On Lagrangian-based Lower Bounds for the Sequential Ordering Problem with Time Windows and Precedence Relationships |
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algorithm ALTERNATE SEQUENCES consists of finding constraints 3.4 Cornell University cut lifting Date Forcing Constraints dates are required denote the ordered DFCs digraph G dual multipliers DUE DATE FORCING Execute procedure updating false Obtain feasible finding a minimum given node Hamiltonian path problem Lagrangian relaxation last node local search sequence minimum weight Hamiltonian node g nodes pair NP-hard Obtain as given optimal solution ordered set pair i,j partial sequence path from node potential pp(j precedence forcing constraints precedence relationships predecessor path procedure for obtaining procedure restricted TRIA-1 relaxation techniques release and due release date resp Restricted TRIA-2 local root at node search sequence 6.2 search sequence 6.4 sequence 5.5 sequence 6.3 sequence is sp(f sequence see Figure SEQUENTIAL ORDERING PROBLEM set of nodes setup sp(x splf tightening TRIA-1 local search TRIA-2 local search type of constraints weight Hamiltonian path window and precedence