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29 January 2022

MIP tricks

When formulating a model, many of the problems we encounter involve non-linear formulae. For example, a fixed cost is incurred only if a facility is built, or a variable can take values only in the ranges 5 to 10 or 80 to 100.

Optimization models work best when the objective function and constraints are all linear. In some situations, it is possible to reformulate a model to linearize the non-linear parts. The techniques for linearizing non-linear formulae can make the difference between a model being viable or not.

FICO Xpress Optimization have written a booklet that describes a variety of useful mixed-integer programming (MIP) formulations and linearizations, including:

  • Binary variable logical conditions.
  • Minimum, maximum, and absolute value of binary variables.
  • Multiplication of variables.
  • Variables with disjunctions.
  • Batch sizes.
  • Minimum activity level.

The booklet is available at: MIP formulations and linearizations.