Scheduling Bidirectional Traffic on a Path

Abstract

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively. * This research was carried out in the framework of Matheon supported by Einstein Foundation Berlin.

Scheduling parallel batching machines in a sequence

“…Further, it may also be interesting to investigate whether SPBM with identical job speed can be solved in polynomial time for a fixed number of machines, for example by means of dynamic programming. by a hardness proof by Disser et al (2015) for a problem featuring bi-directional traffic along a path where a limited number of spots are available where overtaking and crossing of traffic is allowed.…”

“…A related setting in the context of waterways is the scheduling of bi-directional traffic along a narrow river or canal, where a limited number of wider segments is available for the crossing of ships that travel in opposite directions or for the overtaking of ships that travel in the same direction. The complexity of the problem to minimize total waiting time for this setting is settled by Disser et al (2015). We note that the results obtained by Disser et al (2015) do not immediately extend to our setting for the scheduling of locks.…”

“…The complexity of the problem to minimize total waiting time for this setting is settled by Disser et al (2015). We note that the results obtained by Disser et al (2015) do not immediately extend to our setting for the scheduling of locks. One attempt to connect the two problems is to see the narrow canal sections in their problem setting as machines, and the widened sections as the distance separating adjacent machines.…”

Online interval scheduling on two related machines: the power of lookahead

“…Lock scheduling is receiving an increasing amount of attention, especially due to the growing relevance of inland waterway transport as a sustainable, cheap, emission-friendly, and safe alternative to transport over land. We refer to Hermans (2014), Smith et al (2011) and who study single-chamber locks, and to Prandtstetter et al (2015), Disser et al (2015) and , where series of locks are studied.…”

No-Wait Scheduling for Locks

“…Literature Scheduling locks is a problem that is receiving an increasing amount of attention. In particular, when confronted with a series of locks (e.g., along a canal), the problem of operating the locks jointly to minimize total waiting time or emissions is dealt with in Prandtstetter et al (2015) and Passchyn et al (2016a) (see also Disser et al 2015 for a related more abstract setting).…”