## Algorithms and applications for generalized networks |

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algorithm APEX-lll basis exchange step basis graph basis matrix Big-M candidate list chapter Charnes coefficient matrix column vectors computational results computer code constrained generalized network cost coefficients CPU seconds decision rules decision-maker Degenerate Pivots determined developed digraph DNET dual feasible dual method dual variable values efficient enter the basis extended APl method feasible solution flow FORTRAN GN problem graph traversal implement Klingman leave the basis lems linear programming list structures LP problems matrix inverse multipliers NETG NETSG network code node non-zero entries number of pivots objective function operations research optimal partitioning performed pivot selection PNET-l primal simplex prob procedures for solving pseudo dual variable pure network problems quasi-tree reduced round-off error simplex algorithm simplex method singularly constrained SUPERK techniques tion Total Pivots total solution transportation problems transshipment problems traversal underlying generalized network updated vertex vertices zero