Single facility scheduling with nonlinear processing times
Computers and Industrial Engineering
Scheduling deteriorating jobs on a single processor
Operations Research
V-shaped policies for scheduling deteriorating jobs
Operations Research
Scheduling jobs under simple linear deterioration
Computers and Operations Research
Parallel machine scheduling with time dependent processing times
Discrete Applied Mathematics
The complexity of scheduling starting time dependent tasks with release times
Information Processing Letters
Online computation and competitive analysis
Online computation and competitive analysis
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling linear deteriorating jobs with an availability constraint on a single machine
Theoretical Computer Science
Scheduling deteriorating jobs on a single machine with release times
Computers and Industrial Engineering
Time-Dependent Scheduling
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Preemptive scheduling with simple linear deterioration on a single machine
Theoretical Computer Science
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Traditional scheduling assumes that the processing time of a job is fixed. Yet there are numerous situations that the processing time increases (deteriorates) as the start time increases. Examples include scheduling cleaning or maintenance, fire fighting, steel production and financial management. Scheduling of deteriorating jobs was first introduced on a single machine by Browne and Yechiali, and Gupta and Gupta independently. In particular, lots of work has been devoted to jobs with linear deterioration. The processing time p j of job J j is a linear function of its start time s j , precisely, p j =a j +b j s j , where a j is the normal or basic processing time and b j is the deteriorating rate. The objective is to minimize the makespan of the schedule. We first consider simple linear deterioration, i.e., p j =b j s j . It has been shown that on m parallel machines, in the online-list model, LS (List Scheduling) is $(1+b_{\rm max})^{1-\frac{1}{m}}$ -competitive. We extend the study to the online-time model where each job is associated with a release time. We show that for two machines, no deterministic online algorithm is better than (1+b max )-competitive, implying that the problem is more difficult in the online-time model than in the online-list model. We also show that LS is $(1+b_{\rm max})^{2(1-\frac{1}{m})}$ -competitive, meaning that it is optimal when m =2.