Bicriterion scheduling with truncated learning effects and convex controllable processing times

Abstract

This paper investigates single-machine scheduling in which the processing time of a job is a function of its position in a sequence, a truncation parameter, and its resource allocation. For a convex resource consumption function, we provide a bicriteria analysis where the first is to minimize total weighted flow (completion) time, and the second is to minimize total resource consumption cost. If the weights are positional-dependent weights, we prove that three versions of considering the two criteria can be solved in polynomial time, respectively. If the weights are job-dependent weights, the computational complexity of the three versions of the two criteria remains an open question. To solve the problems with job-dependent weights, we present a heuristic (an upper bound) and a branch-and-bound algorithm (an exact solution).

Study on Single-Machine Group Scheduling with Due-Window Assignment and Position-Dependent Weights

“…A future extension is to the group scheduling in the flowshop, parallel machines setting, or two-stage assembly flowshop. Other future research may study extending the group scheduling to scenario-dependent processing times (Wu et al [34][35][36]) or variable processing times (Wang et al [37,38]).…”

A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

“…Recently, there has been increasing attention to scheduling problems involving both controllable processing times and learning effects (see [15,19,20,34,35]). Yin and Wang [39] considered single machine scheduling problem with controllable processing times and learning effects, i.e., the actual processing time P j of job J j in position r is P j (x j , r) = (p j −x j )r a , where p j is normal processing time of J j , x j is compression of the processing time of job J j , 0 ≤ x j ≤ m j , m j is maximum reduction in processing time of job J j , and a ≤ 0 is a learning effect.…”

Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

“…e actual processing time of a job is affected by the sum-of-actual processing times of previous jobs and by a job-dependent truncation parameter. More recent papers considered deteriorating jobs: Li et al [11], Liang et al [12], Gawiejnowicz and Kurc [13], and Wang et al [14].…”