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An exact algorithm for project scheduling with multiple modes. (English) Zbl 0885.90059
Summary: We consider an extension of the classical resource-constrained project scheduling problem (RCPSP), which covers discrete resource-resource and time-resource tradeoffs. As a result a project scheduler is permitted to identify several alternatives or modes of accomplishment for each activity of the project. The solution procedure to be presented is a considerable generalization of the branch-and-bound algorithm proposed by Demeulemeester and Herroelen, which is currently the most powerful method for optimally solving the RCPSP. More precisely, we extend their concept of delay alternatives by introducing mode alternatives. The basic enumeration scheme is enhanced by dominance rules which increase the performance of the algorithm. We then report on our computational results obtained from the comparison with the most rapid procedure reported in the literature.
MSC:
90B35Scheduling theory, deterministic
References:
[1]Bartusch M, Möhring RH, Radermacher, FJ (1988) Scheduling project networks with resource constraints and time windows. Ann Oper Res 16:201–240 · doi:10.1007/BF02283745
[2]Boctor FF (1993) Heuristics for scheduling projects with resource restrictions and several resource-duration modes. Int J Prod Res 31:2547–2558 · doi:10.1080/00207549308956882
[3]Brucker P, Schoo A, Thiele O (1996) A branch-and-bound algorithm for the resource-constrained project scheduling problem. Osnabrücker Schriften zur Mathematik, No. 178, University of Osnabrück, Germany
[4]Christofides N, Alvarez-Valdes R, Tamarit JM (1987) Project scheduling with resource constraints: A branch and bound approach. Eur J Oper Res 29:262–273 · Zbl 0614.90056 · doi:10.1016/0377-2217(87)90240-2
[5]Demeulemeester E (1992) Optimal algorithms for various classes of multiple resource-constrained project scheduling problems. PhD Dissertation, Katholieke Universiteit Leuven, Belgium
[6]Demeulemeester E, Herroelen W (1992) A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Manag Sci 38:1803–1818 · Zbl 0761.90059 · doi:10.1287/mnsc.38.12.1803
[7]Drexl A (1991) Scheduling of project networks by job assignment. Manag Sci 37:1590–1602 · Zbl 0729.91011 · doi:10.1287/mnsc.37.12.1590
[8]French S (1982) Sequencing and scheduling: An introduction to the mathematics of the job-shop. Wiley, New York
[9]Garey MR, Johnson DS (1979) Computers and intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA
[10]Hartmann S, Sprecher A (1996) A note on ”Hierarchical models for multi-project planning and scheduling”. Europ J Oper Res 94:377–383 · Zbl 0953.90518 · doi:10.1016/0377-2217(95)00158-1
[11]Kolisch R (1995) Project scheduling under resource constraints – Efficient heuristics for several problem classes. Physica, Heidelberg
[12]Kolisch R, Sprecher A, Drexl A (1995) Characterization and generation of a general class of resource-constrained project scheduling problems. Manag Sci 41, No. 11
[13]Mingozzi A, Maniezzo V, Ricciardelli S, Bianco L (1994) An exact algorithm for project scheduling with resource constraints based on a new mathematical formulation. University of Bologna, Department of Mathematics, Technical Report No. 32, Bologna
[14]Patterson JH, Slowinski R, Talbot FB, Weglarz J (1989) An algorithm for a general class of precedence and resource constrained scheduling problems. In: Slowinski R, Weglarz J (eds.): Advances in project scheduling. Elsevier, Amsterdam, pp. 3–28
[15]Radermacher FJ (1985/86) Scheduling of project networks. Ann Oper Res 4:227–252 · Zbl 0693.90046 · doi:10.1007/BF02022042
[16]Schräge L (1971) Solving resource-constrained network problems by implicit enumeration – nonpreemptive case. Oper Res 18:263–278 · Zbl 0197.46005 · doi:10.1287/opre.18.2.263
[17]Slowinski R (1980) Two approaches to problems of resource allocation among project activities: A comparative study. J Oper Res Soc 31:711–723
[18]Speranza MG, Vercellis C (1993) Hierarchical models for multiproject planning and scheduling. Europ J Oper Res 64:312–325 · Zbl 0779.90046 · doi:10.1016/0377-2217(93)90185-P
[19]Sprecher A (1994) Resource-constrained project scheduling: Exact methods for the multi-mode case. Lecture Notes in Economics and Mathematical Systems, Vol. 409, Springer, Berlin et al.
[20]Sprecher A, Hartmann S, Drexl A (1994) Project scheduling with discrete time-resource and resource-resource tradeoffs. Manuskripte aus den Instituten für Betriebswirtschaftslehre, No. 357, University of Kiel, Germany
[21]Sprecher A, Kolisch R, Drexl A (1995) Semi-active, active and non-delay schedules for the resource-constrained project scheduling problem. Europ J Oper Res 80:94–102 · Zbl 0927.90054 · doi:10.1016/0377-2217(93)E0294-8
[22]Stinson JP, Davis EW, Khumawala BM (1978) Multiple resourceconstrained scheduling using branch and bound. AIIE Trans 10:252–259
[23]Talbot FB (1982) Resource-constrained project scheduling with time-resource tradeoffs: The nonpreemptive case. Manag Sci 28:1197–1210 · Zbl 0493.90042 · doi:10.1287/mnsc.28.10.1197