Annals of Operations Research

, Volume 102, Issue 1, pp 237–261

Four Payment Models for the Multi-Mode Resource Constrained Project Scheduling Problem with Discounted Cash Flows

  • Gündüz Ulusoy
  • Funda Sivrikaya-Şerifoğlu
  • Şule Şahin

DOI: 10.1023/A:1010914417817

Cite this article as:
Ulusoy, G., Sivrikaya-Şerifoğlu, F. & Şahin, Ş. Annals of Operations Research (2001) 102: 237. doi:10.1023/A:1010914417817


In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and out-flows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it.

project scheduling resource constraints discounted cash flow payment models 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Gündüz Ulusoy
    • 1
  • Funda Sivrikaya-Şerifoğlu
    • 2
  • Şule Şahin
    • 3
  1. 1.Manufacturing Systems Engineering, Faculty of Engineering and Natural SciencesSabancı UniversityIstanbulTurkey
  2. 2.Abant İzzet Baysal University Management SchoolBoluTurkey
  3. 3.Department of Industrial EngineeringBoğaziçi UniversityIstanbulTurkey

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