Approximation algorithms for problems in scheduling with set-ups

Abstract

In this paper, we present new approximation results for the offline problem of single machine scheduling with sequenceindependent 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.

On Competitive Analysis for Polling Systems

“…The results look worse than competitive ratio 2, however here we use SRPT as the benchmark, which means the actual competitive ratio could be smaller than θ + 1. The work [12] does not show the tightness of algorithms. Before presents a mixed strategy in Section 4, we next present algorithms for the offline algorithm.…”

“…We know the clearing problem with fixed number of queues is polynomial time solvable [35,18]. The problem with dynamic number of queues is solvable using a 2-approximating algorithm provided in [12]. However here we say that if p min > 0 and τ is bounded, simple algorithms exist for the clearing problem and their competitive ratios are proved to be tight and optimal.…”

Approximating Weighted Completion Time for Order Scheduling with Setup Times

“…This special case requires that the jobs can be renamed so that job j i+1 contains, for each operation o ∈ j i , an operation o such that f (o) = f (o ) and p(o ) > p(o). A related positive result is due to Divakaran and Saks [8]. They designed a 2-approximation algorithm for our problem in case all jobs consist of a single operation.…”

An Online Algorithm for a Problem in Scheduling with Set-ups and Release Times

“…A brief summary of this work is contained in [9], more details can be found in [2,18] and [3]. Here we focus only on work related to the maximum flow time criterion.…”

“…If J is GREEN then the optimal schedule is: [2,4] and G 1 during [4,5] • R 1 during [5,8] and R 2 during [8,9] • For even j ∈ [1, L), G j during [4j + 1, 4j…”