Abstract
This paper concerns a CPM network in which individual job times are random variables. Specifically the time for each job consists of a component which is a linear function of the investment (up to some maximum) in that job and a random variable that is independent of the investment. It is desired to find the minimum investment required as a function of expected project completion time. The problem is solved by a cutting plane technique in which the investment allocations yield feasibility cuts. Because of the special structure of this problem, these cuts can be generated by solving a sequence of longest path problems in an acyclic network.
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© 1985 The Mathematical Programming Society, Inc.
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Wollmer, R.D. (1985). Critical path planning under uncertainty. In: Cottle, R.W. (eds) Mathematical Programming Essays in Honor of George B. Dantzig Part II. Mathematical Programming Studies, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121082
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DOI: https://doi.org/10.1007/BFb0121082
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