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# Optimal acquisition, inventory and production decisions for a closed-loop manufacturing system with legislation constraint

• In order to improve the utilization efficiency of resources, more and more countries have required manufacturing firms to remanufacture or reuse used products through legislation. For many firms, the profit from reusing used products may be less than the profit from producing new products, so how to make decisions under such legislation constraint is a major concern by these firms. In this paper, we study the optimal acquisition, inventory and production decision problem for such firms under a two-period setting, where firms have two different production ways: (i) production with new raw materials, and (ii) production with used products. The return quantity of used products at the second period depends on the demand of the first period and the acquisition effort. The problem is formulated as a stochastic dynamic programming model. We give the optimal production rule and the optimal inventory decision at the second period, and prove the existence of an optimal policy with a simple structure at the first period. Moreover, based on our theoretical analysis, we calculate the optimal decisions under different parameter settings, and discuss how the firm does react when facing with specific market and production conditions.
Mathematics Subject Classification: Primary: 90B05, 90B30; Secondary: 93E20.

 Citation:

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