Is Big M method and penalty method same?

There are two types of methods: Interior penalty methods, also known as barrier methods. ==>In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm to problems that contain “greater-than” constraints.

What do we apply in order to determine the optimal solution?

Answer & Solution An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.

What is the role of artificial variable in Big M method?

The purpose of introducing artificial variables is just to obtain an initial basic feasible solution. However, addition of these artificial variables causes violation of the corresponding constraints. Therefore we would like to get rid of these variables and would not allow them to appear in the optimum simplex table.

What is the disadvantage of Big M method over two phase method?

Theoretically, there is a (maybe huge) value of M, s.t. the big-M-method will end up with the optimal solution – but that value is problem dependent and a really big M might lead to numerical problems on a computer. This is an important drawback of the big-M-method.

Why do we use 2 phase method?

The two-phase simplex method is used to solve Standard Linear Programming (STP) problems when we do not have a starting basic feasible solution (BFS).

Why Big M method is called penalty method?

==>When used in the objective function, the Big M method sometimes refers to formulations of linear optimization problems in which violations of a constraint or set of constraints are associated with a large positive penalty constant, M. (hence the need for M to be “large enough.”)

What is penalty in operation research?

Penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem.