

4. The method of claim 1 , wherein the optimized pricing plan lists the optimized price for each item of the item group for each time interval of the time period.

5. The method of claim 1 , wherein the optimized pricing plan lists the optimized price for each item of the item group for each location.

6. The method of claim 1 , wherein optimizing the mathematical programming model to yield an optimized boundary for the objective function comprises:

expressing the objective function using one or more slack variables; and

optimizing the one or more slack variables to determine the optimized boundary.

7. The method of claim 1 , further comprising:

accessing a rounding rule for rounding the optimized price of an item for each item of the item group;

accessing a plurality of propagation rules, each propagation rule for determining the optimized price of a first item according to the optimized price of a second item, each propagation rule associated with an item of the item group; and

repeating the following for each item of the item group:

applying the rounding rule to the item of the item group; and

applying the propagation rule for determining the optimized price of the item according to a price of another item, if the item is associated with a propagation rule.

8. The method of claim 1 , further comprising:

determining a price change for each item in accordance with the optimized pricing plan;

assessing a cost associated with each price change; and

adjusting the price change in response to the cost associated with the price change.

9. The method of claim 1 , wherein:

assigning a priority to the price changes of the one or more items comprises prioritizing the price changes by associating a greater price change with a higher priority and associating a smaller price change with a lower priority; and

the price of the items that have the highest priorities are changed in a first time interval and the prices of the items that have lower priority are changed in a second time interval.

10. The method of claim 1 , further comprising:

repeating the steps of accessing, determining, repeating, optimizing, and generating to generate a plurality of local optimized results;

determining a global optimized result from the local optimized results; and

generating the optimized pricing plan from the global optimized result.

11. The method of claim 1 , further comprising:

accessing a plurality of demand models;

accessing demand data describing the item group;

evaluating the demand models in accordance with the demand data;

selecting a demand model of the evaluated demand models in response to the evaluation; and

calculating a price elasticity using the selected demand model.

12. A system of generating an optimized pricing plan, comprising:

a database stored therein a hierarchy comprising a sequence of levels, each level comprising an objective function, and a set of objective function constraints, wherein each objective function represents a primary objective or one or more secondary objectives; and

a computer system coupled with the database, the computer system configured to:

assign a first fixed price to a first item and a second fixed price to a second item, according to one of the set of objective function constraints;

prevent a rule violation resulting from the first and second fixed prices by de-linking the first and second items within a plurality of items;

determine a mathematical programming model representing a pricing plan problem for an item group comprising the plurality of items, the mathematical programming model comprising a set of initial constraints;

repeat for each level of the sequence of levels, until a last level is reached:

adding the set of objective function constraints to the set of initial constraints;

optimizing the mathematical programming model to yield an optimized boundary for the objective function;

generating an optimized constraint from the optimized boundary; and

adding the optimized constraint to the set of objective function constraints of the next level of the sequence of levels;

optimize an objective function of the last level of the sequence of levels subject to the set of objective function constraints to yield an optimized result, the set of objective function constraints comprising the optimized constraint generated from the optimized boundary of a previous level;

generate an optimized pricing plan in accordance with the optimized result, the optimized pricing plan associating an optimized price with each item of the item group;

determine a number of price changes for ones of the plurality of items in accordance with the optimized pricing plan;

determine when the number of price changes for the ones of the plurality of items exceeds a predetermined number of price changes;

assign a priority to the prices of the ones of the plurality of items that (1) have larger price changes, (2) are image items used to track competitors, or (3) have more stable prices; and

change the prices of the ones of plurality of items that have the highest priority.

13. The system of claim 12 , wherein:

the mathematical programming model comprises a non-linear programming model; and

the computer system is further configured to optimize the objective function of the last level by optimizing the objective function using a non-linear programming technique.

14. The system of claim 12 , wherein the computer system is further configured to:

split a category of items into a plurality of item groups, each item group comprising a set of items related by one or more item constraints; and

select one of the plurality of item groups for which to generate the optimized pricing plan.

15. The system of claim 12 , wherein the optimized pricing plan lists the optimized price for each item of the item group for each time interval of the time period.

16. The system of claim 12 , wherein the optimized pricing plan listing lists the optimized price for each item of the item group for each location.

17. The system of claim 12 , wherein the computer system is further configured to optimize the mathematical programming model to yield an optimized boundary for the objective function by:

expressing the objective function using one or more slack variables; and

optimizing the one or more slack variables to determine the optimized boundary.

18. The system of claim 12 , wherein the computer system is further configured to:

access a rounding rule for rounding the optimized price of an item for each item of the item group;

access a plurality of propagation rules, each propagation rule for determining the optimized price of a first item according to the optimized price of a second item, each propagation rule associated with an item of the item group; and

repeat the following for each item of the item group:

applying the rounding rule to the item of the item group; and

applying the propagation rule for determining the optimized price of the item according to a price of another item, if the item is associated with a propagation rule.

19. The system of claim 12 , wherein the computer system is further configured to:

determine a price change for each item in accordance with the optimized pricing plan;

assess a cost associated with each price change; and

adjust the price change in response to the cost associated with the price change.

20. The system of claim 12 , wherein:

assign a priority to the price changes of the one or more items comprises prioritize the price changes by associating a greater price change with a higher priority and associating a smaller price change with a lower priority; and

the price of the items that have the highest priorities are changed in a first time interval and the prices of the items that have lower priority are changed in a second time interval.

21. The system of claim 12 , wherein the computer system is further configured to:

repeat the steps of accessing, determining, repeating, optimizing, and generating to generate a plurality of local optimized results;

determine a global optimized result from the local optimized results; and

generate the optimized pricing plan from the global optimized result.

22. The system of claim 12 , wherein the computer system is further configured to:

access a plurality of demand models;

access demand data describing the item group;

evaluate the demand models in accordance with the demand data;

select a demand model of the evaluated demand models in response to the evaluation; and

calculate a price elasticity using the selected demand model.

23. A non-transitory computer-readable medium embodied with software for generating an optimized pricing plan, the software when executed using a computer is configured to:

access a hierarchy comprising a sequence of levels, each level comprising an objective function and a set of objective function constraints, wherein each objective function represents a primary objective or one or more secondary objectives;

assign a first fixed price to a first item and a second fixed price to a second item, according to one of the set of objective function constraints;

prevent a rule violation resulting from the first and second fixed prices by de-linking the first and second items within a plurality of items;

determine a mathematical programming model representing a pricing plan problem for an item group comprising the plurality of items, the mathematical programming model comprising a set of initial constraints;

repeat for each level of the sequence of levels, until a last level is reached:

adding the set of objective function constraints to the set of initial constraints;

optimizing the mathematical programming model to yield an optimized boundary for the objective function;

generating an optimized constraint from the optimized boundary; and

adding optimized constraint generated from the optimized boundary to the set of objective function constraints of the next level of the sequence of levels;

optimize an objective function of the last level of the sequence of levels subject to the set of objective function constraints to yield an optimized result, the set of objective function constraints comprising the optimized constraint generated from the optimized boundary of a previous level;

generate an optimized pricing plan in accordance with the optimized result, the optimized pricing plan associating an optimized price with each item of the item group;

determine a number of price changes for ones of the plurality of items in accordance with the optimized pricing plan;

determine when the number of price changes for the ones of the plurality of items exceeds a predetermined number of price changes;

assign a priority to the prices of the ones of the plurality of items that (1) have larger price changes, (2) are image items used to track competitors, or (3) have more stable prices; and

change the prices of the ones of plurality of items that have the highest priority.

24. The computer-readable medium of claim 23 , wherein:

the mathematical programming model comprises a non-linear programming model; and

the software is further configured to optimize the objective function of the last level by optimizing the objective function using a non-linear programming technique.

25. The computer-readable medium of claim 23 , wherein the software is further configured to:

split a category of items into a plurality of item groups, each item group comprising a set of items related by one or more item constraints; and

select one of the plurality of item groups for which to generate the optimized pricing plan.

26. The computer-readable medium of claim 23 , wherein the optimized pricing plan lists the optimized price for each item of the item group for each time interval of the time period.

27. The computer-readable medium of claim 23 , wherein the optimized pricing plan lists the optimized price for each item of the item group for each location.

28. The computer-readable medium of claim 23 , wherein the software is further configured to optimize the mathematical programming model to yield an optimized boundary for the objective function by:

expressing the objective function using one or more slack variables; and

optimizing the one or more slack variables to determine the optimized boundary.

29. The computer-readable medium of claim 23 , wherein the software is further configured to:

access a rounding rule for rounding the optimized price of an item for each item of the item group;

access a plurality of propagation rules, each propagation rule for determining the optimized price of a first item according to the optimized price of a second item, each propagation rule associated with an item of the item group; and

repeat the following for each item of the item group:

applying the rounding rule to the item of the item group; and

applying the propagation rule for determining the optimized price of the item according to a price of another item, if the item is associated with a propagation rule.

30. The computer-readable medium of claim 23 , wherein the software is further configured to:

determine a price change for each item in accordance with the optimized pricing plan;

assess a cost associated with each price change; and

adjust the price change in response to the cost associated with the price change.

31. The computer-readable medium of claim 23 , wherein:

assign a priority to the price changes of the one or more items comprises prioritize the price changes by associating a greater price change with a higher priority and associating a smaller price change with a lower priority; and

the price of the items that have the highest priorities are changed in a first time interval and the prices of the items that have lower priority are changed in a second time interval.

32. The computer-readable medium of claim 23 , wherein the software is further configured to:

repeat the steps of accessing, determining, repeating, optimizing, and generating to generate a plurality of local optimized results;

determine a global optimized result from the local optimized results; and

generate the optimized pricing plan from the global optimized result.

33. The computer-readable medium of claim 23 , wherein the software is further configured to:

access a plurality of demand models;

access demand data describing the item group;

evaluate the demand models in accordance with the demand data;

select a demand model of the evaluated demand models in response to the evaluation; and

calculate a price elasticity using the selected demand model.