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1 results

  • 11 - Numerical Solution of LP Problems Using the Simplex Method

  • from Part III - Formulation and Solution of Linear Programming (LP) Problems
  • Vassilios S. Vassiliadis, University of Cambridge, Walter Kähm, Ehecatl Antonio del Rio Chanona, Imperial College London, Ye Yuan
  • Book:
    Optimization for Chemical and Biochemical Engineering
    Published online:
    17 December 2020
    Print publication:
    14 January 2021, pp 123-132

  • Summary

    The chapter aims to introduce completely the theory behind the simplex method for Linear Programming, by building slowly the material from the solution set of rectangular linear (affine) systems of equations to vertex solutions.The simplex method is introduced as a natural way to progress from one vertex to the next, on the constraint polytope, always improving the objective until the optimal solution is reached.Use of artificial variables and the two-phase simplex method is made to deal with finding an initial feasible basis for the simplex method.Pathological cases of LP problems are also considered, and how the simplex method would detect them is highlighted.