Approximation algorithms for problems in scheduling with set-ups

• Published in: Discrete Applied Mathematics Vol. 156; no. 5; pp. 719 - 729
• Main Authors: Divakaran, Srikrishnan, Saks, Michael
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.03.2008; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Analysis of algorithms; Applied sciences; Approximation algorithms; Approximations and expansions; Batch scheduling; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Computer systems performance. Reliability; Exact sciences and technology; Mathematical analysis; Mathematics; Operations research; Scheduling with set-ups; Sciences and techniques of general use; Software; Theoretical computing; Approximation algorithms; Operations research; Analysis of algorithms; Batch scheduling; Scheduling with set-ups; Availability; Computer theory; Polynomial approximation; Scheduling; Approximation algorithm; Precedence constraint; Due date; Optimization; Polynomial time; Input; Maximum; Completion; Schedule; Independent set; Combinatorics; Performance; Algorithm analysis; Single machine
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2007.08.010

In this paper, we present new approximation results for the offline problem of single machine scheduling with sequence-independent set-ups and item availability, where the jobs to be scheduled are independent (i.e., have no precedence constraints) and have a common release time. We present polynomial-time approximation algorithms for two versions of this problem. In the first version, the input includes a weight for each job, and the goal is to minimize the total weighted completion time. On any input, our algorithm produces a schedule whose total weighted completion time is within a factor 2 of optimal for that input. In the second version, the input includes a due date for each job, and the goal is to minimize the maximum lateness of any job. On any input, our algorithm produces a schedule with the following performance guarantee: the maximum lateness of a job is at most the maximum lateness of the optimal schedule on a machine that runs at half the speed of our machine.