Abstract
This paper surveys the current research in resource constrained project scheduling. Although CPM and PERT have gained wide acceptance and use, the problem of limiting resources used by each activity remains unsolved for practical-sized problems.
The past research follows three basic approaches. The problem may be formulated as an integer linear program and solved by standard integer programming techniques. A second approach is to directly employ some enumerative scheme for constructing an optimal schedule. Finally, the problem may be formulated in terms of minimaximal paths in a disjunctive graph and solved by network flow methods and implicit enumeration. The approaches will be compared and the essential difficulties of the several methods will be identified.
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References
Egon Balas, “Finding a minimaximal path in a disjunctive PERT network,” Theory of Graphs International Symposium, pp. 21–30, Gordon & Breach, New York, 1967.
Egon Balas, “Discrete programming by the filter method,” Operations Research, 15, 915–957 (1967).
Egon Balas, “Project scheduling with resource constraints,” IBM New York Scientific Center Report 320–2960, January 1969.
Egon Balas, “Project scheduling with resource constraints,” In Applications of Mathematical Programming Techniques, pp. 187–200 edited by E. M. L. Beale, American Elsevier, New York, 1970.
Egon Balas, “Machine sequencing via disjunctive graphs: an implicit enumeration algorithm,” Operations Research, 17, 941–957, (1969).
Egon Balas, “Machine sequencing: disjunctive graphs and degree constrained subgraphs,” NRLQ, 17, 1–10 (1970).
Bikash Bhadury, “An experimental investigation of a model for sequencing N jobs on M machines in parallel,” unpublished thesis, North Carolina State University (1970).
E. H. Bowman, “The schedule-sequencing problem,” Opns. Res., 7, 621–624 (1959).
G. H. Brooks and C. R. White, “An algorithm for finding optimal or near-optimal solutions to the production-scheduling problem,” J. Ind. Eng., 16, 34–40 (1965).
C. B. Chapman, “Allocation of resources to variable timetables,” Opl. Res. Q., 21, 81–90, (1970).
G. B. Dantzig, and D. R. Fulkerson, “Minimizing the number of tankers to meet a fixed schedule,” NRLQ, 1, 217–222 (1954).
E. W. Davis, “An exact algorithm for the multiple constrained-resource project scheduling problem,” Ph.D. dissertation, Department of Administrative Sciences, Yale University, 1968.
E. W. Davis, “Computational experience with a new multiresource algorithm, in Project Planning by Network Analysis, pp. 256–260, edited by H.J.M. Lombaers, North Holland Publishing Co., Amsterdam — London, 1969.
E. W. Davis, and G. E. Heidorn, “An algorithm for optimal project scheduling under multiple resource constraints,” Mgt. Sci., 17, B803–816 (1970).
S. E. Elmaghraby, “The sequencing of n jobs on n parallel processors with extensions to the scarce resources problem of activity networks,” Proceedings of the Inaugural Conference of the Scientific Computation Center and the Institute of Statistical Studies and Research, pp. 230–255 Cairo, 1969.
M. Fisher, “Optimal Solution of scheduling problems using LaGrange multipliers: Part II,” Proceedings of Symposium on Theory of Scheduling and Its Applications, Raleigh, N. C., May 15–17, 1972.
M. Florian and P. Trepant, “An implicit enumeration algorithm for the machine sequencing problem,” Department d’informatique, Universite de Montreal (1969).
M. Florian and P. Trepant, and G. McMahon, “An implicit enumeration algorithm for the machine sequencing problem,” Mgt. Sci. 17, B782–792 (1971).
B. Giffler and G. L. Thompson, “Algorithms for solving production scheduling problems,” Opns. Res., 8, 487–503 (1960).
S. Gorenstein, “An algorithm for project (job) scheduling with resource constraints,” Opns. Res., 20, 835–850 (1972).
H. H. Greenberg, “A branch and bound solution to the general scheduling problem,” Opns, Res., 16, 353–361 (1968).
Allen L. Gutjahr and G. L. Nemhauser, “An algorithm for the assembly line balancing problem,” Mgt. Sci. 11, 308–315 (1964).
T. J. R. Johnson, “An algorithm for the resource constrained project scheduling problem,” Ph.D. thesis, Massachusetts Institute of Technology, 1967.
W. Karush, “On scheduling a network of activities under resource constraints over time,” SP-2654, System Development Corporation (1966).
J. E. Kelley, Jr., “Critical-path planning and scheduling: mathematical basis”,Opns. Res., 9, 296–320 (1961).
J. E. Kelley, Jr., “The critical path method: resource planning and scheduling,” in Industrial Scheduling, pp. 347–365 edited by J. F. Muth and G. L. Thompson, Prentice-Hall, Englewood Cliffs, N. J. (1963).
S. Lambourn, “Resource allocation and multi-project scheduling (RAMPS), a new tool in planning and control,” Computer Journal, 5, 699–719 (1966).
E. L. Lawler, Notes on Combinatorial Optimization, manuscript, 1969.
F. K. Levy, G. L. Thompson, and J. D. Wiest, “Multi-ship, multi shop workload-smoothing program,” NRLQ, 8, 37–44 (1962).
D. G. Malcomb, J. H. Roseboom, C. E. Clark, and W. Fazar, “Applications of a technique for research and development program evaluation,” Opns. Res., 7, 646–669 (1959).
A. S. Manne, “On the job-shop scheduling problem,” Opns. Res., 7, 219–223 (1959).
A. Mason and C. L. Moodie, “A branch and bound algorithm for minimizing cost in project scheduling,: Mgt. Sci. 18, B158–173 (1971).
J. H. Mize, “A hueristic scheduling model for multi-project organizations,” unpublished Ph.D. thesis, Purdue University, August, 1964.
J. J. Moder and C. R. Phillips, Project Management with CPM and PERT, Reinhold Corporation, New York, New York, 1964.
A. A. B. Pritsker, L. J. Watters, and P. M. Wolfe, “Multiproject scheduling with limited resources: a zero-one programming approach,” Mgt. Sci. 16, 93–108 (1969).
J. F. Raimond, “An algorithm for the exact solution of the machine scheduling problem,” I.B.M. New York Scientific Center 320–2930 (1968).
J. F. Raimond, “Minimaximal paths in disjunctive graphs by direct search,” I.B.M. J. of Res. and Dev., 13, 391–399 (1969).
B. Roy and B. Sussman, “Les problems d’ordonnancement avec constraintes disjonctives,” SEMA, Note D.S., No. 9 bis decembre 1964.
Linus Schrage, “Solving resource constrained network problems by implicit enumeration-nonpreemptive case,” Opns. Res., 18, 263–278 (1970).
B. Sussman, “Scheduling problems with interval disjunctions,” Tech. Rep. No. 70–5; Operations Research House, Stanford University (1970).
H. Wagner, “An integer programming model for machine scheduling,” NRLQ, 6, 131–139 (1959).
J. D. Wiest, “Some properties of schedules for large projects with limited resources, Opns. Res., 12, 359–418, (1964).
J. D. Wiest, “A hueristic method for scheduling large projects with limited resources,” Mgt. Sci., 13, 359–377, (1967).
Victor Zaloom, “An examination of the expected minimum time to complete a resource constrained project,” Ph.D. thesis, Department of Industrial Engineering, University of Houston (1970).
Victor Zaloom, “On the resource constrained project scheduling problem,” AIIE trans., 3, No. 4 (1971).
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Bennington, G.E., McGinnis, L.F. (1973). A Critique of Project Planning with Constrained Resources. In: Elmaghraby, S.E. (eds) Symposium on the Theory of Scheduling and Its Applications. Lecture Notes in Economics and Mathematical Systems, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80784-8_1
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DOI: https://doi.org/10.1007/978-3-642-80784-8_1
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