Mathematics of Operations Research

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• A Dynamic Network Model of Interbank Lending-Systemic Risk and Liquidity Provisioning AI翻译
  作者：Capponi, Agostino; Sun, Xu; Yao, David D.
  作者单位：Columbia University; State University System of Florida; University of Florida
  摘要：We develop a dynamic model of interbank borrowing and lending activities in which banks are organized into clusters, and adjust their monetary reserve levels to meet prescribed capital requirements. Each bank has its own initial monetary reserve level and faces idiosyncratic risks characterized by an independent Brownian motion, whereas system wide, the banks form a hierarchical structure of clusters. We model the interbank transactional dynamics through a set of interacting measure-valued pro...
• Price of Anarchy in Networks with Heterogeneous Latency Functions AI翻译
  作者：Kapoor, Sanjiv; Shin, Junghwan
  作者单位：Illinois Institute of Technology
  摘要：We address the performance of selfish network routing in multicommodity flows where the latency or delay function on edges is dependent on the flow of individual commodities, rather than on the aggregate flow. An application of this study is the analysis of a network with differentiated traffic, that is, in transportation networks where there are multiple types of traffic and in networks where traffic is prioritized according to type classification. We consider the inefficiency of equilibrium ...
• Last-Mile Shared Delivery: A Discrete Sequential Packing Approach AI翻译
  作者：Cao, Junyu; Olvera-Cravioto, Mariana; Shen, Zuo-Jun (max)
  作者单位：University of California System; University of California Berkeley; University of North Carolina; University of North Carolina Chapel Hill
  摘要：We propose a model for optimizing the last-mile delivery of n packages from a distribution center to their final recipients, using a strategy that combines the use of ride-sharing platforms (e.g., Uber or Lyft) with traditional in-house van delivery systems. The main objective is to compute the optimal reward offered to private drivers for each of the n packages such that the total expected cost of delivering all packages is minimized. Our technical approach is based on the formulation of a di...
• Characterization, Robustness, and Aggregation of Signed Choquet Integrals AI翻译
  作者：Wang, Ruodu; Wei, Yunran; Willmot, Gordon E.
  作者单位：University of Waterloo
  摘要：This article contains various results on a class of nonmonotone, law-invariant risk functionals called the signed Choquet integrals. A functional characterization via comonotonic additivity is established along with some theoretical properties, including six equivalent conditions for a signed Choquet integral to be convex. We proceed to address two practical issues currently popular in risk management, namely robustness (continuity) issues and risk aggregation with dependence uncertainty, for ...
• The Euclidean k-Supplier Problem AI翻译
  作者：Nagarajan, Viswanath; Schieber, Baruch; Shachnai, Hadas
  作者单位：University of Michigan System; University of Michigan; International Business Machines (IBM); IBM USA; Technion Israel Institute of Technology
  摘要：The k-supplier problem is a fundamental location problem that involves opening k facilities to minimize the maximum distance of any client to an open facility. We consider the k-supplier problem in Euclidean metrics (of arbitrary dimension) and present an algorithm with approximation ratio 1 + root 3 < 2.74. This improves upon the previously known 3-approximation algorithm, which also holds for general metrics. Our result is almost best possible as the Euclidean k-supplier problem is NP-hard t...
• Control-Stopping Games for Market Microstructure and Beyond AI翻译
  作者：Gayduk, Roman; Nadtochiy, Sergey
  作者单位：University of Michigan System; University of Michigan; Illinois Institute of Technology
  摘要：In this paper, we present a family of control-stopping games that arise naturally in equilibrium-based models of market microstructure as well as in other models with strategic buyers and sellers. A distinctive feature of this family of games is the fact that the agents do not have any exogenously given fundamental value for the asset, and they deduce the value of their position from the bid and ask prices posted by other agents (i.e., they are pure speculators). As a result, in such a game, t...
• Counting Integral Points in Polytopes via Numerical Analysis of Contour Integration AI翻译
  作者：Hirai, Hiroshi; Oshiro, Ryunosuke; Tanaka, Ken'ichiro
  作者单位：University of Tokyo
  摘要：In this paper, we address the problem of counting integer points in a rational polytope described by P(y) = {x is an element of R-m: Ax = y, x >= 0}, where A is an n x in integer matrix and y is an n-dimensional integer vector. We study the Z transformation approach initiated in works by Brion and Vergne, Beck, and Lasserre and Zeron from the numerical analysis point of view and obtain a new algorithm on this problem. If A is nonnegative, then the number of integer points in P(y) can be comput...
• Budgeted Prize-Collecting Traveling Salesman and Minimum Spanning Tree Problems AI翻译
  作者：Paul, Alice; Freund, Daniel; Ferber, Aaron; Shmoys, David B.; Williamson, David P.
  作者单位：Brown University; Massachusetts Institute of Technology (MIT); Cornell University
  摘要：We consider constrained versions of the prize-collecting traveling salesman and the prize-collecting minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. Rooted variants of the problems have the additional constraint that a given vertex, the root, must be contained in the tour/tree. We present a 2-approximation algorithm for the rooted and unrooted versions of both the tree and tour variants. The algo...
• Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications AI翻译
  作者：Aid, Rene; Basei, Matteo; Callegaro, Giorgia; Campi, Luciano; Vargiolu, Tiziano
  作者单位：Universite PSL; Universite Paris-Dauphine; University of California System; University of California Berkeley; University of Padua; University of London; London School Economics & Political Science
  摘要：We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric runn...
• Asymptotic Optimality of Power-of-d Load Balancing in Large-Scale Systems AI翻译
  作者：Mukherjee, Debankur; Borst, Sem C.; van Leeuwaarden, Johan S. H.; Whiting, Philip A.
  作者单位：University System of Georgia; Georgia Institute of Technology; Eindhoven University of Technology; Nokia Corporation; Nokia Bell Labs; Tilburg University; Macquarie University
  摘要：We consider a system of N identical server pools and a single dispatcher in which tasks with unit-exponential service requirements arrive at rate.(N). In order to optimize the experienced performance, the dispatcher aims to evenly distribute the tasks across the various server pools. Specifically, when a task arrives, the dispatcher assigns it to the server pool with the minimum number of tasks among d(N) randomly selected server pools. We construct a stochastic coupling to bound the differenc...