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Department of Electrical Engineering and Information Technology

Scheduling Problems and Solutions

About the lecture

The following topics will be discussed:

  • Introduction to the lecture and the topic
    1. Organization
    2. Scheduling Language
    3. Classes of Schedules
    4. Complexity
  • Single machine environment
    1. Makespan and total weighted completion time
    2. Lateness and tardiness jobs
    3. Total tardiness and total earliness and tardiness
    4. Online problems
    5. Bicriterial problems
  • Parallel machine environments
    1. Makespan
    2. Total weighted completion time and lateness
    3. Online problems
  • Store systems
    1. Flow store
    2. Job store and open store

Note: For students of computer science this module takes place under the title "Schedulingprobleme - Algorithmen und Anwendungen". For more details, see the Event Dates section.



The lecture will be held in English.

Lecturer: Prof. Dr.-Ing. Uwe Schwiegelshohn


  • Tuesday, 10.15 - 12.00, BCI ZB-E04, starting 09.04.2024
  • Wednesday, 10.15 - 12.00 a.m., BCI HS-ZE02, starting 10.04.2024


Lecturer: Samin Jamalabadi

Date: Thursday, 10.15 - 12.00, BCI ZB-E04, starting 18.04.2024

Classroom Exercises: To support the exercise content, presence exercise sheets will be distributed irregularly, which are to be prepared by the participants and solved together in the exercise.


Lecturer: Samin Jamalabadi

Date: to be announced, practical course on three dates in the semester.

Each student should have a Retina account(information on Retina accounts).

Organizational notes

Current information in connection with the lecture, exercise and examinations (dates) are published exclusively via Moodle. Furthermore, the Moodle workspace with its various communication possibilities (chat, mailing lists, forum, etc.) is used for collaborative work within the lecture.

Interested students please register in the LSF. Only participants who have registered in the LSF will be automatically transferred from the LSF to the Moodle workspace. For further announcements in the context of the lecture and the exercise, Moodle will be used exclusively.

For the subject "Scheduling Problems and Solutions", students must complete the following examinations:

  • Successful completion of the practical course (not for students of computer science).
  • Successful participation in the oral examination
  • Event numbers:
    • Lecture: 08 0385
    • Exercise: 08 0386
    • Practical course: 08 0387
  • 3rd semester in Master ET/IT and A&R
    • Extent SWS: 4 V, 2 Ü, 1 P
    • Credits: 10
    • Module 2-16, ETIT-235 resp. AR-202
  • 2nd / 3rd semester in Master's programs in Computer Science
    • Title: Schedulingprobleme - Algorithmen und Anwendungen
    • Extent SWS: 3 V, 1 Ü
    • Credits: 6
    • Module INF-MSc-612
    • For students of computer science the participation in the practical course is optional. They are also allowed to choose one of the topics Parallel Machines and Shop Problems, while the topic Single Machines is mandatory.

The lecture is largely based on:

Michael Pinedo (New York University), "Scheduling Theory, Algorithms, and Systems," Springer 4th edition 2012, ISBN 1461419867.

Further Reading:

This is a list of publications that describe solutions to problems covered in the lecture. These publications are recommended if you are interested in additional information on these problems and their solutions. They are not required for the exam.

The publications are arranged by date of publication.

  • U. Schwiegelshohn, "An alternative proof of the Kawaguchi-Kyan bound for the Largest-Ratio-First rule," Operations Research Letters, 39(4):255-259, 2011.
  • P. Liu and X. Lu, "On-line scheduling of parallel machines to minimize total completion times," Computers & Operations Research, 36:2647-2652, 2009.
  • S. Leonardi and D. Raz, "Approximating total flow time on parallelmachines," Journal of Computer and System Sciences, 73(6):875-891,2007.
  • E.J. Anderson and C.N. Potts, "Online scheduling of a single machine to minimize total weighted completion time," Mathematics of Operations Research, 29(3):686-697, 2004.
  • J. F. Rudin III and R. Chandrasekaran, "Improved bound for the online scheduling problem," SIAM Journal on Computing, 32:717-735, 2003.
  • M. Goldwasser, "Patience is a virtue: The effect of slack on the competitiveness for admission control," Journal of Scheduling, 6:193-211, 2003.
  • L. Epstein and R. van Stee, "Lower bounds for on-line single-machine scheduling," Theoretical Computer Science, 299:439-450, 2003.
  • R. van Stee and H.L. Poutre, "Minimizing the total completion time on-line on a single machine, using restarts," Proceedings of the European Symposium of Algorithms, Springer, LNCS 2461, 872-883, 2002.
  • A.S. Schulz and M. Skutella, "The power of a-points in preemptive single machine scheduling," Journal of Scheduling, 5:121-133, 2002.
  • B. DasGupta and M. Palis, "Online real-time preemptive scheduling of jobs with deadlines on multiple machines," Journal of Scheduling, 4:297-312, 2001.
  • P. Berman, M. Charikar, and M. Karpinski, "On-line load balancing for related machines," Journal of Algorithms, 35:108-121, 2000.
  • S. Albers, "Better bounds for online scheduling," SIAM Journal on Computing, 29:459-473. 1999.
  • H. Hoogeveen and A.P.A. Vestjens, "Optimal on-line algorithms for single-machine scheduling," in 5th International Integer Programming and Combinatorial Optimization Conference, LNCS 1084:404-414. Springer, 1996.
  • D. B. Shmoys, J. Wein, D.P. Williamson, "Scheduling Parallel Machines On-line," SIAM Journal on Computing, 24(6):1313-1331, 1995.
  • J. Du, J.Y.-T. Leung, and G.H. Young, "Scheduling Chain-Structured Tasks to Minimize Makespan and Mean Flow Time," Information and Computation 92:219-236, 1991.
  • K.R. Baker and G.D. Scudder, "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, 38:22-36, 1990.
  • E.L. Lawler, "A dynamic programming algorithm for preemptive scheduling of a single machine to minmize the number of late jobs," Annals of Operations Research, 26:125-133,1990.
  • U Faigle, W. Kern, and G. Turan, "On the performance of on-line algorithms for particular problems," Acta Cybernetica, 9:107-119, 1989.
  • T. Kawaguchi and S. Kyan, "Worst case bound of an LRF schedule for the meanweighted flow-time problem," SIAM Journal of Computing, 15(4):1119-1129, 1986.
  • J.K. Lenstra and A.H.G. Rinnooy Khan, "Scheduling chains on a single machine," European Journal of Operation Research, 4:270-275, 1980.
  • M.R. Garey and D.S. Johnson, "Computers and Intractability," W. H. Freeman, 1979.
  • E.L. Lawler and J. Labetoulle, "On preemptive scheduling of unrelated parallel processors by linear programming," Journal of the Assoc. Comput. Mach. magazine, 25(4), 612-619, 1978.
  • M.R. Garey and D.S. Johnson, "Strong NP-completeness results: motivation, examples, and implications," Journal of the Assoc. Comput. Mach. magazine, 25(3):499-508, 1978.
  • E.L. Lawler, "Sequencing jobs to minimize total weighted completion time subject to precedence constraints," Annals of Discrete Mathematics, 2:75-90,1978
  • J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker, "Complexity of machine scheduling problems" Annals of Discrete Mathematics, 1:343-362, 1977.
  • J.D. Ullman, "NP-Complete Scheduling Problems," Journal of Computer and System Sciences, 10:384-393, 1975.
  • J. Bruno, E.G. Coffman Jr, and R. Sethi, "Scheduling Independent Tasks To Reduce Mean Finishing Time," Communications of the Assoc. Comput. Mach, 17(7): 387-382, 1974.
  • E.G. Coffman Jr. and R. L. Graham, "Optimal Scheduling for Two-processor Systems," Acta Informatica, 1(3):200-213, 1971.
  • E.L.Lawler and J.M. Moore, "A Functional Equation and Its Application to Resource Allocation and Sequencing Problems," Management Science, 16:77-89, 1969.