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Optimal project selection: Stochastic knapsack with finite time horizon

Author

Listed:
  • L L Lu

    (AT&T Laboratories)

  • S Y Chiu

    (GTE Laboratories)

  • L A Cox

    (Cox Associates)

Abstract

A time-constrained capital-budgeting problem arises when projects, which can contribute to achieving a desired target state before a specified deadline, arrive sequentially. We model such problems by treating projects as randomly arriving requests, each with a funding cost, a proposed benefit, and a known probability of success. The problem is to allocate a non-renewable initial budget to projects over time so as to maximise the expected benefit obtained by a certain time, T, called the deadline, where T can be either a constant or a random variable. Each project must be accepted or rejected as soon as it arrives. We developed a stochastic dynamic programming formulation and solution of this problem, showing that the optimal strategy is to dynamically determine ‘acceptance intervals’ such that a project of type i is accepted when, and only when, it arrives during an acceptance interval for projects of type i.

Suggested Citation

  • L L Lu & S Y Chiu & L A Cox, 1999. "Optimal project selection: Stochastic knapsack with finite time horizon," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(6), pages 645-650, June.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:6:d:10.1057_palgrave.jors.2600721
    DOI: 10.1057/palgrave.jors.2600721
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    Citations

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    Cited by:

    1. Jacko, Peter, 2009. "An index for dynamic product promotion and the knapsack problem for perishable items," DES - Working Papers. Statistics and Econometrics. WS ws093111, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    3. Alexander G. Nikolaev & Sheldon H. Jacobson, 2010. "Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs," Operations Research, INFORMS, vol. 58(4-part-1), pages 1023-1027, August.
    4. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    5. Chen, Kai & Ross, Sheldon M., 2014. "An adaptive stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(3), pages 625-635.
    6. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.

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