一类具有优先关系的顺序控制问题的最优策略
Optimal strategies for a class of sequential control problems with precedence relations
摘要：
考虑以下多阶段项目管理问题。每个项目分为几个阶段。所有项目都在决策者根据到该点的观察选择的同一点进入下一阶段。在每个阶段中，可以按任何顺序执行项目。当用一个单位的资源进行项目时，项目状态按照马尔可夫链变化。已知马尔可夫链的概率分布直到未知参数。当被追求时，项目根据项目的阶段和状态以及未知参数生成随机奖励。决策者面临两个问题：（a）如何在每个阶段内为项目分配资源，以及（b）何时进入下一个阶段，以便总的预期回报尽可能大。在本文中，我们制定了上述问题作为一个随机调度问题，并提出了渐近最优策略，最小化从完美的信息支付的短缺。给出了具体的例子来说明我们的方法。
英文摘要：
Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown parameter. When pursued, the project generates a random reward depending on the phase and the state of the project and the unknown parameter. The decision maker faces two problems: (a) how to allocate resources to projects within each phase, and (b) when to enter the next phase, so that the total expected reward is as large as possible. In this paper, we formulate the preceding problem as a stochastic scheduling problem and propose asymptotic optimal strategies, which minimize the shortfall from perfect information payoff. Concrete examples are given to illustrate our method.
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