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Multiphase Simplex Formulation

This article delves into the differences between traditional simplex linear programming (LP) and more advanced methodologies like lexicographic minimization and goal programming (GP). It highlights how deviation variables are employed instead of slack, surplus, and artificial variables, enabling greater flexibility with goals rather than strict constraints. Additionally, the article discusses alternative optimal solutions and the importance of compromise in design situations. It also covers graphical and numerical approaches, including direct lexicographic minimization routines and sequential algorithms within the context of Multiphase Simplex.

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Multiphase Simplex Formulation

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  1. Difference with simplex LP model: lexicographic minimization rather than single objective minimization use of deviation variables rather than slack, surplus, and artificial variables no constraints, only goals like in Goal Programming alternative optimal solutions exist, if the solution space associated with the problem is other than a single point. Multiphase Simplex Formulation • Please note: • Multiphase Simplex is also known as Multiplex. • Goal Programming is a subset of Multiplex. • For your project and other design problems, start with compromise DSP formulation because it allows (design) constraints. For solving compromise DSP, convert it to GP or Multiplex formulation.

  2. Graphical approach (good for understanding) Numerical approaches (based on two-phase and other simplex algorithms): • "direct" lexicographic minimization routines • sequential algorithms Methods of Solution

  3. Graphical Approach See Handout

  4. Multiplex Formulation and Algorithm See handout on Multiplex algorithm

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