In classical newsvendor model, piece-wise linear shortage and excess costs are balanced out to determine the optimal order quantity. However, for critical perishable commodities, severity of the costs may be much more than linear. In this paper we discuss a generalisation of the newsvendor model with piece-wise polynomial cost functions to accommodate their severity. In addition, the stochastic demand has been assumed to follow a completely unknown probability distribution. Subsequently, non-parametric estimator of the optimal order quantity has been developed from a random polynomial type estimating equation using a random sample on demand. Strong consistency of the estimator has been proven when the true optimal order quantity is unique. The result has been extended to the case where multiple solutions for optimal order quantity are available. Probability of existence of the estimated optimal order quantity has been studied through extensive simulation experiments. Simulation results indicate that the non-parametric method provides robust yet efficient estimator of the optimal order quantity in terms of mean square error.
翻译:在古典的Newsvendor 模型中,可以平衡整片线性短缺和超额成本,以确定最佳订单数量。然而,对于关键的易腐商品,成本的严重程度可能远大于线性。我们在本文件中讨论将新闻商店模型的概略化,使用零碎的多面性成本功能来适应其严重程度。此外,还假定随机需求会随着完全未知的概率分布而变化。随后,利用随机抽样,从随机多面性估算方程式中开发出非参数性的最佳订单数量估算器。当真正的最佳订单数量是独特的时,估计数字的高度一致性已经得到证明。结果已推广到有多种最佳订单数量解决方案的案例中。通过广泛的模拟实验研究了估计最佳订单数量的可能性。模拟结果表明,非参数性方法提供了以中度方误表示的最佳订单数量可靠而有效的估计器。