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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

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## Multiphase Simplex Formulation

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**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.**Graphical approach (good for understanding)**Numerical approaches (based on two-phase and other simplex algorithms): • "direct" lexicographic minimization routines • sequential algorithms Methods of Solution**Graphical Approach**See Handout**Multiplex Formulation and Algorithm**See handout on Multiplex algorithm

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