Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems
Operations Research Forthcoming
34 Pages Posted: 8 Aug 2018 Last revised: 8 Mar 2021
Date Written: June 16, 2020
In this paper, we establish two preservation results of additive convexity for a class of optimal transformation problems and a class of optimal disposal problems. For both classes of problems, there are multiple resources and our results show that if these resources have different priorities to be transformed/disposed under the optimal policy, then the additive convexity and bounded monotonicity of the objective function are preserved to the value function after optimization. A key observation is that an optimal transformation problem with prioritized optimal decisions is equivalent to a serial inventory problem with zero lead times. We demonstrate the applications of our results to several stochastic optimization problems in operations management.
Keywords: dynamic programming, additive convexity, serial inventory systems, remanufacturing systems, inventory rationing, expediting, disposal, capacity management
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