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We study huge-scale assortment optimization problems to maximize expected revenue under customer choice, addressing a fundamental challenge in industries such as transportation, retail, and healthcare. The choice-based linear programming…
Combinatorial bilevel congestion pricing (CBCP), a variant of the mixed (continuous/discrete) network design problems, seeks to minimize the total travel time experienced by all travelers in a road network, by strategically selecting toll…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Market price systems constitute a well-understood class of mechanisms that under certain conditions provide effective decentralization of decision making with minimal communication overhead. In a market-oriented programming approach to…
Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a…
Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…
We study \emph{combinatorial procurement auctions}, where a buyer with a valuation function $v$ and budget $B$ wishes to buy a set of items. Each item $i$ has a cost $c_i$ and the buyer is interested in a set $S$ that maximizes $v(S)$…
Allocating conflicting jobs among individuals while respecting a budget constraint for each individual is an optimization problem that arises in various real-world scenarios. In this paper, we consider the situation where each individual…
We study a large economy in which firms cannot compute exact solutions to the non-linear equations that characterize the equilibrium price at which they can sell future output. Instead, firms use polynomial expansions to approximate prices.…
Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
A key challenge in combinatorial auctions is designing bid formats that accurately capture agents' preferences while remaining computationally feasible. This is especially true for electricity auctions, where complex preferences complicate…
Multilevel programming is the standard framework for modeling hierarchical decision-making. In this paper, we characterize the computational complexity of deciding the existence of feasible and optimal solutions, as well as computing the…
Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class,…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items…
We present a practical, market-based solution to the resource provisioning problem in a set of heterogeneous resource clusters. We focus on provisioning rather than immediate scheduling decisions to allow users to change long-term job…
Core-selecting combinatorial auctions (CAs) restrict the auction result in the core such that no coalitions could improve their utilities by engaging in collusion. The minimum-revenue-core (MRC) rule is a widely used core-selecting payment…