Optimality Conditions and Exact Neighborhoods for Sequencing Problems

Based on several scheduling examples some classes of polynomially solvable sequencing problems with and without precedence constraints are considered. Suucient conditions for the existence of an adjacent pair interchange (API)-relation are derived in the case of sum-and bottleneck-objective functions. Furthermore, we obtain new conditions which are necessary and suucient for the optimality of permutations. It is shown that exact neighborhoods exist for all considered problems. These are neighborhoods in which each local optimum is a global one. Additionally, the neighborhoods are polynomially bounded and optimal solutions can be found by Iterative Improvement procedures in a polynomial number of iterations.