On Optimal Scheduling

We consider a decision-maker sequentially choosing among alternatives when periodic payoffs depend on both chosen and unchosen alternatives in that period. We show that when flow payoffs are the sum or product of payoffs from chosen and unchosen alternatives, the optimal policy is an index policy. We characterize key properties of the optimal dynamics and present an algorithm for computing the indices explicitly. Furthermore, we use the results to generalize Weitzman’s (1979) classic “Pandora’s boxes” problem to allow for complementarities. We illustrate the framework’s usefulness through applications, including decision problems with disappearing alternatives, repeated bargaining, dynamic supervision, and dynamic occupational choice.