In this paper, the parallel machine scheduling problem with DeJong's learning effect, is addressed. The objective function to be minimized is the makespan. This problem is proofed to be NP-Hard in the strong sense. This is the challenging theoretical side of the studied problem. Furthermore, several real-life situations in manufacturing and computer science are modeled using the current problem. Several algorithms intended to solve the studied problem within a reasonable computing time are proposed in literature. Among these algorithms the exact methods, which failed to solve the studied problem to optimality even for small size instances. In this paper several new heuristics and meta-heuristics are proposed. These heuristics are classified into three types. The first type is based on Longest Processing Time (LPT) rule. The innovation is the modification of the LPT rule in a way to cope efficiently with the learning effect concept, by randomizing the selection of the next scheduled job. The second type of heuristics, is taking advantage of an exact Branch and Bound algorithm, developed originally for the classical parallel machine scheduling problem. The contribution for this kind of heuristics is lying in the modification of the processing time values, according to a prefixed selected functions. The third type of methods is based in an adaptation of the Genetic Algorithm to the learning effect concept. This adaptation consists in enlarging the area of selection of the parameters values. To assess the performance and the efficiency of the proposed heuristics, a newly developed lower bound is proposed. This lower bound is based on a relaxation of the studied problem, which allows to obtain a minimum cost flow problem.

Finally, an extensive experimental study is conducted over a benchmark test problems. The obtained results provide strong evidence that the proposed procedures outperform the earlier existing ones.

在本文中，解决了具有 DeJong 学习效应的并行机调度问题。要最小化的目标函数是完工时间。这个问题在强烈的意义上被证明是 NP-Hard。这是所研究问题的具有挑战性的理论方面。此外，制造和计算机科学中的几个现实情况是使用当前问题建模的。文献中提出了几种旨在在合理的计算时间内解决所研究问题的算法。在这些算法中，精确的方法即使对于小规模的实例也无法将所研究的问题解决到最优。在本文中，提出了几种新的启发式和元启发式方法。这些启发式分为三种类型。第一种类型基于最长处理时间 ( LPT)） 规则。创新是LPT的修改通过随机选择下一个预定工作，以有效应对学习效果概念的方式进行规则。第二种启发式方法是利用精确的分支定界算法，该算法最初是为经典并行机调度问题开发的。根据带前缀的选定函数，这种启发式方法的贡献在于修改处理时间值。第三种方法基于遗传算法对学习效果概念的适应。这种适应包括扩大参数值的选择范围。为了评估所提出的启发式方法的性能和效率，提出了一个新开发的下界。该下限基于所研究问题的松弛，

最后，对基准测试问题进行了广泛的实验研究。获得的结果提供了强有力的证据，表明所提出的程序优于早期现有的程序。