Solving mixed integer programming problems using automatic reformulation
Operations Research
Capacitated facility location: separation algorithms and computational experience
Mathematical Programming: Series A and B - Special issue on computational integer programming
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Network Formulations of Mixed-Integer Programs
Mathematics of Operations Research
Improved lower bounds for the capacitated lot sizing problem with setup times
Operations Research Letters
A computational analysis of lower bounds for big bucket production planning problems
Computational Optimization and Applications
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The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and has also strong links with the challenging big-bucket multi-item lot-sizing problem. We provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub- and super-modularity of an associated set function, thereby providing an interesting link with flow-cover type inequalities. The second proof is by projecting a tight extended formulation, therefore also showing that these inequalities suffice to describe the convex hull of the feasible solutions to this problem. We finally show how to solve the separation problem associated to the path-modular inequalities in O(n3) time.