The competition between heuristic and optimization approaches for process synthesis and process operations problems has caused major controversy in recent years. Heuristics offer fast solutions but no guarantee of optimality. Mathematical programming approaches, on the other hand, offer rigor but suffer from combinatorial explosion of computational requirements. The use of analytical investigations is proposed as a theoretical means to characterize the behavior of heuristics and optimization algorithms and produce a framework that combines the strengths of the two approaches while eliminating their weaknesses. The approach contrasts and complements the current practice in process systems engineering, which is entirely empirical in nature. The proposed paradigm is demonstrated in the context of the multiperiod capacity expansion problem for chemical process networks, a problem having much in common with both process synthesis and operations problems. Analytical investigations for this problem lead to the development of a heuristic that is proved to be asymptotically optimal under standard assumptions about the problem parameters. In the more general context of process synthesis and operations, analytical investigations present a large away of opportunities.