Computers & Operations Research 33 (2006) 2099 – 2112 www.elsevier.com/locate/cor Single-machine group scheduling with a time-dependent learning effect Wen-Hung Kuo a , Dar-Li Yang b, ∗ a Department of Industrial Engineering and Technology Management, Da-Yeh University, Chang-Hwa, Taiwan 515, ROC b Department of Information Management, National Formosa University,Yun-Lin,Taiwan 632, ROC Available online 7 January 2005 Abstract In many realistic situations, the more time you practice, the better learning effect you obtain. Thus, we propose a time-dependent learning effect and introduce it into the single-machine group scheduling problems. The two objectives of scheduling problems are to minimize the makespan and the total completion time, respectively.We also provide two polynomial time algorithms to solve these problems.  2004 Elsevier Ltd. All rights reserved. Keywords: Group scheduling; Time-dependent; Learning effect 1. Introduction In classical scheduling problems, the processing times of jobs are assumed to be constant values. However, this assumption is not appropriate for the modeling of many modern industrial processes where very often a job, executed in the same or almost the same conditions, has a varied processing time. For example, a worker has to assemble a large number of similar products. The processing time for the worker to assemble one product depends on his knowledge, skills, organization of the working place, and other aspects. With repetition the worker learns how to produce the product more efficiently. Consequently, he is better skilled, his knowledge has increased, and the working place is better organized. As a result, the processing time for the worker to assemble one product decreases. This phenomenon is known as the “learning effect” in the literature. The learning effect was first applied to the industry more than 60 years ∗ Corresponding author. Tel.: +886 5 631 5004; fax: +886 5 633 8302. E-mail addresses: whkuo@mail.dyu.edu.tw (W.-H. Kuo), dlyang@nfu.edu.tw (D.-L. Yang). 0305-0548/$ - see front matter  2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2004.11.024