An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution
提出CAVE算法，无需假设需求分布，仅利用库存剩余数据，通过分段线性凹函数逼近价值函数，解决重复决策下的库存优化问题，实验证明在报童和两阶段配送问题中接近最优。
We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the value function using a technique called the Concave, Adaptive Value Estimation (CAVE) algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs—the newsvendor stochastic inventory problem and two-stage distribution problems.