Abstract
The paper deals with the network optimization problem of minimizing regular project cost subject to an arbitrary precedence relation on the sets of activities and to arbitrarily many resource constraints. The treatment is done via a purely structural approach that considerably extends the disjunctive graph concept. It is based on so-called feasible posets and includes a quite deep and useful representation theorem. This theorem permits many insights concerning the analytical behaviour of the optimal value function, the description and counting of all essentially different optimization problems, the nature of Graham anomalies, connections with the on-line stochastic generalizations, and several others. In addition, it also allows the design of a quite powerful class of branch-and-bound algorithms for such problems, which is based on an iterative construction of feasible posets. Using so-called distance matrices, this approach permits the restriction of the exponential part of the algorithm to the often comparatively small set of ‘resource and cost essential’ jobs. The paper reports on computational experience with this algorithm for examples from the building industry and includes a rough comparison with the integer programming approach by Talbot and Patterson.
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Radermacher, F.J. Scheduling of project networks. Ann Oper Res 4, 227–252 (1985). https://doi.org/10.1007/BF02022042
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DOI: https://doi.org/10.1007/BF02022042