Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Polyhedra for lot-sizing with Wagner-Whitin costs
Mathematical Programming: Series A and B
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
Mixing Sets Linked by Bidirected Paths
SIAM Journal on Optimization
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Let Abe the edge-node incidence matrix of a bipartite graph G= (U,V;E), Ibe a subset of the nodes of G, and bbe a vector such that 2bis integral. We consider the following mixed-integer set:$$X(G,b,I)=\{x\,:\,Ax\geq b,\,x\geq 0,\,x_i\mbox{ integer for all }i\in I\}.$$We characterize conv(X(G,b,I)) in its original space. That is, we describe a matrix (C,d) such that conv(X(G,b,I)) = {x: Cx茂戮驴 d}. This is accomplished by computing the projection onto the space of the x-variables of an extended formulation, given in [1], for conv(X(G,b,I)). We then give a polynomial-time algorithm for the separation problem for conv(X(G,b,I)), thus showing that the problem of optimizing a linear function over the set X(G,b,I) is solvable in polynomial time.