Scheduling activities in project network with feeding precedence relations: an earliest start forward recursion algorithm
针对活动执行强度可变的生产过程，提出一种前向递归算法，能在O(m log n)时间内计算每个活动的最早开始和结束时间，并确定最优执行强度以最小化项目完成时间。
Abstract In some production processes, the effort associated with a certain activity for its execution can vary over time. In this case, the amount of work per time unit devoted to each activity, so as its duration, is not univocally determined. This kind of problem can be represented by an activity project network with the so-called feeding precedence relations , and activity variable execution intensity. In this paper, we propose a forward recursion algorithm able to find the earliest start and finish times of each activity, in $$O(m \log n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> time, with n and m being the number of activities and the number of precedence relations, respectively. In particular, this requires the calculation of the (optimal) execution intensity profile, for each activity, that warrants the earliest start schedule and the minimum completion time of the project.