The branch and bound tree that follows shows the incomplete solution of a minimizing ILP by LP-based
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The branch and bound tree that follows shows the incomplete solution of a minimizing ILP by LP-based Algorithm 12A, with numbers next to nodes indicating LP relaxation solution values.
Node 4 has just produced the first incumbent solution, and nodes a to d remain unexplored.
(a) Show which unexplored nodes could be immediately terminated by the parent bound if the incumbent at node 4 had objective function value 120. How about 118?
(b) Determine the best lower bound on the ultimate ILP optimal value that is available after processing of node 4.
(c) Assuming that the incumbent at node 4 has objective value 125, compute the maximum absolute and percent objective value error in accepting the incumbent as an approximate optimum.
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