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作者：Abdallah, Tarek; Asadpour, Arash; Reed, Josh
作者单位：Northwestern University; City University of New York (CUNY) System; Baruch College (CUNY); New York University
摘要：Bundle-size pricing (BSP) is a multidimensional selling mechanism where the firm prices the size of the bundle rather than the different possible combinations of bundles. In BSP, the firm offers the customer a menu of different sizes and prices. The customer then chooses the size that maximizes her surplus and customizes her bundle given her chosen size. Although BSP is commonly used across several industries, little is known about the optimal BSP policy in terms of sizes and prices, along wit...
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作者：Russo, Daniel
作者单位：Columbia University
摘要：This note gives a short, self-contained proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multiarmed bandit problem with discount factor.. The Gittins index of an arm is shown to equal the gamma-quantile of the posterior distribution of the arm's mean plus an error term that vanishes as gamma -> 1. In this sense, for sufficiently patient agents, a Gittins index measures the highest plausible mean-reward of an arm in a mann...
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作者：Li, Xiaocheng; Ye, Yinyu
作者单位：Imperial College London; Stanford University
摘要：We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are independently and identically drawn from an unknown distribution and revealed sequentially over time. Virtually all existing online algorithms were based on learning the dual optimal solutions/prices of the linear programs (LPs), and their analyses were focused on the aggregate objective value and so...
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作者：Ma, Qingyin; Stachurski, John
作者单位：Capital University of Economics & Business; Australian National University
摘要：Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation to open up a new line of attack. Our paper studies this idea systematically with a focus on boosting computational efficiency. We provide a characterization of the set of valid transformations of the Bellman equation, for which validity means that the transformed Bellman equation maintains the link to optimality held by the ...
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作者：Das, Bikramjit; Dhara, Anulekha; Natarajan, Karthik
作者单位：Singapore University of Technology & Design
摘要：Since the seminal work of Scarf (A min-max solution of an inventory problem) in 1958 on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The model is criticized at times for being conservative because the worst-case distribution is discrete with a few support points. However, it is the order quantity prescribed by the model that is of practical relevance. Interestingly, the order ...
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作者：Gong, Xiting; Wang, Tong
作者单位：Chinese University of Hong Kong; Shanghai Jiao Tong University
摘要：In this paper, we establish two preservation results of additive convexity for a class of optimal transformation problems and a class of optimal disposal problems. For both classes of problems, there are multiple resources; our results show that if these resources have different priorities to be transformed/disposed under the optimal policy, then the additive convexity and bounded monotonicity of the objective function are preserved to the value function after optimization. A key observation i...
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作者：Lin, Kyle Y.
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School
摘要：A defender dispatches patrollers to circumambulate a perimeter to guard against potential attacks. The defender decides on the time points to dispatch patrollers and each patroller's direction and speed, as long as the long-run rate at which patrollers are dispatched is capped at some constant. An attack at any point on the perimeter requires the same amount of time, during which it will be detected by each passing patroller independently with the same probability. The defender wants to maximi...
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作者：Chan, Timothy C. Y.; Fernandes, Craig; Puterman, Martin L.
作者单位：University of Toronto; University of British Columbia
摘要：To develop a novel approach for performance assessment, this paper considers the problem of computing value functions in professional American football. We provide a theoretical justification for using a dynamic programming approach to estimating value functions in sports by formulating the problem as a Markov chain for two asymmetric teams. We show that the Bellman equation has a unique solution equal to the bias of the underlying infinite horizon Markov reward process. This result provides, ...
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作者：Wu, Manxi; Amin, Saurabh; Ozdaglar, Asuman E.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We study a routing game in an environment with multiple heterogeneous information systems and an uncertain state that affects edge costs of a congested network. Each information system sends a noisy signal about the state to its subscribed traveler population. Travelers make route choices based on their private beliefs about the state and other populations' signals. The question then arises, How does the presence of asymmetric and incomplete information affect the travelers' equilibrium route ...
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作者：Stolyar, Alexander L.; Wang, Qiong
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study the classical single-item inventory system in which unsatisfied demands are backlogged. Replenishment lead times are random, independent identically distributed, causing orders to cross in time. We develop a new inventory policy to exploit implications of lead time randomness and order crossover, and evaluate its performance by asymptotic analysis and simulations. Our policy does not follow the basic principle of constant base stock (CBS) policy, or more generally, (s, S) and (R, q) p...
