5 votes
Accepted

The linearization of the (Iff-and-only-Iff) expression

One possible way to linearize such a constraint would be by dividing this expression into four parts and then linearizing each of which separately. $$ Iff \quad (w=1) \rightarrow (x \rightarrow y) \...
  • 7,271
4 votes

The linearization of the (Iff-and-only-Iff) expression

@A.Omidi gave a nice derivation using conjunctive normal form. In this case, the big-M approach with $M=1$ yields the same formulation: $$w = 1 \implies x=y$$ can be enforced via $$-(1-w) \le x-y \le ...
  • 27.1k
2 votes

multi-commodity flow vs integer programming

I am a bit confused about the 2nd constraint. Nevertheless in the derived STU (combination of show type, start time, end time), exclude combinations like (o,16,19), (o,17,20)..(m,18,19) etc because ...
  • 2,527
1 vote

Array of string in OPL

.mod {string} cluster=...; string darkstore [cluster][1..4]=...; string demandpoint [cluster][1..4]=...; .dat ...
1 vote

Optimization solver that satisfies variable values within set membership

AMPL automatically linearizes var purchase {CUSTOMER} in VALUE; where VALUE is a set of numbers. The linearization creates some ...
  • 618
1 vote

Maximization problem with preferences on variables

How is this following constraint Either $b_z + y \le b_x+z +b_y\le x + b_z +yb_y$ Or let's break it $b_x+z \le x + b_z$ $b_z + y \le z +b_y $
  • 2,527
1 vote

How to find the maximizing number of expected delivered units of a probabilistic minimum cost flow problem?

Since you seem to have figured out a distribution for minimum cost flow (appears like Log-normal) you can try 2- stage stochastic programming using SAA techniques. LINDO Systems or model offers a ...
  • 2,527

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