The Quickest Delivery on the Super Pipeline Based Logistic System

In this paper, we consider the problem of delivering replenishments from source to sink nodes on a delivery line in minimum time interval, where the halfway stopping and intercrossing are forbidden. We call this problem the quickest delivery problem, and define it in a mathematical way. We point out that this problem is equivalent to the problem of moving time-position segments along the time axis such that any two segments are not intersected with each other and the total time is minimized. Based on this point, we formulate the quickest delivery problem as a minimization problem, with the non- intercrossing constraints as non-intersection constraints among time-position segments in four cases. We can solve this minimization problem by using optimization toolboxes. Experiments confirm the effectiveness of our model.