Group Scheduling Problems with Time-Dependent and Position-Dependent DeJong’s Learning Effect

Abstract

In this paper, we introduce a group scheduling model with time-dependent and position-dependent DeJong's learning effect. e objectives of scheduling problems are to minimize makespan, the total completion time, and the total weighted completion time, respectively. We show that the problems remain solvable in polynomial time under the proposed model.Example 2. As seen in Example 1, we change the objective to the total completion time minimization. By Algorithm 2, we solve the problem as follows:Step 1: In group G 1 , the optimal job sequence is J 11 ⟶ J 12 . In group G 2 , the optimal job sequence is J 23 ⟶ J 22 ⟶ J 21 .Step 2: To groups G 1 and G 2 , calculate

Single-Machine Group Scheduling Model with Position-Dependent and Job-Dependent DeJong’s Learning Effect

“…The group order was related to the objective functions. Sun et al [18] considered a single-machine scheduling problem. A learning effect similar to DeJong's learning effect was based on the sum of previous processing times and positions.…”

Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

“…There are a few models that take into account that job processing times may be affected simultaneously by factors of different kind. For example, a number of models in which time-dependent job deterioration and DeJong's learning effect are mixed were analyzed by Zhang et al (2018) and Sun et al (2020). We refer the reader to Agnetis et al (2014), Strusevich and Rustogi (2017), Azzouz et al (2017), andGawiejnowicz (2020) for more details on different scheduling models of the kind discussed in this section.…”

Group Scheduling with Learning Effect and Random Processing Time

“…Yang and Chand [31] constructed three basic models: there is no forgetting, partial forgetting, and total forgetting in job processing, and the processing time of jobs is related to the location. e authors in [32][33][34][35] continue to study this problem and obtain many important results.…”