考虑固定和凸变动成本以及两类需求的动态生产策略

Dynamic Production Policy with Fixed and Convex Variable Costs and Two Demand Sources

考虑一个采用周期盘点库存的单产品制造商,其生产成本包括固定和凸变动成本;需求分为随机性与确定性两类,其中随机需求可以延期交货,但确定性需求和前一期的延期交货必须满足。制造商需要决策各周期的生产水平,其目标是最小化计划期内总期望成本。通过建立随机动态规划模型,证明最优值函数的某种凸性,并应用该性质刻画最优策略。研究发现,当初始库存低于确定性需求时,生产水平随初始库存递增;而当初始库存足够高时,则不需要生产。数值实验表明,当不考虑必须满足确定性需求这个限制条件时,所得策略的结构与最优策略明显不同。

Consider a single-product manufacturer facing a periodically-reviewed inventory problem.The production cost includes a fixed cost and a convex variable cost.And the demand is classified into two types,a deterministic source and a random source,where the random source can be backlogged,but the deterministic source and the backorders from the previous period must be satisfied.The manufacturer needs to decide the production level in each period and the goal is to minimize the expected total cost over a planning horizon.We develop a stochastic dynamic programming model,show some convexity of optimal value functions and apply this property to characterize the optimal production policy.From this,we find that the produce-up-to level increases in the initial inventory level when the initial inventory level is below the deterministic demand,and producing nothing is optimal when the initial inventory level is high enough.Numerical study shows that the structure of the policy is obviously different with the optimal one when the constraint that the deterministic demand must be satisfied is ignored.