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A Branch and Cut Algorithm for Resource-Constrained Project Scheduling Problem Subject to Nonrenewable Resources with Pre-Scheduled Procurement

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Abstract

In the project scheduling literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is very common that these resources are procured along the project horizon according to some pre-scheduled plan. In this paper, we study an extended form of the resource-constrained project scheduling problem that is subject to this type of nonrenewable resources in addition to the renewable resources. In order to solve this problem, we propose a branch and cut algorithm. We incorporate with the algorithm some technics and fathoming rules to shorten the solving process. The algorithm is capable of specifying lower bounds for the problem in any middle stage of the solving process. The lower bounds can be useful to deal with large instances, for which the solving processes may be too long. We point out parameters affecting the degree of difficulty of the problem, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using our algorithm and also CPLEX solver. We analyze the algorithm behavior respect to the changes in instances degree of difficulties and compare its performances in different cases with the CPLEX solver.

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References

  1. Bottcher J. et al.: Project scheduling under partially renewable resource constraints. Manag. Sci. 45(4), 543–559 (1999)

    Article  Google Scholar 

  2. Bard J.F., Kontoravdis G., Yu G.: A branch-and-cut procedure for the vehicle routing problem with time windows. Trans. Sci. 36(2), 250–269 (2002)

    Article  MATH  Google Scholar 

  3. Zhu G., Bard J.F., Yu G.: A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem. INFORMS. J. Comput. 18(3), 377–400 (2006)

    Article  MATH  Google Scholar 

  4. Kis T.: A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Math. Program. 103(3), 515–539 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Carruthers J.A., Battersby A.: Advances in critical path methods. J. Oper. Res. Soc. 17, 359–380 (1966)

    Article  Google Scholar 

  6. Brucker P. et al.: Resource-constrained project scheduling: Notation, classification, models, and methods. Eur. J. Oper. Res. 112(1), 3–41 (1999)

    Article  MATH  Google Scholar 

  7. Boctor F.F.: Some efficient multi-heuristic procedures for resource-constrained project scheduling. Eur. J. Oper. Res. 49(1), 3–13 (1990)

    Article  Google Scholar 

  8. Cho J.H., Kim Y.D.: A simulated annealing algorithm for resource-constrained project scheduling problems. J. Oper. Res. Soc. 48, 736–744 (1997)

    Article  MATH  Google Scholar 

  9. Hartmann S., Kolisch R.: Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem. Eur. J. Oper. Res. 127(2), 394–407 (2000)

    Article  MATH  Google Scholar 

  10. Xiong, J. et al.: A two-stage preference-based evolutionary multi-objective approach for capability planning problems. Knowl.-Based Syst. 31, 128–139 (2012)

  11. Xiong, J. et al.: A knowledge-based evolutionary multi-objective approach for stochastic extended resource investment project scheduling problems (2013)

  12. Lova A. et al.: An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes. Int. J. Prod. Econ. 117(2), 302–316 (2009)

    Article  Google Scholar 

  13. Demeulemeester E., Herroelen W.: Project Scheduling a Research Handbook. Kluwer, New York (2002)

    MATH  Google Scholar 

  14. Schirmer A.: Project Scheduling with Scarce Resources. Verlag Dr. Kovac, Hamburg (2000)

    Google Scholar 

  15. Schirmer A., Drexl A.: Allocation of partially renewable resources: Concept, capabilities, and applications. Networks 37(1), 21–34 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Alvares-Valdes R. et al.: A scatter search algorithm for project scheduling under partially renewable resources. J. Heuristics 12(1-2), 95–113 (2006)

    Article  Google Scholar 

  17. Alvares-Valdes R. et al.: GRASP and path relinking for project scheduling under partially renewable resources. Eur. J. Oper. Res. 189(3), 1153–1170 (2008)

    Article  Google Scholar 

  18. Pritsker A.A.B., Watters L.J., Wolfe P.M.: Multiproject scheduling with limited resources: a zero-one programming approach. Manag. Sci. 16, 93–107 (1969)

    Article  Google Scholar 

  19. Lova A., Tormos P., Barber F.: Multi-mode resource constrained project scheduling: Scheduling schemes, priority rules and mode selection rules. Inteligencia Artif. 30, 69–96 (2006)

    Google Scholar 

  20. Carlier J., Pinson E.: An algorithm for solving the jobshop problem. Manag. Sci. 35, 164–176 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  21. Balas E.: Facets of the knapsack polytope. Math. Program. 8(1), 146–164 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hammer P.L., Johnson E.L., Peled U.N.: Facet of regular 0–1 polytopes. Math. Program. 8(1), 179–206 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wolsey L.: Faces for a linear inequality in 0–1 variables. Math. Program. 8(1), 165–178 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  24. Crowder H., Johnson E., Padberg M.W.: Solving large-scale 0-1 linear programming programs. Oper. Res. 31, 803–834 (1983)

    Article  MATH  Google Scholar 

  25. Glover F.: Surrogate constraints. Oper. Res. 16, 741–749 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  26. Glover F.: A multiple-dual algorithm for the zero-one integer programming problem. Oper. Res. 13, 879–919 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  27. Geoffrion, A.M.: Implicit Enumeration Using an Imbedded Linear Program. Rand Corporation (1967)

  28. Glover F., Sherali H.D., Lee Y.: Generating cuts from surrogate constraint analysis for zero-one and multiple choice programming. Comput. Optim. Appl. 8(2), 151–172 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  29. Yu G.: Min-max optimization of several classical discrete optimization problems. J. Opt. Theory. Appl. 98(1), 221–242 (1998)

    Article  MATH  Google Scholar 

  30. Balas E.: An additive algorithm for solving linear programs with zero-one variables. Oper. Res. 13, 517–546 (1965)

    Article  MathSciNet  Google Scholar 

  31. Zhu, G.; Bard, J.F.; Yu, G.: A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem. INFORMS J. Comput. 18(3), 377–390 (2006)

    Article  MATH  Google Scholar 

  32. PSPLIB—Project Scheduling Library. June 1, (2012); Available from: http://129.187.106.231/psplib

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Authors and Affiliations

  1. Industrial Engineering Department, Sharif University of Technology, Azadi St., Tehran, Iran

    Ali Shirzadeh Chaleshtarti & Shahram Shadrokh

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  1. Ali Shirzadeh Chaleshtarti
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  2. Shahram Shadrokh
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Correspondence to Ali Shirzadeh Chaleshtarti.

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Shirzadeh Chaleshtarti, A., Shadrokh, S. A Branch and Cut Algorithm for Resource-Constrained Project Scheduling Problem Subject to Nonrenewable Resources with Pre-Scheduled Procurement. Arab J Sci Eng 39, 8359–8369 (2014). https://doi.org/10.1007/s13369-014-1319-9

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  • DOI: https://doi.org/10.1007/s13369-014-1319-9

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