System and method of assortment, space, and price optimization in retail store
A computer-implemented method involves modeling of product decisions in a retail store. The product decision variables are profit, assortment, placement, promotion, and inventory. Various rules and constraints such as facing elasticity, shelf replenishment costs, shelf space, carrying costs, facing capacity, slotting fees, and cannibalization are defined for multiple product decision variables. An objective function utilizes the rules and constraints for the multiple product decision variables. The objective function model is resolved by uses nested loops to solve for a first variable, and then using the first variable to solve for a second variable. Each decision variable in the objective function is controllable by externally determined multipliers. The objective function simultaneously models each of the multiple product decision variables by iteratively resolving the objective function into values which optimize sales, revenue, and profit for the retail store. The model is output in graphic format.
1. A computer-implemented method of modeling, comprising:
defining, by a computer, rules and constraints for product decision variables, wherein the product decision variables include assortment, space, inventory, placement, price and promotion;
providing, by the computer, an objective function that utilizes the rules and constraints for the product decision variables;
iteratively resolving, by the computer, the objective function into values which optimize sales, revenue, and profit for a retail business; and
simultaneously optimizing, by the computer, the product decision variables including assortment, space, inventory, placement, price and promotion for the retail business by said iteratively resolving of the objective function into the values which optimize the sales, revenue, and profit for the retail business;
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
2. The computer-implemented method of claim 1 , wherein the rules and constraints are selected from the group consisting of facing elasticity, shelf replenishment costs, shelf space, carrying costs, facing capacity, slotting fees, and cannibalization.
3. The computer-implemented method of claim 1 , wherein a report provides the optimized product decision variables in graphic format.
4. The computer-implemented method of claim 1 , wherein the objective function is resolved by using nested loops to solve for a first variable and then using the first variable to solve for a second variable.
5. A method of modeling, comprising:
defining, by a computer, rules and constraints for a plurality of product decision variables, wherein the product decision variables include assortment, space, inventory, placement, price and promotion and each of the product decision variables is controllable by externally determined multipliers;
providing, by the computer, an objective function in terms of the rules and constraints for the plurality of product decision variables and the externally determined multipliers;
resolving, by the computer, the objective function into values which optimize sales, revenue, and profit for a retail business; and
simultaneously optimizing, by the computer, the plurality of product decision variables including assortment, space, inventory, placement, price and promotion for the retail business by said resolving of the objective function into the values which optimize the sales, revenue, and profit for the retail business;
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
6. The method of claim 5 , wherein the rules and constraints are selected from the group consisting of facing elasticity, shelf replenishment costs, shelf space, carrying costs, facing capacity, slotting fees, and cannibalization.
7. The method of claim 5 , wherein a report provides the optimized product decision variables in graphic format.
8. The method of claim 5 , wherein the objective function is iteratively resolved by using nested loops to solve for a first variable and then using the first variable to solve for a second variable.
9. A computer program product usable with a programmable computer processor having a non-transitory computer readable program code embodied therein, adapted to implement a method of modeling, comprising:
computer readable program code which defines rules and constraints for product decision variables including assortment, space, inventory, placement, price, and promotion;
computer readable program code which provides an objective function in terms of the rules and constraints for the product decision variables;
computer readable program code which resolves the objective function into values which optimize sales, revenue, and profit for a retail business; and
computer readable program code which simultaneously optimizes the product decision variables including assortment, space, inventory, placement, price and promotion for the retail business by said resolving of the objective function into the values which optimize the sales, revenue, and profit for the retail business;
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
10. The computer program product of claim 9 , wherein the rules and constraints are selected from the group consisting of facing elasticity, shelf replenishment costs, shelf space, carrying costs, facing capacity, slotting fees, and cannibalization.
11. The computer program product of claim 9 , wherein each decision variable in the objective function is controllable by externally determined multipliers.
12. A computer system for modeling, comprising:
means for defining rules and constraints for product decision variables including assortment, space, inventory, placement, price and promotion;
means for providing an objective function in terms of the rules and constraints for the product decision variables;
means for resolving the objective function into values which optimize sales, revenue, and profit for a retail business; and
means for simultaneously optimizing the product decision variables including assortment, space, inventory, placement, price and promotion for the retail business by said resolving of the objective function into the values which optimize the sales, revenue, and profit for the retail business;
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
13. The computer system of claim 12 , wherein the rules and constraints are selected from the group consisting of facing elasticity, shelf replenishment costs, shelf space, carrying costs, facing capacity, slotting fees, and cannibalization.
14. The computer system of claim 12 , wherein each decision variable in the objective function is controllable by externally determined multipliers.
15. The computer program product of claim 9 , wherein a report provides the optimized product decision variables in graphic format.
16. The computer program product of claim 9 , wherein the objective function is resolved by using nested loops to solve for a first variable and then using the first variable to solve for a second variable.
17. The computer system of claim 12 , wherein a report provides the optimized product decision variables in graphic format.
18. The computer-implemented method of claim 12 , wherein the objective function is resolved by using nested loops to solve for a first variable and then using the first variable to solve for a second variable.
19. The computer-implemented method of claim 1 , wherein the price is a price charged by the retail business.
20. The computer-implemented method of claim 5 , wherein the price is a price charged by the retail business.
21. The computer program product of claim 9 , wherein the price is a price charged by the retail business.
22. The computer system of claim 12 , wherein the price is a price charged by the retail business.
23. The computer-implemented method of claim 1 , wherein each decision variable in the objective function is controllable by externally determined multipliers.
24. The computer program product of claim 9 , wherein the computer readable program code which resolves the objective function into values which optimize sales, revenue, and profit for a retail business comprises:
computer readable program code which iteratively resolves the objective function into values which optimize sales, revenue, and profit for a retail business.
25. The computer system of claim 12 , wherein the means for resolving the objective function into values which optimize sales, revenue, and profit for a retail business comprises:
means for iteratively resolving the objective function into values which optimize sales, revenue, and profit for a retail business.
26. A computer-implemented method comprising:
defining, by a computer, rules and constraints for product decision variables;
providing, by the computer, an objective function that utilizes the rules and constraints for the product decision variables; and
simultaneously modeling each of the product decision variables by iteratively resolving the objective function into values which optimize sales, revenue, and profit for a retail business; and
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
27. A computer-implemented method comprising:
defining, by a computer, rules and constraints for product decision variables;
providing, by the computer, an objective function that utilizes the rules and constraints for the product decision variables; and
simultaneously modeling each of the product decision variables by resolving the objective function into values which optimize sales, revenue, and profit for a retail business; and
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
28. A computer program product usable with a programmable computer processor having a non-transitory computer readable program code embodied therein, adapted to implement a method of modeling, comprising:
computer readable program code which defines rules and constraints for product decision variables;
computer readable program code which provides an objective function that utilizes the rules and constraints for the product decision variables; and
computer readable program code which simultaneously models each of the product decision variables by resolving the objective function into values which optimize sales, revenue, and profit for a retail business; and
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.
29. A computer system comprising:
means for defining rules and constraints for product decision variables;
means for providing an objective function that utilizes the rules and constraints for the product decision variables; and
means for simultaneously modeling each of the product decision variables by resolving the objective function into values which optimize sales, revenue, and profit for a retail business; and
wherein the objective function is
max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and
max θ is the maximized objective function
π is profit
x is a decision variable
us is units sales
λ ds is Lagrange multiplier or externally determined multiplier for dollar sales
DS is dollar sales
λ im is Lagrange multiplier or externally determined multiplier for price image
PI is price image
λ sa is Lagrange multiplier or externally determined multiplier for shelf area
SA is shelf area.