Summary: We show, using small examples, that two algorithms previously published for the bilevel linear programming problem (BLP) [see J. F. Bard
, ibid. 31, 670-684 (1983; Zbl 0525.90086
); and W. F. Bialas
and M. H. Karwan
, Manage. Sci. 30, 1004-1020 (1984; Zbl 0559.90053
)] may fail to find the optimal solution and thus must be considered to be heuristics. A proof is given that solving BLP problems is NP-hard, which makes it unlikely that there is a good, exact algorithm.