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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.

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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