Multiphase Simplex Formulation

1
Multiphase Simplex Formulation

• 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.

• 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
Methods of Solution

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

3
Graphical Approach
See Handout
4
Multiplex Formulation and Algorithm
See handout on Multiplex algorithm