Online scheduling with machine cost and rejection
Discrete Applied Mathematics
Online scheduling with general machine cost functions
Discrete Applied Mathematics
Semi-online algorithms for scheduling with machine cost
Journal of Computer Science and Technology
New upper and lower bounds for online scheduling with machine cost
Discrete Optimization
Optimal semi-online algorithms for scheduling with machine activation cost
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
The generalization of scheduling with machine cost
Theoretical Computer Science
Information Sciences: an International Journal
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For most scheduling problems the set of machines is fixed initially and remains unchanged. Recently Imreh and Noga proposed adding the concept of machine cost to scheduling problems and considered the so-called List Model problem. For this problem, we are given a sequence of independent jobs with positive sizes, which must be processed non-preemptively on a machine. No machines are initially provided, and when a job is revealed the algorithm has the option to purchase new machines. The objective is to minimize the sum of the makespan and cost of machines. In this paper, a modified model of List Model is presented where preemption is allowed. For this model, it is shown that better performance is possible. We present an online algorithm with a competitive ratio of $(2\sqrt{6} + 2)/5\approx 1.3798$ while the lower bound is 4/3. For the semi-online problem with decreasing sizes, we design an optimal algorithm with a competitive ratio of 4/3, which improves the known upper bound of 3/2. The algorithm does not introduce any preemption, and hence is also an optimal semi-online algorithm for the non-preemptive semi-online problem. For the semi-online problem with known largest size, we present an optimal algorithm with a competitive ratio of 4/3.