26,287 research outputs found
How the structure of precedence constraints may change the complexity class of scheduling problems
This survey aims at demonstrating that the structure of precedence
constraints plays a tremendous role on the complexity of scheduling problems.
Indeed many problems can be NP-hard when considering general precedence
constraints, while they become polynomially solvable for particular precedence
constraints. We also show that there still are many very exciting challenges in
this research area
Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model
We consider online scheduling on multiple machines for jobs arriving
one-by-one with the objective of minimizing the makespan. For any number of
identical parallel or uniformly related machines, we provide a
competitive-ratio approximation scheme that computes an online algorithm whose
competitive ratio is arbitrarily close to the best possible competitive ratio.
We also determine this value up to any desired accuracy. This is the first
application of competitive-ratio approximation schemes in the online-list
model. The result proves the applicability of the concept in different online
models. We expect that it fosters further research on other online problems
Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
In the paper we consider the problem of scheduling identical jobs on 4
uniform machines with speeds respectively.
Our aim is to find a schedule with a minimum possible length. We assume that
jobs are subject to some kind of mutual exclusion constraints modeled by a
bipartite incompatibility graph of degree , where two incompatible jobs
cannot be processed on the same machine. We show that the problem is NP-hard
even if . If, however, and ,
, then the problem can be solved to optimality in time
. The same algorithm returns a solution of value at most 2 times
optimal provided that . Finally, we study the case and give an -time -approximation algorithm in
all such situations
Tactical fixed job scheduling with spread-time constraints
We address the tactical fixed job scheduling problem with spread-time constraints.
In such a problem, there are a fixed number of classes of machines and a fixed number of groups of jobs. Jobs of the same group can only be processed by machines of a given set of classes. All jobs have their fixed
start and end times. Each machine is associated with a cost according to its machine class. Machines have spread-time constraints, with which each machine
is only available for L consecutive time units from the start time of the earliest job assigned to it. The objective is to minimize the total cost of the machines used to process all the jobs. For this strongly NP-hard problem, we develop a branch-and-price algorithm, which solves instances with up to 300 jobs, as compared with CPLEX, which cannot solve instances of 100 jobs.
We further investigate the influence of machine flexibility by computational experiments. Our results show that limited machine flexibility is sufficient in most situations
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