We study robust assortment optimization under the nested logit model with uncertainty in nest-level utility shifts and dissimilarity factors. Under competitive alternatives and fully captured nests, we establish a minimax equality and show that the robust value equals the optimal value of the deterministic problem evaluated at the lower-bound parameters. Moreover, an optimal nested-by-revenue assortment for this deterministic problem forms a saddle point with the lower-bound parameters, yielding a tractable linear programming reformulation.
We study periodic-review lost-sales assemble-to-order (ATO) systems, where optimal replenishment is computationally intractable. We analyze independent base-stock (IBS) policies, which control each component with a separate base-stock level. Under any non-hold-back allocation policy, we prove that a class of IBS policies is asymptotically optimal as all unit lost-sales penalties grow large. The analysis extends to backlogging systems and provides the first theoretical performance guarantee for these simple, widely used policies in ATO systems.
This note investigates k-out-of-n:F systems with components and redundancies having statistically dependent lifetimes. For components with WSAI lifetimes conditioned on the redundancy lifetime, we show that allocating the active redundancy to the less reliable component engenders a stochastically larger system lifetime. For component and redundancy lifetimes linked by an Archimedean copula, we prove that allocating more homogeneous redundancies to weaker components also produces a more reliable system. These new findings substantially generalizes some results in the recent literature.
This paper discusses strong α-core of set payoff games to maximize each objective of players in the real world. We first present the existence of strong α-core based on the conditions of continuity and properly cone quasi-concavity of set payoff functions. Furthermore, we investigate the essential stability when the set payoff functions of agents are perturbed. Moreover, we show that our model differs from those in the literature through some examples.
Aided by the AI tool GPT5.5 Pro, we provide a counterexample to a conjecture made by Ramachandra and Natarajan (2025) [Pairwise independent correlation gap, Operations Research Letters, 107255, 6040].
