非立即变质品的订购、定价与保鲜投资决策

考虑了一个非立即变质品的订购、定价与保鲜技术投资联合决策问题,其中产品的需求依赖于销售价格,变质率随时间变化,系统不允许缺货.此外,产品的时变变质率和保鲜期可以通过保鲜技术的投资得到控制,并采用一般形式的资本投资回报率构建模型.目的是决定最优的补货、定价和保鲜技术投资策略(包括是否投资和投资多少)以最大化系统的平均利润.证明了对于给定的定价和保鲜技术投资策略,最优补货策略唯一存在.在此基础上给出了一个寻找模型最优解的多阶段迭代求解算法.最后通过数值算例展示了模型和算法的应用,进一步采用数值方法对模型的数学性质进行了探讨,并对参数的灵敏度进行了分析.结果显示:当订购成本和产品购买成本较小或库存持有成本和产品初始保鲜期较大时,最优保鲜技术投资将为零,即不投资保鲜技术对系统最优.

Ordering,pricing and preservation investment decision for non-instantaneously deteriorating items

This paper considers a joint ordering, pricing and preservation technology investment decision problem for non-instantaneously deteriorating items with generalized price sensitive demand rate, time-varying deterioration rate and no shortage. Besides, the deterioration rate and the no-deterioration period are not exogenous and can be controlled by means of effective capital investment in preservation technology. General productivities of invested capital on the deterioration rate and no-deterioration period are adopted to formulate the model. The major objective is to determine the optimal replenishment, pricing and preservation technology investment strategies (including whether or not invest in preservation technology and how much to invest) in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. A multi-stage iteration algorithm is presented to find the optimal solution of the proposed model. Finally, the numerical example is given to illustrate the application of proposed model, the mathematical properties of the model are further discussed through numerical method, and the sensitivity analysis is carried out. The result shows that if the ordering cost and purchasing cost are small, or inventory holding cost and initial no-deterioration period are large, then the optimal preservation technology investment cost is zero, that is, do not invest in preservation technology.