A rolling schedule is formed by solving a multi-period problem and implementing only the first period's decisions; one period later the multi-period model is updated and the process repeated. In this paper, we provide a general framework for analyzing rolling schedules, and we examine analytically a fundamental quadratic-cost model for the effects of such factors as the length of the planning interval, the uncertainty in forecasts, and the periodicity of demand. For the quadratic model our main result is that cost performance improves monotonically as the planning horizon is lengthened. We also find that the use of terminal conditions in the multi-period model can dramatically improve rolling schedule performance.