Mixed‐integer linear optimization for optimal lift‐gas allocation with well‐separator routing

The lift‐gas allocation problem with well‐separator routing constraints is a mixed‐integer nonlinear program of considerable complexity. To this end, a mixed‐integer linear formulation (compact) is obtained by piecewise‐linearizing the nonlinear curves, using binary variables to express the linearization and routing decisions. A new formulation (integrated) combining the decisions on linearization and routing is developed by using a single binary variable. The structures of both formulations are explored to generate lifted cover cuts. Numerical tests show that the solution of the integrated formulation using cutting‐plane generation is faster in spite of having more variables than the compact formulation.