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We present a stochastic model of make-to-stock firms based on a buffer flow system with jumps. The cumulative production and the cumulative demand are governed by two Poisson counting processes with random intensities parameterized by production capacity and price respectively. Optimal operating and pricing policies (short-run decisions) and optimal capacity (long-run) decisions are explored by application of a two-stage optimization device. Detailed computations regarding the Poisson buffer flow system and a variation on the basic model with learning effects are also presented.
Lode Li (Mon,) studied this question.
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