Formulation and Solution of Binary Optimization Problems
Problem: A company that wants to select magazine publishers for an advertising campaign.
Data: The data that the company has collected is shown in the table below:
Data: The data that the company has collected is shown in the table below:
The model also needs seven interior variables to choose the number of groups to purchase from each publisher. Let's go over those variables GA to GG. So GA will be the number of groups purchased from Publisher A.
Objective function: It is reasonable to think that the company will like to maximize total exposure while not exceeding its advertising budget.
Constraints:
GA <= 5A
GB <= 10B
GC <= 4C
GD <= 20D
GE <= 5E
GF <= 1F
GG <= 2G
B + D <= 1
C + G <= 1
Fixed cost + Variable cost <= 25000
Objective function: It is reasonable to think that the company will like to maximize total exposure while not exceeding its advertising budget.
Constraints:
GA <= 5A
GB <= 10B
GC <= 4C
GD <= 20D
GE <= 5E
GF <= 1F
GG <= 2G
B + D <= 1
C + G <= 1
Fixed cost + Variable cost <= 25000
Excel model and optimal solution:
The optimal solution engages publishers A, B, E and G. It prescribes the purchase 13 groups which result in a total exposure of 876,200.