Answer by RobPratt for Bin Packing with Relational Penalization
Here is a simpler symmetry-less formulation based on the one proposed by @RenaudM. For $i \le j$, let binary variable $r_{i,j}$ indicate that the bin represented by item $i$ contains item $j$. (Here,...
View ArticleAnswer by Marco Lübbecke for Bin Packing with Relational Penalization
This is very related to the bin packing with conflicts problem (see eg. here), where you model the conflict as "soft" (with a binary variable to indicate violation, with a penalty in the objective...
View ArticleAnswer by Renaud M. for Bin Packing with Relational Penalization
If you are just looking for a formulation here is one (not particularly good due to symmetries, I'll rework it if I can think of something better in this regard).Let $K$ be an arbitrary upper bound on...
View ArticleBin Packing with Relational Penalization
There are $ N $ bins with equal capacity $ C $. In addition, there are $ N $ objects $x_1, x_2, \dots, x_N $ that need to be accommodated using the least amount of bins. Each object $x_i$ has a volume...
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