Three discotic liquid-crystalline binary mixtures, characterized by their extent of bidispersity in molecular thickness, were investigated with molecular dynamics simulations. Each equimolar mixture contained A-type (thin) and B-type (thick) discogens. The temperature-dependence of the orientational order parameter reveals that A-type liquid samples produce ordered phases more readily, with the (hexagonal) columnar phase being the most structured variant. Moderately and strongly bidisperse mixtures produce globally-segregated samples for temperatures corresponding to ordered phases; the weakly bidisperse mixture displays microheterogeneities. Ordered phases in the B-type liquid are induced partially by the presence of the A-type fluid. In the moderately bidisperse mixture, order is induced through orientational frustration: a mixed prenematic-like phase precedes global segregation to yield nematic and columnar mesophases upon further cooling. In the strongly bidisperse mixture, order is induced less efficiently through a paranematic-like mechanism: a highly-ordered A-type fluid imparts order to B-type discogens found at the interface of a fully-segregated sample. This ordering effect permeates into the disordered B-type domain until nematic and columnar phases emerge upon further cooling. At sufficiently low temperatures, all samples investigated exhibit the (hexagonal) columnar mesophase.