Structural properties of a class of robust inventory and queueing control problems

Abstract

In standard stochastic dynamic programming, the transition probability distributions of the underlying Markov Chains are assumed to be known with certainty. We focus on the case where the transition probabilities or other input data are uncertain. Robust dynamic programming addresses this problem by defining a min-max game between Nature and the controller. Considering examples from inventory and queueing control, we examine the structure of the optimal policy in such robust dynamic programs when event probabilities are uncertain. We identify the cases where certain monotonicity results still hold and the form of the optimal policy is determined by a threshold. We also investigate the marginal value of time and the case of uncertain rewards.

A novel single-period inventory problem with uncertain random demand and its application

“…For example, Kamburowski [6] provided new theoretical foundations for analyzing the case under incomplete information about probability distribution of random demand, Rossi et al [24] introduced a novel strategy to address the issue of demand estimation by combining confidence interval analysis and inventory optimization, Wu et al [31] studied a risk-averse situation with quantity competition and price competition based on conditional value-at-risk criterion and Sayın et al [25] considered both random demand and random supply and provided the optimal ordering policy and optimal portfolio at the same time. For the case with partial information, several authors such as Qiu and Shang [23], Turgay et al [27] and Wang et al [29] also apply robust optimization to handle the distribution uncertainty of probability parameters in the newsvendor or inventory problems.…”