This paper explores the improvements in manufacturing efficiency that can be achieved by broadening the scope of production scheduling to include both the sequencing of work and the coordination of the resource inputs required to perform work. Recognizing that some resources are inherently flexible and thus can be reassigned dynamically to processing centers as needed, and that job processing times are often a function of the amount of resource dedicated to specific operations, we formulate the flexible-resource scheduling problem with the objective of simultaneously determining the permutation job sequence, resource allocation policy, and operation start times that optimize system performance. Focusing on flexible-resource scheduling in flow shop production systems, we discuss problem complexity, identify properties of and establish lower bounds for optimal schedules, develop optimal and heuristic solution approaches, and report the results of extensive computational experimentation designed to explore the operational benefits of resource flexibility. The computational results demonstrate that the performance improvements associated with flexible-resource scheduling are substantial, and suggest that the heuristic provides an effective means for solving larger problems.