Integer knapsack and flow covers with divisible coefficients polyhedra, optimization and separation

Yves Pochet and Laurence Wolsey ()
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Yves Pochet: CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
Laurence Wolsey: CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

No 1992018, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Three regions arising as surrogates in certain network design problems are the knapsack set X = {x [ belong ] [Z^n_+] : [ sum^n_j=1] C_jx_j ≥ b}, the simple capacitated flow set Y = {(y, x) [belong ] [R^1_+] x [Z^n_+] : y ≤ b,y ≤ [ sum^n_j=1] C_jx_j} and the set Z = {(y, x) [ belong ] [R^n_+] x [Z^n_+] : [ sum^n_j=1] y_i ≤ b, y_i ≤ C_jx_j for j = 1,...,n}, where the capacity C_(j+1) is an integer multiple Cj for all j. We present algorithms for optimization over the sets X and Y, as well as different descriptions of the convex hulls and fast combinatorial algorithms for separation. Some partial results are given for the set Z and another extensions.

Date: 1992-06-01
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