Summary: This article presents an extension of a dynamic programming algorithm for scheduling production of multiple items on a single machine with time- varying deterministic demands. The extension handles time-varying deterministic material supply constraints. The algorithm minimizes the sum of changeover and inventory holding costs under two assumptions. First, we assume that in each time period, within the planning horizon, the machine must either be shut down or be producing some one item for the entire time period. Second, we assume that inventory holding costs are the same for all items and are representable as a non-decreasing function.