基于物价指数上涨的最优在线租赁决策模型

考虑到现实租赁市场设备租金费用及购买价格随着时间推移总体呈现出持续性上涨特征, 建立了基于物价指数上涨的在线租赁决策模型, 首先分析了该问题的最优离线策略, 其次运用在线算法理论给出了该问题的确定性最优在线租赁策略及其竞争比. 从提高策略的竞争性能角度出发, 基于风险控制思想, 给出了该问题的随机性最优在线租赁策略及其竞争比, 并运用两人零和博弈分析技巧严格证明了此策略是该问题的唯一随机性最优竞争策略. 进一步指出了确定性和随机性最优策略的竞争性能均随着购买价格上涨而下降, 也随着物价指数上涨而降低. 最后, 结合数值分析发现当存在通货膨胀因素时, 最优决策日期相对提前, 但策略的竞争性能显著降低, 这表明物价指数变动对在线租赁决策具有显著影响.

Optimal online rental decision model with increasing price index

In actual rental market, based on the inflation characteristics that the rental cost each period and purchase price of an equipment generally continue to rise as time goes, we propose online rental decision model with increasing price index. By using online algorithm, we first investigate optimal offline strategies, and then present deterministic optimal online strategy and its competitive ratio. From the view of improving competitive performance of online strategy, basing on the idea of risk control, we propose randomized online strategy and its competitive ratio, and strictly prove that this strategy is an only randomized optimal online strategy for this problem by using analysis technique of two person zero-sum game. Moreover, we further point out that the competitive performance of deterministic and randomized optimal strategies are declined as the purchasing price of the equipment and the price index increase, respectively. Finally, numerical analysis illustrates that when there is inflation, the optimal decision date is relatively advanced, but the competitive performance of online strategy decreases significantly. Thus, it shows that the changes of price index have a significant effect on online rental decision.