IDEAS home Printed from https://ideas.repec.org/a/wly/navlog/v19y1972i1p123-136.html
   My bibliography  Save this article

The payment scheduling problem

Author

Listed:
  • Richard C. Grinold

Abstract

Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.

Suggested Citation

  • Richard C. Grinold, 1972. "The payment scheduling problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(1), pages 123-136, March.
    • Handle: RePEc:wly:navlog:v:19:y:1972:i:1:p:123-136
    DOI: 10.1002/nav.3800190110
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.3800190110
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.3800190110?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. S. Selcuk Erenguc & Suleyman Tufekci & Christopher J. Zappe, 1993. "Solving time/cost trade‐off problems with discounted cash flows using generalized benders decomposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 25-50, February.
    2. Peymankar, Mahboobeh & Davari, Morteza & Ranjbar, Mohammad, 2021. "Maximizing the expected net present value in a project with uncertain cash flows," European Journal of Operational Research, Elsevier, vol. 294(2), pages 442-452.
    3. Thomas Schmitt & Bruce Faaland, 2004. "Scheduling recurrent construction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1102-1128, December.
    4. Joseph G. Szmerekovsky & George L. Vairaktarakis, 2006. "Maximizing project cash availability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 272-284, June.
    5. Wenhui Zhao & Nicholas G. Hall & Zhixin Liu, 2020. "Project Evaluation and Selection with Task Failures," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 428-446, February.
    6. Hermans, Ben & Leus, Roel & Looy, Bart Van, 2023. "Deciding on scheduling, secrecy, and patenting during the new product development process: The relevance of project planning models," Omega, Elsevier, vol. 116(C).
    7. Nursel Kavlak & Gündüz Ulusoy & Funda Sivrikaya Şerifoğlu & Ş. İlker Birbil, 2009. "Client‐contractor bargaining on net present value in project scheduling with limited resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 93-112, March.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navlog:v:19:y:1972:i:1:p:123-136. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1931-9193 .

    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.