Profit maximization models for exponential decay processes
Profit maximization models for exponential decay processes
复制标题
指数衰减过程的利润最大化模型
DOI：
10.1016/0377-2217(85)90117-1
复制
发表时间：
1985
影响因子：
6.4
通讯作者：
V. Udayabhanu
中科院分区：
文献类型：
--
作者：
S. Sethi;G. Thompson;V. Udayabhanu
许多真实的世界过程可以被建模为指数衰减过程。例如：机器更换、油井开采、广告商誉、维修和清洁活动等。本文分析了一系列贴现或非贴现、确定性或随机性指数衰减模型。我们刻画了每个模型的有限和无限时域最优解。我们表明，该解决方案的特点是石油钻井问题的以下方式：一旦一口井的足够的能力是钻，石油从它，直到剩余的石油减少到一个固定的截止水平，然后井被遗弃，并钻一个新的井。随着时间的推移，由此产生的过程似乎与一个石油来源在固定的截止水平上持续产生石油收入的过程相同。换句话说，当一口油井的产能大于临界水平时，从该油井获得的超额收入仅足以支付新井的钻探成本。虽然本文中分析的模型是理想化的，提出的结果应该提供更现实的情况下的分析指导。
A number of real world processes can be modelled as exponential decay processes. Examples are: machine replacement, oil well extraction, advertising goodwill, repair and cleaning activities, etc.. In this paper we analyze a series of discounted or undiscounted, deterministic or stochastic exponential decay models. We characterize finite and infinite horizon optimal solutions for each model. We show that the solution can be characterized for the oil drillers problem in the following way: Once a well of sufficient capacity is drilled, oil is pumped from it until the oil remaining decreases to a fixed cut-off level; then the well is abandoned, and a new well is drilled. The resulting process when repeated over time appears to be the same as an oil source which produces oil revenue continuously at the fixed cut-off level. In other words, the excess revenue received from an oil well when its capacity is greater than the cut-off level is just sufficient to pay for drilling costs for a new well. Although the models analyzed in this paper are idealized, the results presented should provide a guide to the analysis of more realistic situations.