This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher ap...
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We consider the "classical" single-product dynamic pricing problem allowing the "scale" of demand intensity to be modulated by an exogenous "market size" stochastic process. This is a nat...
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We consider the "classical" single-product dynamic pricing problem allowing the "scale" of demand intensity to be modulated by an exogenous "market size" stochastic process. This is a natural model of dynamically changing market conditions. We show that for a broad family of Gaussian market-size processes, simple dynamic pricing rules that are essentially agnostic to the specification of this market-size process perform provably well. The pricing policies we develop are shown to compensate for forecast imperfections (or a lack of forecast information altogether) by frequent reoptimization and reestimation of the "instantaneous" market size.
We study a general problem of allocating limited resources to heterogeneous customers over time under model uncertainty. Each type of customer can be serviced using different actions, each of which stochastically cons...
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We study a general problem of allocating limited resources to heterogeneous customers over time under model uncertainty. Each type of customer can be serviced using different actions, each of which stochastically consumes some combination of resources and returns different rewards for the resources consumed. We consider a general model in which the resource consumption distribution associated with each customer type-action combination is not known but is consistent and can be learned over time. In addition, the sequence of customer types to arrive over time is arbitrary and completely unknown. We overcome both the challenges of model uncertainty and customer heterogeneity by judiciously synthesizing two algorithmic frameworks from the literature: inventory balancing, which "reserves" a portion of each resource for high-reward customer types that could later arrive based on competitive ratio analysis, and online learning, which "explores" the resource consumption distributions for each customer type under different actions based on regret analysis. We define an auxiliary problem, which allows for existing competitive ratio and regret bounds to be seamlessly integrated. Furthermore, we propose a new variant of upper confidence bound (UCB), dubbed lazyUCB, which conducts less exploration in a bid to focus on "exploitation" in view of the resource scarcity. Finally, we construct an information-theoretic family of counterexamples to show that our integrated framework achieves the best possible performance guarantee. We demonstrate the efficacy of our algorithms on both synthetic instances generated for the online matching with stochastic rewards problem under unknown probabilities and a publicly available hotel data set. Our framework is highly practical in that it requires no historical data (no fitted customer choice models or forecasting of customer arrival patterns) and can be used to initialize allocation strategies in fast-changing environments.
We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In par...
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We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In particular, each customer has a rank cutoff, characterizing the number of products that she will focus on during the course of her choice process. Given that we offer a certain assortment of products, the choice process of a customer with rank cutoff k proceeds as follows. The customer associates random utilities with all of the products as well as the no-purchase option. The customer ignores all alternatives whose utilities are not within the k largest utilities. Among the remaining alternatives, the customer chooses the available alternative that provides the largest utility. Under the assumption that the utilities follow Gumbel distributions with the same scale parameter, we provide a recursion to compute the choice probabilities. Considering the assortment optimization problem to find the revenue-maximizing assortment of products to offer, we show that the problem is NP-hard and give a polynomial time approximation scheme. Because the customers ignore the products below their rank cutoffs in our variant of the multinomial logit model, intuitively speaking, our variant captures choosier choice behavior than the standard multinomial logit model. Accordingly, we show that the revenue-maximizing assortment under our variant includes the revenue-maximizing assortment under the standard multinomial logit model, so choosier behavior leads to larger assortments offered to maximize the expected revenue. We conduct computational experiments on both synthetic and real data sets to demonstrate that incorporating rank cutoffs can yield better predictions of customer choices and yield more profitable assortment recommendations.
Several real-world problems in engineering and applied science require the selection of sequences that maximize a given reward function. Optimizing over sequences as opposed to sets requires exploring an exponentially...
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Several real-world problems in engineering and applied science require the selection of sequences that maximize a given reward function. Optimizing over sequences as opposed to sets requires exploring an exponentially larger search space and can become prohibitive in most cases of practical interest. However, if the objective function is submodular (intuitively, it exhibits a diminishing return property), the optimization problem becomes more manageable. Recently, there has been increasing interest in sequence submodularity in connection with applications such as recommender systems and online ad allocation. However, mostly ad hoc models and solutions have emerged within these applicative contexts. In consequence, the field appears fragmented and lacks coherence. In this paper, we offer a unified view of sequence submodularity and provide a generalized greedy algorithm that enjoys strong theoretical guarantees. We show how our approach naturally captures several application domains, and our algorithm encompasses existing methods, improving over them. (C) 2021 The Authors. Published by Elsevier B.V.
The problem of the edge coloring partial k ‐tree into two partial p ‐ and q ‐trees with p , q < k is considered. An algorithm is provided to construct such a coloring with p + q = k . Usefulness of this result i...
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The problem of the edge coloring partial k ‐tree into two partial p ‐ and q ‐trees with p , q < k is considered. An algorithm is provided to construct such a coloring with p + q = k . Usefulness of this result in a Lagrangian decomposition framework to solve certain combinatorial optimization problems is discussed. ® 1997 John Wiley & Sons, Inc.
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