There is no theory in strategic management and other related fields for identifying decision problems that cannot be solved by organizations using rational analytical technologies of the type typically taught in MBA programs. Furthermore, some and perhaps many scholars in strategic management believe that the alternative of heuristics or “rules of thumb” is little more than crude guesses for decision making when compared to rational analytical technologies. This is reflected in a paucity of research in strategic management on heuristics. I propose a theory of “organizational intractability” based roughly on the metaphor provided by “computational intractability” in computer science. I demonstrate organizational intractability for a common model of the joint strategic planning and resource allocation decision problem. This raises the possibility that heuristics are necessary for deciding many important decisions that are intractable for organizations. This possibility parallels the extensive use of heuristics in artificial intelligence for computationally intractable problems, where heuristics are often the most powerful approach possible. Some important managerial heuristics are documented from both the finance and strategic management literatures. Based on all of this, I discuss some directions for theory of and research on organizational intractability and heuristics in strategic management.