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

Abstract

We consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job j ∈ J is characterized by a length p j , and an arrival time t j ; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.

Hiking in the scheduling landscape

“…Pinson and Spieksma [132] consider the lock scheduling problem in the online setting and allow for possible lookahead as to find a feasible schedule with zero total waiting time. Verstichel et al [163] present a mathematical programming formulation for the lock scheduling problem considering multiple chambers and introduce heuristic methods.…”