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

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  • POCHET, Yves

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • WOLSEY, Laurence

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

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.

Suggested Citation

  • POCHET, Yves & WOLSEY, Laurence, 1992. "Integer knapsack and flow covers with divisible coefficients polyhedra, optimization and separation," LIDAM Discussion Papers CORE 1992018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1992018
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