Theory and Methodology Machine scheduling with a rate-modifying activity q C.-Y. Lee a, * , V.J. Leon b a Department of Industrial Engineering, Texas A&M University, College Station, TX 77843-3131, USA b Department of Engineering Technology & Industrial Distribution and Department of Industrial Engineering, Texas A&M University, College Station, TX 77843-3131, USA Received 1 February 1998; accepted 1 January 1999 Abstract Motivated by a problem commonly found in electronic assembly lines, this paper deals with the problem of scheduling jobs and a rate-modifying activity on a single machine. A rate-modifying activity is an activity that changes the production rate of the equipment under consideration. Hence the processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. The decisions under consideration are when to schedule the rate-modifying activity and the sequence of jobs to optimize some performance measure. In this paper, we develop polynomial algorithms for solving problems of minimizing makespan, and total completion time respectively. We also develop pseudo-polynomial algorithms for solving problems of total weighted completion time under the agreeable ratio assumption. We prove that the problem of minimizing maximum lateness is NP-hard and also provide a pseudo-polynomial time algorithm to solve it optimally. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Machine scheduling; Job scheduling; Rate-modifying activity; Polynomial algorithms; Performance measure 1. Introduction This paper deals with the problem of scheduling jobs and a rate-modifying activity on a single machine. A rate-modifying activity is an activity that changes the production rate of the equipment under consideration. For instance, it may be nec- essary to stop processing of jobs for a period of time to bring a machine from a sub-nominal pro- duction rate to a nominal one. In this example, a job will take longer to process if scheduled before the rate-modifying activity than after it. In this paper it is assumed that no job processing can occur while the rate-modifying activity takes place. The decisions under consideration are when to schedule the rate-modifying activity and the se- quence of jobs to optimize some regular perfor- mance measure. This work is motivated by a problem com- monly found in electronic assembly lines where European Journal of Operational Research 128 (2001) 119±128 www.elsevier.com/locate/dsw * Corresponding author. Tel.: +1 409 862 7795; fax: +1 409 847 9005; e-mail: cylee@acs.tamu.edu q This research was supported in part by NSF Grant DMI- 9610229, and the US Army Contract DAAB07-95-C-D321. 0377-2217/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 9 9 ) 0 0 0 6 6 - 1