Technical Note—Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

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; 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.