Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work

Abstract

We consider the problem of scheduling n independent and simultaneously available jobs without preemption on a single machine, where the machine has a fixed maintenance activity. The objective is to find the optimal job sequence to minimize the total amount of late work, where the late work of a job is the amount of processing of the job that is performed after its due date. We first discuss the approximability of the problem. We then develop two pseudo‐polynomial dynamic programming algorithms and a fully polynomial‐time approximation scheme for the problem. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 172–183, 2016

Heuristic based genetic algorithms for the re-entrant total completion time flowshop scheduling with learning consideration

“…The numbers (1,2,3,4) in parenthesis in the Tables 1 and 2 show the overall process of computation of average rankings of AEPs for the four algorithms. Friedman test, and Iman and Davenport tests 47 Table 3 presents the family of hypotheses ordered by their p-values and the adjustments of α by Nemenyi's (α NM ), Holm's (α HM ) and Shaffer's static (α SH ) procedures.…”

“…However, as done in Section 3, we employ nonparametric statistical tests to check whether there exists any significant difference among the performances of the four GA-based algorithms for the large size of jobs. The numbers (1,2,3,4) in parenthesis in Tables 8 and 9 show the overall process of computation of average rankings of RPDs for the four GA-based algorithms. The four observed R j 's, computed in F =2.647.…”

“…Most of classical scheduling models consider that the job processing time is fixed and constant 1,2,3 . However, it is invalid in many practical situations.…”

Exact algorithms for single-machine scheduling problems with a variable maintenance

“…In particular, they showed that the algorithms found exact solutions based on the dispatching rules of the shortest processing time (SPT) and earliest due date (EDD) as categorized by Blackstone, Phillips, & Hogg (1982). More recently, Yin, Xu, Cheng, Wu, & Wang (2016) considered an SMSP with independent and simultaneously available jobs without preemption, where the machine has a fixed maintenance activity. The authors proposed two pseudo-polynomial dynamic programming algorithms and a fully polynomial-time approximation scheme to minimize the total amount of late work.…”

Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

“…This observation has been already used in the literature while constructing optimal algorithms for the late work criterion (cf., e.g., [13,15]). However, the polynomial approximation schemes have been proposed only for the late work criterion for the single machine problems (cf., [11,30,31]). They have not been studied for multiple machine problems with early/late work criteria yet.…”