Zhi Chen We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller’s pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller’s pricing problem as a stochastic program over an infinite-dimensional space of pricing policies … Read more
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study two popular approximation schemes for distributionally robust … Read more
The $p$-hub center problem is a fundamental model for the strategic design of hub location. It aims at constructing $p$ fully interconnected hubs and links from nodes to hubs so that the longest path between any two nodes is minimized. Existing literature on the $p$-hub center problem under uncertainty often assumes a joint distribution of … Read more
We extend the notion of globalized robustness to consider distributional information beyond the support of the ambiguous probability distribution. We propose the globalized distributionally robust counterpart that disallows any (resp., allows limited) constraint violation for distributions residing (resp., not residing) in the ambiguity set. By varying its inputs, our proposal recovers several existing perceptions of … Read more
Consider a seller seeking a selling mechanism to maximize the worst-case revenue obtained from a buyer whose valuation distribution lies in a certain ambiguity set. For a generic convex ambiguity set, we show via the minimax theorem that strong duality holds between the problem of finding the optimal robust mechanism and a minimax pricing problem … Read more
We study adjustable distributionally robust optimization problems where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such an ambiguity set has great modeling flexibility in characterizing uncertain probability distributions, the corresponding adjustable problems remain computationally intractable and challenging. To overcome this issue, we propose a greedy improvement procedure that consists … Read more
We develop a Python package called RSOME for modeling a wide spectrum of robust and distributionally robust optimization problems. RSOME serves as a modeling platform for formulating various optimization problems subject to distributional ambiguity in a highly readable and mathematically intuitive manner. Compared with the MATLAB version, RSOME in Python is more versatile and well … Read more
This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution … Read more
We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally … Read more
This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more