Time (in)consistency of multistage distributionally robust inventory models with moment constraints

Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is posit that nature selects worst-case distribution for any relevant stochastic primitives from some pre-specified family. Several communities have observed subtle phenomena known as time inconsistency can arise this framework. In particular, it becomes possible policy optimal at zero may not be the associated optimization problem decision-maker recomputes her each point time, implications implementability. If exists both formulations, we say consistent, and weakly consistent. every strongly We study these context of managing an over when only mean, variance, support demand stage. provide several illustrative examples showing here question consistency quite subtle. complement observations by providing simple sufficient conditions weak strong consistency. Although similar was previously identified Shapiro setting mean known, our rich enough exhibit variety additional interesting behaviors.