Variants of the Two Machine Flow Shop Problem connected with factorization of matrix functions

Article Abstract:

Variants of the Two Machine Flow Shop Problem have been examined. In the variants, the makespan is known and the objective is to determine a schedule that meets the makespan, thereby minimizing obstacles to achieving the job. The max-variant and sum-variant are both linked with factorization problems for certain rational matrix functions. Flow shop problems involving the variants and the corresponding factorization problems have been found to be equivalent to a certain degree.

Research, Shop mathematics

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New facets and a branch-and-cut algorithm for the weighted clique problem

Article Abstract:

A polyhedral approach to the weighted maximal b-clique problem is considered and four new classes of facet defining inequalities for the associated b-clique polytope are introduced. A description of a branch-and-cut algorithm is given and results indicate that the new algorithm is more efficient than previous algorithms.

Problem solving, Branch and bound algorithms

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The edge-weighted clique problem: Valid inequalities, facets and polyhedral computations

Article Abstract:

The edge-weighted clique problem is considered.

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