Abstract
This paper surveys recent results for stochastic discrete programming models of hierarchical planning problems. Practical problems of this nature typically involve a sequence of decisions over time at an increasing level of detail and with increasingly accurate information. These may be modelled by multistage stochastic programmes whose lower levels (later stages) are stochastic versions of familiar NP-hard deterministic combinatorial optimization problems and hence require the use of approximations and heuristics for near-optimal solution. After a brief survey of distributional assumptions on processing times under which SEPT and LEPT policies remain optimal for m-machine scheduling problems, results are presented for various 2-level scheduling problems in which the first stage concerns the acquisition (or assignment) of machines. For example, heuristics which are asymptotically optimal in expectation as the number of jobs in the system increases are analyzed for problems whose second stages are either identical or uniform m-machine scheduling problems. A 3-level location, distribution and routing model in the plane is also discussed.
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Dempster, M.A.H. (1982). A Stochastic Approach to Hierarchical Planning and Scheduling. In: Dempster, M.A.H., Lenstra, J.K., Rinnooy Kan, A.H.G. (eds) Deterministic and Stochastic Scheduling. NATO Advanced Study Institutes Series, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7801-0_15
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DOI: https://doi.org/10.1007/978-94-009-7801-0_15
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