Note—Some Equivalent Objectives for Dynamic Network Flow Problems
这篇注记证明，在最大动态网络流问题中，可以同时实现三个重要目标：最早到达调度、最后流量到达时间最小化以及平均到达时间最小化。对研究疏散模型或动态网络优化的学者有用。
Many important problems can be modeled as dynamic (time-expanded) network flow problems. For example, in building evacuation we might use twenty nodes to represent a room at 3 minute intervals over an hour, and use arcs to indicate the feasible passages, over time, among the various rooms. The purpose of this note is to demonstrate that it is possible to satisfy at least three important objectives simultaneously in a maximal dynamic network flow problem. These are (1) construction of an earliest arrival schedule (i.e., a solution which maximizes flow in the first p periods, for every p), (2) minimization of the period at which the last unit of flow arrives at the sink, and (3) minimization of the average time for all flow to arrive at the sink.