Complex sentence: LeMay's entire command... were appalling, "despite the SAC deputy commander, Major General McMullen, having,"... instructed all bomber units to improve their effectiveness and so established a competition, the first so-called "Bomb Comp" in 1948.
Split into simpler sentences: LeMay's entire command... were appalling, despite the SAC deputy commander, Major General McMullen, having instructed all bomber units to improve their effectiveness. To motivate crews and improve operational effectiveness command-wide, SAC established a competition, the first so-called "Bomb Comp" in 1948.