This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a mobile searcher that must locate a hidden target in an environment that consists of a set of unbounded, concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. Both types of problems capture fundamental aspects of resource allocation under uncertainty. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems, we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using the same underlying approach.