Big M Method

The Big M Method is an optimisation technique used in linear programming to handle artificial variables in problems with infeasibilities or constraints that do not naturally have a feasible solution. It is often employed when using the Simplex Method to solve linear programming problems that have greater-than or equal to (≥) or equality ( = ) constraints.

In the Big M Method, a large positive number, denoted as M, is added to the objective function for each artificial variable. These artificial variables are introduced to transform the constraints into equations. The objective is to minimise or maximise the original function, while the artificial variables should ideally be driven to zero in the optimal solution. By using a sufficiently large M, the artificial variables have a large cost associated with them, ensuring they are eliminated in the optimisation process, as their presence would result in a sub-optimal solution.

This method allows the Simplex algorithm to proceed even in the presence of constraints that are difficult to handle directly, ensuring a feasible solution is reached.

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