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What is a mixed-integer programming problem?
A mixed-integer programming (MIP) problem is one where some of the decision variables are constrained to be integer values (i.e. whole numbers such as -1, 0, 1, 2, etc.) at the optimal solution. The use of integer variables greatly expands the scope of useful optimization problems that you can define and solve.
What makes a constraint linear?
A linear constraint is a mathematical expression where linear terms (i.e., a coefficient multiplied by a decision variable) are added or subtracted and the resulting expression is forced to be greater-than-or-equal, less-than-or-equal, or exactly equal to a right-hand side value.
How to specify an IF-THEN constraint with an integer?
How to specify an IF-THEN constraint with an Integer Linear Programming (ILP) solver Problem : For example: if (A> 0) then B>= 0. (Note that “<=” denotes “less than or equal”.) Answer : if (A> 0) then B>= 0 ( A> 0 and B>= 0 ) or ( A<= 0 ) ( 0 < Aand 0 <= B) or ( A<= 0 )
When is one of the two constraints active?
The conversion guarantees that only one of the two constraints can be active at anyone time. If yij = 0, the first constraint is active, and the second is redundant (because its left-hand side will include M, which is much larger than pi). If yij = 1, the first constraint is redundant, and the second is active.
What are the constraints for continuous variables x and Y?
For continuous variables x and y, the constraints are: The problem is on modeling nonlinear behaviour of gas storage pumping efficiency, which decreases for high load in case of very large gas storages (decrease is seen for storages with capacity above 5 million cubic meters). I have to write these constrains using MIP (or LP) formulation.
How to enforce if-then constraints in MIP programming?
Finally, you can enforce the implication “if z = 1 then y ≤ 10 ” using the discussion here: In an integer program, how can I “activate” a constraint only if a decision variable has a certain value? Thanks for contributing an answer to Operations Research Stack Exchange!