big-m-method

Big-M method

What is the Big-M method?

• The Big-M method is an adaption of the simplex algorithm

  • It is an alternative to the two-stage simplex method

• The Big-M method can be used to

  • solve problems involving constraints that contain ≥

  • solve minimisation (as well as maximisation) linear programming problems

• The Big-M method has the advantage of not requiring two stages

  • Each tableau requires just one objective row

• The big-M method has the disadvantage that some of the algebra can get awkward to track and follow

• is an arbitrarily large positive number

  • This is so expressions such as  are definitely negative and  will definitely be positive

  • is never actually assigned a value, nor would it need to be calculated

How do I rewrite the constraints and objective function for the Big-M method?

• STEP 1 Use slack, surplus and artificial variables to convert the constraints of a linear programming problem into equations

• STEP 2 Rearrange each constraint containing an artificial variable such that the artificial variable is the subject

• STEP 3 Subtract from the objective function, where

  •  is the sum of the artificial variables ()

  • is an arbitrarily large, positive number