ᎏᎏ X CA/U ⫻ X CO/EXCA/E/XCA/U
4.13 Scheduling Conflicts
The discussion so far assumed that the only constraints on the schedule are precedence relations among activities. On the basis of these constraints, the early and late time of each event and the early and late start and finish of each activity are calculated.
In most projects, there are additional constraints that must be addressed, such as those associated with resource availability and the budget. In some cases, ready time and due-date constraints also exist. These constraints specify a time window in which an activity must be performed. In addition, there may be a tar- get completion date for the project or a due date for a milestone. If these due dates are earlier than the cor- responding dates derived from the CPM analysis, then the accompanying schedule will not be feasible.
There are several ways to handle these types of infeasibilities, such as 1. Reducing some activity durations by allocating more resources to them.
2. Eliminating some activities or reducing their lengths by using a more effective technology. For example, conventional painting, which requires the application of several layers of paint and a long drying time, may be replaced by anodizing — a faster but more expensive process.
3. Replacing some precedence relations of the “finish to start” type by other precedence relations, such as “start to start,” without affecting quality, cost, or performance. When this is possible, a sig- nificant amount of time may be saved.
It is common to start the scheduling analysis with each activity being performed in the most economical way and assuming “finish to start” precedence relations. If infeasibility is detected, then one or more of the foregoing courses of action can be used to circumnavigate the cause of the problem.
References and Further Readings
Estimating the Duration of Project Activities
Banks, J., Carson J.S., Nelson, B.L., and Nicol, D.M., Discrete-Event System Simulation, 3rd ed., Prentice- Hall, Upper Saddle River, NJ, 2001.
Britney, R.R., Bayesian point estimation and the PERT scheduling of stochastic activities, Manage. Sci., 22, 938–948, 1976.
Dodin, B., Bounding the project completion time distribution in PERT networks, Oper. Res., 33, 862–881, 1985.
Grubbs, F., Attempts to validate certain PERT statistics or ‘picking on PERT,’ Oper. Res., 10, 912–915, 1962.
Hershauer, J.C. and Nabielsky, G., Estimating activity times, J. Syst. Manage., 23, 17–21, 1972.
Montgomery, D.C. and Runger, G.C., Applied Statistics and Probability for Engineers, 3rd ed., Wiley, New York, 2003.
Perry, C. and Greig, I.D., Estimating the mean and variance of subjective distributions in PERT and deci- sion analysis, Manage. Sci., 21, 1477–1480, 1975.
Project Scheduling
Clark, K.B. and Fujimoto, T., Overlapping problem solving in product development, in Managing International Manufacturing, Ferdows, K., Ed., North-Holland, New York, 1989.
Goldratt, E., Critical Chain, North River Press, Great Barrington, MA, 1997.
Hartley, K.O., The project schedule, in Project Management: A Reference for Professionals, Kimmon, R.L.
and Lowree, J.H., Eds., Marcel Dekker, New York, 1989.
Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, 7th ed., McGraw-Hill, Boston, 2001.
Meredith, J.R. and Mantel, S.J., Jr., Project Management: A Managerial Approach, 4th ed., Wiley, New York, 1999.
Neumann, K., Schwindt, C., and Zimmermann, J., Project Scheduling with Time Windows and Scarce Resources: Temporal and Resource Constrained Project Scheduling with Regular and Nonregular Objective Functions, Lecture Notes in Economics and Mathematical Systems, Vol. 508, Springer, Amsterdam, 2002.
Steyn, H., An investigation into the fundamentals of critical chain project scheduling, Int. J. Proj. Sched., 19, 363–369, 2000.
Vazsonyi, A., The history of the rise and fall of the PERT method, Manage. Sci., 16, B449–B455, 1970.
Webster, F.M., Survey of CPM Scheduling Packages and Related Project Control Programs, Project Management Institute, Drexel Hill, PA, 1991.
CPM Approach
Badiru, A.B. and Pulat, P.S., Comprehensive Project Management: Integrating Optimization Models, Management Principles, and Computers, Prentice-Hall, Englewood Cliffs, NJ, 1995.
Cornell, D.G., Gotlieb, C.C., and Lee, Y.M., Minimal event-node network of project precedence relations, Commun. ACM, 16, 296–298, 1973.
Jewell, W.S., Divisible activities in critical path analysis, Oper. Res., 13, 747–760, 1965.
Kelley, J.E., Jr. and Walker, M.R., Critical path planning and scheduling, Proceedings of the Eastern Joint Computer Conference, Boston, pp. 160–173, 1979.
PERT Approach
Burgher, P.H., PERT and the auditor, Account. Rev., 39, 103–120, 1964.
Dodin, M.B., Determining the K most critical paths in PERT networks, Oper. Res., 32, 859–877, 1984.
Dodin, M.B. and Elmaghraby, S.E., Approximating the criticality indices of the activities in PERT net- works, Manage. Sci., 31, 207–223, 1985.
Fazar, W., Program evaluation and review technique, Am. Stat., 13, 10, 1959.
Fisher, D.L., Saisi, D., and Goldstein, W.M., Stochastic PERT networks: OP diagrams, critical paths and the project completion time, Comp. Oper. Res., 12, 471–482, 1985.
PERT, Program Evaluation Research Task, Phase I Summary Report, Vol. 7, Special Projects Office, Bureau of Ordinance, Department of the Navy, Washington, DC, 1958, pp. 646–669.
Van Slyke, R.M., Monte Carlo methods and the PERT problem, Oper. Res., 11, 839–860, 1963.
PERT and CPM Assumptions
Chase, R.B., Jacobs, F.R., and Aquilano, N.J., Operations Management for Competitive Advantage, 10th ed., McGraw-Hill, Boston, 2003.
Golenko-Ginzburg, D., On the distribution of activity time in PERT, J. Oper. Res. Soc., 39, 767–771, 1988.
Littlefield, T.K. and Randolph, P.H., PERT duration times: mathematics or MBO, Interfaces, 21, 92–95, 1991.
Sasieni, M.W., A note on PERT times, Manage. Sci., 16, 1652–1653, 1986.
Schonberger, R.J., Why projects are always late: a rationale based on manual simulation of a PERT/CPM network, Interfaces, 11, 66–70, 1981.
Wiest, J.D. and Levy, F.K., A Management Guide to PERT/CPM, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1977.
Computational Issues
Draper, N. and Smith, H., Applied Regression Analysis, 3rd ed., John Wiley & Sons, New York, 1998.
Hindelang, T.J. and Muth, J.F., A dynamic programming algorithm for decision CPM networks, Oper.
Res., 27, 225–241, 1979.
Jensen, P.A. and Bard, J.F., Operations Research Models and Methods, John Wiley & Sons, New York, 2003.
Kulkarni, V.G. and Provan, J.S., An improved implementation of conditional Monte Carlo estimation of path lengths in stochastic networks, Oper. Res., 33, 1389–1393, 1985.
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