IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v129y2011i1p79-85.html
   My bibliography  Save this article

Due date assignment in repetitive projects

Author

Listed:
  • Azaron, Amir
  • Fynes, Brian
  • Modarres, Mohammad

Abstract

This paper is concerned with the study of the constant due-date assignment policy in repetitive projects, where the activity durations are exponentially distributed random variables. It is then extended to the case where activity durations follow generalized Erlang distributions. The main feature of this research over the classical PERT networks is that the projects are generated according to a renewal process and share the same facilities. Our approach is first to obtain the project completion time distribution, for each generated project, by constructing a proper continuous-time Markov chain, and then to compute the optimal constant lead time for each particular project. The repetitive projects are represented as proper networks of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. It is assumed that each project's end result has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order for a project's end result arrives. This constant value is the constant lead time that a project might expect between its starting and completion times. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per project. Finally, the results are verified by Monte Carlo simulation.

Suggested Citation

  • Azaron, Amir & Fynes, Brian & Modarres, Mohammad, 2011. "Due date assignment in repetitive projects," International Journal of Production Economics, Elsevier, vol. 129(1), pages 79-85, January.
    • Handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:79-85
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(10)00326-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Salah E. Elmaghraby, 1967. "On the Expected Duration of PERT Type Networks," Management Science, INFORMS, vol. 13(5), pages 299-306, January.
    2. Paul S. Adler & Avi Mandelbaum & Viên Nguyen & Elizabeth Schwerer, 1995. "From Project to Process Management: An Empirically-Based Framework for Analyzing Product Development Time," Management Science, INFORMS, vol. 41(3), pages 458-484, March.
    3. A. Charnes & W. W. Cooper & G. L. Thompson, 1964. "Critical Path Analyses Via Chance Constrained and Stochastic Programming," Operations Research, INFORMS, vol. 12(3), pages 460-470, June.
    4. Abraham Seidmann & Milton L. Smith, 1981. "Due Date Assignment for Production Systems," Management Science, INFORMS, vol. 27(5), pages 571-581, May.
    5. C. Perry & I. D. Greig, 1975. "Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis," Management Science, INFORMS, vol. 21(12), pages 1477-1480, August.
    6. J. J. Martin, 1965. "Distribution of the Time Through a Directed, Acyclic Network," Operations Research, INFORMS, vol. 13(1), pages 46-66, February.
    7. D. R. Fulkerson, 1962. "Expected Critical Path Lengths in PERT Networks," Operations Research, INFORMS, vol. 10(6), pages 808-817, December.
    8. John Dumond & Vincent A. Mabert, 1988. "Evaluating Project Scheduling and Due Date Assignment Procedures: An Experimental Analysis," Management Science, INFORMS, vol. 34(1), pages 101-118, January.
    9. Fatemi Ghomi, S. M. T. & Rabbani, M., 2003. "A new structural mechanism for reducibility of stochastic PERT networks," European Journal of Operational Research, Elsevier, vol. 145(2), pages 394-402, March.
    10. V. G. Kulkarni & V. G. Adlakha, 1986. "Markov and Markov-Regenerative pert Networks," Operations Research, INFORMS, vol. 34(5), pages 769-781, October.
    11. Schmidt, Craig W. & Grossmann, Ignacio E., 2000. "The exact overall time distribution of a project with uncertain task durations," European Journal of Operational Research, Elsevier, vol. 126(3), pages 614-636, November.
    12. Fatemi Ghomi, S. M. T. & Hashemin, S. S., 1999. "A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network," European Journal of Operational Research, Elsevier, vol. 114(3), pages 610-625, May.
    13. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Longest path analysis in networks of queues: Dynamic scheduling problems," European Journal of Operational Research, Elsevier, vol. 174(1), pages 132-149, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Group scheduling and due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 130(2), pages 230-235, April.
    2. Xingong, Zhang & Yong, Wang, 2015. "Single-machine scheduling CON/SLK due window assignment problems with sum-of-processed times based learning effect," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 628-635.
    3. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    4. Tanja Mlinar & Philippe Chevalier, 2016. "Pooling heterogeneous products for manufacturing environments," 4OR, Springer, vol. 14(2), pages 173-200, June.
    5. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 131(2), pages 747-751, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azaron, Amir & Fatemi Ghomi, S.M.T., 2008. "Lower bound for the mean project completion time in dynamic PERT networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 120-127, April.
    2. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    3. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    4. Davaadorjin Monhor, 2011. "A new probabilistic approach to the path criticality in stochastic PERT," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 615-633, December.
    5. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Longest path analysis in networks of queues: Dynamic scheduling problems," European Journal of Operational Research, Elsevier, vol. 174(1), pages 132-149, October.
    6. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Modelling complex assemblies as a queueing network for lead time control," European Journal of Operational Research, Elsevier, vol. 174(1), pages 150-168, October.
    7. Masoud Arjmand & Amir Abbas Najafi & Majid Ebrahimzadeh, 2020. "Evolutionary algorithms for multi-objective stochastic resource availability cost problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 935-985, September.
    8. Mahtab Afsari & Hesam Javadi Vasigh, 2016. "A Mathematical Modeling for Delivery Time in Dynamic PERT Networks," Modern Applied Science, Canadian Center of Science and Education, vol. 10(3), pages 214-214, March.
    9. Gary Mitchell, 2010. "On Calculating Activity Slack in Stochastic Project Networks," American Journal of Economics and Business Administration, Science Publications, vol. 2(1), pages 78-85, March.
    10. Tetsuo Iida, 2000. "Computing bounds on project duration distributions for stochastic PERT networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 559-580, October.
    11. Fatemi Ghomi, S. M. T. & Hashemin, S. S., 1999. "A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network," European Journal of Operational Research, Elsevier, vol. 114(3), pages 610-625, May.
    12. Hahn, Eugene David, 2008. "Mixture densities for project management activity times: A robust approach to PERT," European Journal of Operational Research, Elsevier, vol. 188(2), pages 450-459, July.
    13. Saeed Yaghoubi, 2015. "Due-date assignment for multi-server multi-stage assembly systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(7), pages 1246-1256, May.
    14. Elmaghraby, Salah E., 2000. "On criticality and sensitivity in activity networks," European Journal of Operational Research, Elsevier, vol. 127(2), pages 220-238, December.
    15. Fatemi Ghomi, S. M. T. & Rabbani, M., 2003. "A new structural mechanism for reducibility of stochastic PERT networks," European Journal of Operational Research, Elsevier, vol. 145(2), pages 394-402, March.
    16. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    17. Vaseghi, Forough & Martens, Annelies & Vanhoucke, Mario, 2024. "Analysis of the impact of corrective actions for stochastic project networks," European Journal of Operational Research, Elsevier, vol. 316(2), pages 503-518.
    18. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    19. R. Alan Bowman, 2003. "Sensitivity curves for effective project management," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 481-497, August.
    20. Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2007. "Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1186-1200, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:79-85. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.