The paper deals with a health care system consisting of multiple hospitals, a distribution center and one regular and one outsourcing suppliers of medicine for the distribution center. Demand of medicine at hospitals is assumed stochastic in practice. The expected cost function of entire supply chain is formulated considering holding cost, shortage cost, outsourcing cost and preservation cost. In this cost function, order quantities from each hospital and rate of deterioration of medicine at distribution center are decision variables. The above expected cost function of supply chain is analyzed by calculus method in light of both continuous and discrete distribution function. Model is also particularly demonstrated for normal and Poisson distribution of the random variables. We use a distribution-free approach to address the situation where information about the random variables is limited to the mean and the variance, and distribution function is unknown. In this case we minimize upper bounds of the expected cost function of the supply chain for all the possible distribution of the random variable. Numerical example is illustrated to justify our proposed models.

该文件涉及一种医疗保健系统，该系统由多家医院，一个配送中心以及该配送中心的一家常规药品供应商和一家外包服务商组成。实际上，医院对药品的需求被认为是随机的。考虑到持有成本，短缺成本，外包成本和保存成本，制定了整个供应链的预期成本函数。在此成本函数中，每个医院的订单数量和配送中心的药品劣化率是决策变量。结合连续分布函数和离散分布函数，运用演算法对上述供应链预期成本函数进行了分析。该模型还特别证明了随机变量的正态分布和泊松分布。我们使用无分布方法来解决以下情况：有关随机变量的信息仅限于均值和方差，并且分布函数未知。在这种情况下，我们将随机变量所有可能的分布的供应链预期成本函数的上限最小化。数值例子说明了我们提出的模型的合理性。