In “Achieving High Individual Service-Levels without Safety Stock? Optimal Rationing Policy of Pooled Resources,” Jiang, Wang, and Zhang analyze a resource rationing problem with service level constraints. They present a general framework to study the two-stage problem when customers require individual and possibly different service levels: (1) the capacity level of pooled resources in anticipation of random demand of multiple customers and (2) how the capacity should be allocated to fulfill customer demands after demand realization. The modeling framework generalizes and unifies many existing models in the literature and includes second-stage allocation costs. The authors propose a simple randomized rationing policy for any fixed feasible capacity level and show the optimality of this policy for very general service level constraints, including type I and type II constraints and beyond. They also discuss the optimality of index policies.

Robust Assortment Optimization Under the Markov Chain Choice Model Assortment optimization arises widely in many practical applications. In this problem, the goal is to select products to offer customers in order to maximize the expected revenue. We study a robust assortment-optimization problem under the Markov chain choice model, in which the parameters of the choice model are assumed to be uncertain, and the goal is to maximize the worst case expected revenue over all parameter values in an uncertainty set. Our main contribution is to prove a min-max duality result when the uncertainty set is row-wise. The result is surprising as the objective function does not satisfy the properties usually needed for known min-max results. Inspired by the duality result, we develop an efficient iterative algorithm for computing the optimal robust assortment under the Markov chain choice model. Moreover, our results yield operational insights into the effect of changing the uncertainty set on the optimal robust assortment.

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