Bottleneck Resource Allocation in Manufacturing

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Bottleneck Resource Allocation in Manufacturing
Anantaram Balakrishnan
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This precedence graph is circuit-free, and does not require any further reduction. The natural sequence ((j, t) for j = 1, ... , n, t = 0, ... , p) satisfies the required precedence property; the original and enhanced bisection methods are identical if we use this sequence as the y-evaluation sequence S.
Let us now consider how to adapt the bisection method for discrete resource-allocation problems with precedence constraints that are more general than constraints (17). Suppose product j is an
...accessory board and product j' is the mother board for a personal computer. The production policy might specify that the cumulative release of product j at time t must equal or exceed a certain (nonnegative) proportion bjj :. J. Of the cumulative release of product j' at time t' (t and t' might differ if the two board types have different assembly lead times). The parameter h-^ ■•^> might be based upon the relative yields of the two board types, spare parts requirements, and so on. Modeling this policy requires adding precedence constraints of the form: Xjj > bjt j.

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