Perturbation analysis for continuous and discrete flow models: a study of the delivery time impact on the optimal buffer level
研究了一个包含单产品机器、缓冲和随机需求的制造系统，通过连续和离散流模型分析恒定交货时间对最优缓冲水平的影响，并利用无穷小扰动分析优化总平均成本。
In this paper, a manufacturing system composed of a single-product machine, a buffer and a stochastic demand is considered. Two models are presented: continuous and discrete flow models including constant delivery times, machine failures and random demands. The objective is to determine the value of the optimal buffer level, for a hedging point policy which minimises the total average cost function. The cost function is the sum of inventory, transportation and lost sales costs. Infinitesimal perturbation analysis is used for optimisation of the failure-prone manufacturing system. The trajectories of buffer level are studied for the continuous and discrete cases and the infinitesimal perturbation analysis estimators are evaluated. These estimators are shown to be unbiased and then they are implemented in an optimisation algorithm which determines the optimal buffer level in the presence of constant delivery time. Numerical results are presented for continuous and discrete flow models and then compared in order to evaluate the application of the infinitesimal perturbation analysis on the discrete flow model.