Maximizing a submodular function by integer programming: polyhedral results for the quadratic case

Article Abstract:

The problem of maximizing a submodular function (PMSF) was formulated within a 0-1 mixed integer programming (MIP) framework to obtain an MIP model of a variant of the PMSF problem, the quadratic cost partition problem. To solve the latter, a cutting plane/branch-and-bound algorithm was developed based on the correlation between the QCP and the node packing polyhedrons. The correlation concerns the valid inequalities for the convex hull of the incidence vectors of feasible solutions.

Operations research, Management science, Case studies, Combinatorial optimization

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Conflict graphs in solving integer programming problems

Article Abstract:

Use of conflict graphs to find a solution to various problems of integer programming is discussed. Additional information on development and use of conflict graphs is also included.

Analysis, Mathematical models

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On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra

Article Abstract:

The single item capacitated lot-sizing problem is considered.

Operations Research, Planning

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