The general routing polyhedron: a unifying framework

Article Abstract:

The General Routing Problem (GRP) has many practical applications and includes some well-known routing problems as special cases including that involving the Steiner Graphical Traveling Salesman Problem (SGTSP) and Graphical Traveling Salesman Problem (GTSP). It will be shown that a strong polyhedral association exists between the GTSP, SGTSP and GRP. In a sense, it may be said that the only area open to further research in this field is the specification of conditions under which facets of GTSP polyhedra yield facets of GRP polyhedra.

Case studies, Evaluation, Scheduling (Management), Algorithms, Numerical calculations

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The General Routing Problem polyhedron: facets from the RPP and GTSP polyhedra

Article Abstract:

A new type of explicit facet-inducing inequalities called honey-comb constraints was uncovered after an in-depth analysis of General Routing Problem (GRP) polyhedron was undertaken. The inequalities, which generalize the K-C constraints, are found to be helpful in the resolution of GRP, as well as the Rural Postman Problem (RPP). Solution of GRP was also found to be highly probable provided that determination of violated honeycomb inequalities is achieved.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Research, Honeycomb structures, Honeycomb structures (Materials)

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A representation of an efficiency equivalent polyhedron for the objective set of a multiple objective linear program

Article Abstract:

Various efficient solutions have been developed to solve multiple objective linear programming (MOLP) problems. However, these solutions have generally not considered the development of a technique for helping a decision maker choose a final operational solution from a set of efficient solutions. It is shown that a model based on the theory of polyhedral polarity exhibited functional applications for MOLP problems.

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