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Multimode Resource-Constrained Project Scheduling Problem Including Multiskill Labor (MRCPSP-MS) Model and a Solution Method

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Essays in Production, Project Planning and Scheduling

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 200))

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Abstract

The problem that we address in this chapter is an extension of the resource-constrained project scheduling problem (RCPSP). It belongs to the class of project scheduling problems with multilevel (or multimode) activities that permit an activity to be processed by resources operating at appropriate modes where each mode belongs to a different resource level and incurs different cost and duration. Each activity must be allocated exactly one unit of each required resource, and the resource unit may be used at any of its specified levels. The processing time of an activity is given by the maximum of the durations that would result from different resources allocated to that activity. The objective is to find an optimal solution that minimizes the overall project cost, given a delivery date. A penalty is incurred for tardiness beyond the specified delivery date, or a bonus is accrued for early completion. We present a mathematical programming formulation as an accurate problem definition. A filtered beam search (FBS)-based method is used to solve the problem. It was implemented using the C# language. Results of our experimentations on the use of this method are also presented.

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References

  • Arroub, M., Kadrou, Y., & Najid, N. (2010). An efficient algorithm for the multi-mode resource constrained project scheduling problem with resource flexibility. International Journal of Mathematics in Operational Research, 2(6), 748–761.

    Google Scholar 

  • Bandelloni, M., Tucci, M., & Rinaldi, R. (1994). Optimal resource leveling using non-serial dynamic programming. European Journal of Operational Research, 78(2), 162–177.

    Google Scholar 

  • Basnet, C., Tang, G., & Yamaguchi, T. (2001). A beam search heuristic for multi-mode single resource constrained project scheduling. In proceedings of 36th Annual Conference of the Operational Research Society of New Zealand, Christchurch, NZ, Nov-Dec, 1–8

    Google Scholar 

  • Bellman, R., & Dreyfus, S. (1959). Functional approximations and dynamic programming. Mathematical Tables and Other Aids to Computation, 13, 247–251.

    Google Scholar 

  • Berthold, T., Heinz, S., Lübbecke, M. E., Möhring, R. H., & Schulz, J. (2010). A constraint integer programming approach for resource-constrained project scheduling. In proceedings of CPAIOR 2010, LNCS, June, Andrea Lodi, Michela Milano, Paolo Toth (Eds.), Springer, 6140, pp. 51–55.

    Google Scholar 

  • Blazewicz, J., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1983). Scheduling subject to resource constraints: Classification and complexity. Discrete Applied Mathematics, 5(1), 11–24.

    Google Scholar 

  • Boctor, F. F. (1990). Some efficient multi-heuristic procedures for resource constrained project scheduling. European Journal of Operational Research, 49, 3–13.

    Google Scholar 

  • Boctor, F. F. (1993). Heuristics for scheduling projects with resource restrictions and several resource-duration modes. International Journal of Production Research, 31, 2547–2558.

    Google Scholar 

  • Clark, C. E. (1962). The PERT model for the distribution of an activity time. Operations Research, 10(3), 405–406.

    Google Scholar 

  • Davis, E. W. (1966). Resource allocation in project network models—A survey. Journal of Industrial Engineering, 17(4), 177–188.

    Google Scholar 

  • Dean, B. V., Denzler, D. R., & Watkins, J. J. (1992). Multiproject staff scheduling with variable resource constraints. IEEE Transactions on Engineering Management, 39, 59–72.

    Google Scholar 

  • Demeulemeester, E. L., & Herroelen, W. S. (1996). An efficient optimal solution procedure for the preemptive resource-constrained scheduling problem. European Journal of Operational Research, 90, 334–348.

    Google Scholar 

  • Dodin, B. M., & Elmaghraby, S. E. (1985). Approximating the criticality indices in the activities in PERT networks. Management Science, 31, 207–223.

    Google Scholar 

  • Elmaghraby, S. E. (1992). Resource allocation via dynamic programming in activity networks. European Journal of Operational Research, 88, 50–86.

    Google Scholar 

  • Elmaghraby, S. E., & Herroelen, W. S. (1980). On the measurement of complexity in activity networks. European Journal of Operational Research, 5(4), 223–234.

    Google Scholar 

  • Elmaghraby, S. E., & Herroelen, W. S. (1990). The scheduling of activities to maximize the net present value of projects. European Journal of Operational Research, 49, 35–40.

    Google Scholar 

  • Etgar, R., Shtub, A., & LeBlanc, L. J. (1997). Scheduling projects to maximize net present value—The case of time-dependent, contingent cash flows. European Journal of Operational Research, 96, 90–96.

    Google Scholar 

  • Gonçalves, J. F., Mendes, J. J. M., & Resende, M. G. C. (2004). A genetic algorithm for the resource constrained multi-project scheduling problem. Technical ReportTD-668LM4, AT&T Labs Research

    Google Scholar 

  • Guldemond, T., Hurink, J., Paulus, J., & Schutten, J. (2008). Time-constrained project scheduling. Journal of Scheduling, 11(2), 137–148.

    Google Scholar 

  • Hartmann, S. (2001). Project scheduling with multiple modes: A genetic algorithm. Annals of Operational Research, 102, 111–135.

    Google Scholar 

  • Heilmann, R. (2000). Resource-constrained project scheduling: A heuristic for the multi-mode case. OR Spektrum, 23, 335–357.

    Google Scholar 

  • Herroelen, W. (2006). Project scheduling-theory and practice. Production and Operations Management, 14(4), 413–432.

    Google Scholar 

  • Kazaz, B., & Sepil, C. (1996). Project scheduling with discounted cash flows and progress payments. Journal of the Operational Research Society, 47, 1262–1272.

    Google Scholar 

  • Kelley, J. E., & Walker, M. R. (1959). Critical path planning and scheduling. In proceedings of Eastern Joint Computer Conference, Boston, December 1-3, 1959, NY 1960, pp. 160–173

    Google Scholar 

  • Kis, T. (2005). A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Mathematical Programming, 103(3), 515–539.

    Google Scholar 

  • MacCrimmon, K. R., & Ryavec, C. A. (1964). An analytical study of the PERT assumptions. Operations Research, 12(1), 16–37.

    Google Scholar 

  • Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.

    Google Scholar 

  • Mika, M., Waligora, G., & Weglarz, G. (2005). Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models. European Journal of Operational Research, 164(3), 639–668.

    Google Scholar 

  • Nemhauser, G. L., & Wolsey, L. A. (1988). Integer and combinatorial optimization. Wiley-Interscience, Hoboken, NJ, USA

    Google Scholar 

  • Ozdamar, L., & Ulusoy, G. (1995). A survey on the resource-constrained project scheduling problem. IIE Transactions, 27, 574–586.

    Google Scholar 

  • Padman, R., & Dayanand, N. (1997). On modelling payments in projects. Journal of the Operational Research Society, 48, 906–918.

    Google Scholar 

  • Patterson, J. H., Slowinski, R., Talbot, F. B., & Weglarz, J. (1989). An algorithm for a general class of precedence and resource constrained scheduling problems. In R. Slowinski & J. Weglarz (Eds.), Advances in project scheduling (pp. 3–28). Amsterdam: Elsevier.

    Google Scholar 

  • Patterson, J. H., Slowinski, R., Talbot, F. B., & Weglarz, J. (1990). Computational experience with a backtracking algorithm for solving a general class of precedence and resource constrained scheduling problems. European Journal of Operational Research, 49, 68–67.

    Google Scholar 

  • Pritsker, A., Watters, L., & Wolfe, P. (1969). Multi-project scheduling with limited resources: A zero-one programming approach. Management Science, 16, 93–108.

    Google Scholar 

  • Ragsdale, C. (1989). The current state of network simulation in project management theory and practice. Omega: The International Journal of Management Science, 17, 21–25.

    Google Scholar 

  • Ramachandra, G., & Elmaghraby, S. E. (2006). Sequencing precedence-related jobs on two machines to minimize the weighted completion time. International Journal of Production Economics, 100(1), 44–58.

    Google Scholar 

  • Santos, M. A., & Tereso, A. P. (2010). On the multi-mode, multi-skill resource constraint project scheduling problem (MRCPSP-MS). In proceedings of 2nd International Conference on Engineering Optimization (EngOpt 2010), Lisbon, Portugal, September 6–9

    Google Scholar 

  • Santos, M. A., & Tereso, A. P. (2011a). On the multi-mode, multi-skill resource constrained project scheduling problem—computational results. In proceedings of ICOPEV—International Conference on Project Economic Evaluation, Guimarães, Portugal, April 28–29

    Google Scholar 

  • Santos, M. A., & Tereso, A. P. (2011b). On the multi-mode, multi-skill resource constrained project scheduling problem—A software application. In A. GasparCunha, R. Takahashi, G. Schaefer, & L. Costa (Eds.), Soft Computing in Industrial Applications, 96, 239–248

    Google Scholar 

  • Sepil, C., & Ortaç, N. (1997). Performance of the heuristic procedures for constrained projects with progress payments. Journal of the Operational Research Society, 48, 1123–1130.

    Google Scholar 

  • Tereso, A.P., Araújo, M.M., Elmaghraby, S.E. (2004). Adaptive resource allocation in multimodal activity networks. International Journal of Production Economics, 92, 1–10.

    Google Scholar 

  • Tereso, A.P., Mota, J.R., Lameiro, R.J. (2006). Adaptive resource allocation technique to stochastic multimodal projects: A distributed platform implementation in JAVA. Control Cybern, 35, 661–686.

    Google Scholar 

  • Tseng, C. (2008). Two heuristic algorithms for a multi-mode resource-constrained multi-project scheduling problem. Journal of Science and Engineering Technology, 4(2), 63–74.

    Google Scholar 

  • Ulusoy, G., & Cebelli, S. (2000). An equitable approach to the payment scheduling problem in project management. European Journal of Operational Research, 127, 262–278.

    Google Scholar 

  • Vanhoucke, M., Demeulemeester, E., & Herroelen, W. (2000). An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem. Annals of Operations Research, 102, 179–196.

    Google Scholar 

  • Willis, R. J. (1985). Critical path analysis and resource constrained project scheduling theory and practice. European Journal of Operational Research, 21, 149–155.

    Google Scholar 

  • Zhang, H., Li, H., & Tarn, C. M. (2006). Heuristic scheduling of resource-constrained, multiple-mode and repetitive projects. Construction Management and Economics, 24, 159–169.

    Google Scholar 

  • Zimmermann, J., & Engelhardt, H. (1998). Lower bounds and exact algorithms for resource levelling problems. Technical Report WIOR-517, University of Karlsruhe

    Google Scholar 

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Authors and Affiliations

  1. University of Minho, 4710–057, Braga, Portugal

    Mónica A. Santos & Anabela P. Tereso

Authors
  1. Mónica A. Santos
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  2. Anabela P. Tereso
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Correspondence to Mónica A. Santos .

Editor information

Editors and Affiliations

  1. College of Engineering, The University of Oklahoma, Norman, Oklahoma, USA

    P. Simin Pulat

  2. Dept of Industrial & Systems Engineering, Virginia Tech, Blacksburg, Virginia, USA

    Subhash C. Sarin

  3. Dept of Industrial & Systems Engineering, North Carolina State University, Raleigh, North Carolina, USA

    Reha Uzsoy

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Santos, M., Tereso, A. (2014). Multimode Resource-Constrained Project Scheduling Problem Including Multiskill Labor (MRCPSP-MS) Model and a Solution Method. In: Pulat, P., Sarin, S., Uzsoy, R. (eds) Essays in Production, Project Planning and Scheduling. International Series in Operations Research & Management Science, vol 200. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9056-2_11

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