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Random yield and random demand in a production system with downward substitution. (English) Zbl 0979.90011
Summary: We present and solve a single-period, multiproduct, downward substitution model. Our model has one raw material as the production input and produces $$N$$ different products as outputs. The demands and yields for the products are random. We determine the optimal production input and allocation of the $$N$$ products to satisfy demands. The problem is modeled as a two-stage stochastic program, which we show can be decomposed into a parameterized network flow problem. We present and compare three different solution methods: a stochastic linear program, a decomposition resulting in a series of network flow subproblems, and a decomposition where the same network flow subproblems are solved by a new greedy algorithm.

##### MSC:
 90B05 Inventory, storage, reservoirs 90B30 Production models 90C35 Programming involving graphs or networks 60H30 Applications of stochastic analysis (to PDEs, etc.)
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