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Introduction Big - M Method: Examples Two phase Method: Examples
OptimizationBig-M and Two-Phase Methods for LPP
DeepikaBITS Pilani, Hyderabad Campusdeepika@hyderabad.bits-pilani.ac.in
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October 16, 2021
Introduction Big - M Method: Examples Two phase Method: Examples
Outline
Introduction
Big - M Method: Examples
Two phase Method: Examples
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Introduction Big - M Method: Examples Two phase Method: Examples
Introduction: LPP
To solve a linear programming problem, we present generalised versionsof the simplex method:
• Big - M method
• Two phase method
These methods can be used to solve both maximisation and minimisationproblems with ≥, ≤ and = type constraints
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Introduction Big - M Method: Examples Two phase Method: Examples
Big - M Method for the Solution of LPP
• In many LP problems, often we end up with cases where the initialbasic feasible solution (BFS) does not exist.
• In such a case, we can employ the big - M method
• Basic Idea: Introducing artificial variables so that we get initial basicfeasible solution (BFS)
• To prevent these variables from being part of the optimal solution,we penalise them in the objective function
• Then apply the usual simplex method to obtain the optimal solution
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Examples: Big - M Method for the Solution of LPP
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Examples: Big - M Method for the Solution of LPP
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Comments on Big - M Method
Relationship between optimal solutions of the modified problem and theoriginal problem:
• If the modified problem has no optimal solution, then the originalproblem has no optimal solution
• if any of the artificial variables are non-zero in the optimal solutionof the modified problem, then the original problem has no optimalsolution
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Introduction Big - M Method: Examples Two phase Method: Examples
Two Phase method for the Solution of LPP
• In many LP problems, often we end up with cases where the initialbasic feasible solution (BFS) does not exist.
• In such a case, we can employ the two phase method
• In the first phase (phase - I), we formulate a different LPP and findan initial BFS.
• In phase - II, we use the initial BFS to find the optimal solution ofthe original LPP
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Examples: Two phase Method
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Examples: Two phase Method
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