Question

When does approximating integer programming solutions with linear programs introduce unacceptable error?

a) When the constraints are non-linear
b) When the variables are real numbers
c) When the problem is too large
d) When the solution is required to be an integer

Answer 1

Approximating integer programming solutions with linear programs introduces unacceptable error when the solution is required to be an integer. When the problem necessitates integer values, it is important to use integer programming models instead of linear programming to minimize the error introduced by approximations.

Step-by-step explanation:

Approximating integer programming solutions with linear programs introduces unacceptable error when the solution is required to be an integer (option d). Linear programming models allow for fractional solutions, and when the problem requires integer values, these fractional solutions may not be feasible or accurate.

For example, if we have a linear program that represents a scheduling problem, where the variables represent the number of shifts assigned to each employee and the constraints ensure that the total number of shifts matches the demand, using linear programming to approximate the solutions may result in fractional values for the number of shifts assigned, which is not practical for scheduling employees.

Therefore, when the problem necessitates integer values, it is important to use integer programming models instead of linear programming to minimize the error introduced by approximations.