# Maths Bigm Method

May 5th, 2015
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In the previous discussions of the Simplex algorithm I have seen that the method must start with a basic feasible solution. In my examples so far, I have looked at problems that, when put into standard LP form, conveniently have an all slack starting solution. An all slack solution is only a possibility when all of the constraints in the problem have or = constraints, a starting basic feasible solution may not be readily apparent.

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Maths Bigm MethodUnit 1 Lesson 9 : The Big M MethodLearning outcomes The Big M Method to solve a linear programming problem.In the previous discussions of the Simplex algorithm I have seen that the method muststart with a basic feasible solution. In my examples so far, I have looked at problemsthat, when put into standard LP form, conveniently have an all slack starting solution. Anall slack solution is only a possibility when all of the constraints in the problem have or =constraints, a starting basic feasible solution may not be readily apparent. The Big Mmethod is a version of the Simplex Algorithm that first finds a basic feasible solution byadding "artificial" variables to the problem. The objective function of the original LP must,of course, be modified to ensure that the artificial variables are all equal to 0 at theconclusion of the simplex algorithm. Steps 1. Modify the constraints so that the RHS ofeach constraint is nonnegative (This requires that each constraint with a negative RHSbe multiplied by 1. Remember that if you multiply an inequality by any negative number,the direction of the inequality is reversed!). After modification, identify each constraint asa , or = constraint. 2. Convert each inequality constraint to standard form (If constraint iis a < constraint, we add aslack variable si; and if constraint i is a > constraint, we subtract an excess variable ei).3. Add an artificial variable ai to the constraints identified as > or = co

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