Periodic Review Production Models with Variable Capacity, Random Yield, and Uncertain Demand
研究在产能可变、产出随机和需求不确定的环境下，如何制定最优生产计划以最小化总期望成本，并证明了最优策略由单一临界点决定。
We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs (production, holding, and shortage costs), we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero; otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.