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Analyzing linear recursive projects as an absorbing chain. (English) Zbl 1114.60057

The paper studies recursive projects in which some activities may be revisited after a later activity is completed. It describes the project by means of an absorbing Markov chain. Standard results in this field lead to the determination of expected total duration the project spends in an activity, the expected value the project spends in all activities, and the variance of project duration. Two examples are given, the first one can be calculated numerically, the second one analytically.

MSC:

60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
90B22 Queues and service in operations research
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References:

[1] D. E. Carter and B. S. Baker, Concurrent Engineering: The Product Development Environment for the 1990/s, Addison Wesley, New York, 1991.
[2] R. G. Cooper, “Stage-gate systems: a new tool for managing new products,” IEEE Engineering Management Review, pp. 5-12, 1991.
[3] N. Hardie, “The prediction and control of project duration: a recursive model,” International Journal of Project Management, vol. 19, no. 7, pp. 401-409, 2001. · doi:10.1016/S0263-7863(00)00027-2
[4] D. L. Minh, Applied Probability Models, Duxbury/Thomsom Learning, California, 2001.
[5] M. Park and F. Peña-Mora, “Dynamic change management for construction: introducing the change cycle into model-based project management,” System Dynamics Review, vol. 19, no. 3, pp. 213-242, 2003. · doi:10.1002/sdr.273
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