James B. Harris
The first producer Kubrick worked with on Strangelove was his longtime producing partner James B. Harris, who Kubrick had worked with on all of his earlier films like Lolita, Paths of Glory, and The Killing. Not only did these two have a great working relationship, they were also good friends.
After finishing Lolita, they set out together to make a serious film about the bomb. It was actually Harris who suggested Kubrick read Red Alert, the thriller novel that eventually inspired Dr. Strangelove. There was trouble in paradise, though, when Kubrick decided to turn the previously serious thriller into a dark comedy. Harris just couldn't sign off on the idea, and he and Kubrick parted ways (though they stayed friends for the rest of their lives). (Source)
At first, the split with Harris spelled big trouble for Kubrick. The British company Seven Art Productions refused to finance any more Kubrick films without Harris to rein in Kubrick's wackier ideas. So Kubrick had to find another studio to make his film. Eventually, he got Columbia Pictures to sign off on it, but like with all studios big and small, the deal came with strings attached. Luckily for Kubrick, Columbia's big bucks had some pretty sweet strings: Kubrick had to cast Peter Sellers, and Sellers had to play at least four roles.
Who knew big studio execs could actually have good ideas? Of course, these ideas were inspired by Kubrick himself, who'd just finished up his version of Lolita, which...you guessed it...featured Peter Sellers playing multiple roles. In the end, Sellers only ended up playing three roles since he wriggled his way out of playing Major T.J. "King" Kong.
Sellers had all kinds of excuses about why he didn't want to play Kong. He whined that the workload was too much and that he couldn't master the Texan accent, but some say that he actually was afraid of heights and didn't want to do the bomb drop scene. At last, Sellers sprained his ankle while bickering with Kubrick in the cockpit of the B-52, and the director replaced him with real life rodeo star Slim Pickens.