Integer and combinatorial optimization
Integer and combinatorial optimization
The convex hull of two core capacitated network design problems
Mathematical Programming: Series A and B
Polyhedra for lot-sizing with Wagner-Whitin costs
Mathematical Programming: Series A and B
The Continuous Mixing Polyhedron
Mathematics of Operations Research
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
SIAM Journal on Discrete Mathematics
Compact formulations as a union of polyhedra
Mathematical Programming: Series A and B
The mixing-MIR set with divisible capacities
Mathematical Programming: Series A and B
Mixed-Integer Vertex Covers on Bipartite Graphs
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
The Intersection of Continuous Mixing Polyhedra and the Continuous Mixing Polyhedron with Flows
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Network Formulations of Mixed-Integer Programs
Mathematics of Operations Research
New Hardness Results for Diophantine Approximation
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Mixing MIR inequalities with two divisible coefficients
Mathematical Programming: Series A and B
The mixing set with divisible capacities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
On a class of mixed-integer sets with a single integer variable
Operations Research Letters
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Recently there has been considerable research on simple mixed-integer sets, called mixing sets, and closely related sets arising in uncapacitated and constant capacity lot-sizing. This in turn has led to study of more general sets, called network-dual sets, for which it is possible to derive extended formulations whose projection gives the convex hull of the network-dual set. Unfortunately this formulation cannot be used (in general) to optimize in polynomial time. Furthermore the inequalities defining the convex hull of a network-dual set in the original space of variables are known only for some special cases. Here we study two new cases, in which the continuous variables of the network-dual set are linked by a bidirected path. In the first case, which is motivated by lot-sizing problems with (lost) sales, we provide a description of the convex hull as the intersection of the convex hulls of $2^n$ mixing sets, where $n$ is the number of continuous variables of the set. However optimization is polynomial as only $n+1$ of the sets are required for any given objective function. In the second case, generalizing single arc flow sets, we describe again the convex hull as the intersection of an exponential number of mixing sets and also give a combinatorial polynomial-time separation algorithm.