This paper examines a deterministic, discrete-time, finite-horizon, production/distribution problem for a one-plant multi-retailer system. Production may occur at the plant in each time period. Customer demands at each retailer over a finite number of periods are known and must be met without backlogging. The plant as well as the retailers can serve as stocking points. The problem is to find a minimum-cost production/distribution schedule satisfying the known demands. We show that under a certain cost structure a nested policy is optimal, and present an efficient algorithm to find such an optimal policy. Planning horizon results and some computational saving schemes are also presented.