Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-Dependent Competitive Ratios

Ma, Will; Simchi‐Levi, David

doi:10.1287/opre.2019.1957

Cited by 64 publications

(27 citation statements)

References 31 publications

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“…Our results also reproduce the optimal CR under such settings. Our problem is studied in [22], and a discrete counterpart is studied in [26]. Compared with the existing study, we propose a novel divide-and-conquer approach.…”

Section: Related Workmentioning

confidence: 99%

“…The online problem has been studied in [22] under the same revenue function set G. A discrete counterpart of the problem is studied in [26]. In some special cases, our revenue functions cover the linear functions with slopes between [𝑝 min , 𝑝 max ].…”

Section: State Of the Artmentioning

confidence: 99%

“…In the literature, the authors in [22,26] tackle the problem using the well-established online primal-and-dual framework [13,27,28]. They design a threshold function for each inventory with regard to the allocated amount, which can be view as the marginal cost of the inventory.…”

Section: Introductionmentioning

confidence: 99%

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Competitive Online Optimization with Multiple Inventories: A Divide-and-Conquer Approach

Lin¹,

Su²,

Chen³

2022

Preprint

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We study a competitive online optimization problem with multiple inventories. In the problem, an online decision maker seeks to optimize the allocation of multiple capacity-limited inventories over a slotted horizon, while the allocation constraints and revenue function come online at each slot. The problem is challenging as we need to allocate limited inventories under adversarial revenue functions and allocation constraints, while our decisions are coupled among multiple inventories and different slots. We propose a divide-and-conquer approach that allows us to decompose the problem into several single inventory problems and solve it in a two-step manner with almost no optimality loss in terms of competitive ratio (CR). Our approach provides new angles, insights and results to the problem, which differs from the widely-adopted primal-and-dual framework. Specifically, when the gradients of the revenue functions are bounded in a positive range, we show that our approach can achieve a tight CR that is optimal when the number of inventories is small, which is better than all existing ones. For an arbitrary number of inventories, the CR we achieve is within an additive constant of one to a lower bound of the best possible CR among all online algorithms for the problem. We further characterize a general condition for generalizing our approach to different applications. For example, for a generalized one-way trading problem with price elasticity, where no previous results are available, our approach obtains an online algorithm that achieves the optimal CR up to a constant factor.

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Section: Related Workmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

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Competitive Online Optimization with Multiple Inventories: A Divide-and-Conquer Approach

Lin¹,

Su²,

Chen³

2022

Preprint

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“…Zhou et al [30] develop a robust online weighted matching algorithm based on primal-dual schemes for the random order model which account for changes in the underlying distribution and evaluate it on a display ad data set. Ma et al [24] develop an algorithm for online assortment optimization and evaluate it on data from a hotel chain, but their emphasis is on revenue maximization rather than capacity allotment. Chen et al [9] develop a realtime bidding algorithm for display ad allocation and evaluate it on a proprietary display ad data set; their methods closely mirror the water-filling algorithm we study.…”

Section: Related Workmentioning

confidence: 99%

Using Predicted Weights for Ad Delivery

Lavastida¹,

Moseley²,

Ravi³

et al. 2021

SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21)

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We study the performance of a proportional weights algorithm for online capacitated bipartite matching modeling the delivery of impression ads. The algorithm uses predictions on the advertiser nodes to match arriving impression nodes fractionally in proportion to the weights of its neighbors. This paper gives a thorough empirical study of the performance of the algorithm on a data-set of ad impressions from Yahoo! and shows its superior performance compared to natural baselines such as a greedy water-filling algorithm and the ranking algorithm.The proportional weights algorithm has recently received interest in the theoretical literature where it was shown to have strong guarantees beyond the worst-case model of algorithms augmented with predictions. We extend these results to the case where the advertisers' capacities are no longer stationary over time. Additionally, we show the algorithm has near optimal performance in the random-order arrival model when the number of impressions and the optimal matching are sufficiently large.

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“…Even in those instances where the owners have access to some information about future requests, but the information is incomplete, it may be desirable to use an online algorithm because they are robust against forecast errors [8] and distributional misspecifications [9]. Moreover, the decision-maker will not need to customize the algorithm to exploit the type, quantity, and quality of information available.…”

Section: Introductionmentioning

confidence: 99%

The Online Reservation Problem

Goyal

Gupta

2020

Algorithms

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Many sharing-economy platforms operate as follows. Owners list the availability of resources, prices, and contract-length limits. Customers propose contract start times and lengths. The owners decide immediately whether to accept or decline each proposal, even if the contract is for a future date. Accepted proposals generate revenue. Declined proposals are lost. At any decision epoch, the owner has no information regarding future proposals. The owner seeks easy-to-implement algorithms that achieve the best competitive ratio (CR). We first derive a lower bound on the CR of any algorithm. We then analyze CRs of all intuitive “greedy” algorithms. We propose two new algorithms that have significantly better CRs than that of any greedy algorithm for certain parameter-value ranges. The key idea behind these algorithms is that owners may reserve some amount of capacity for late-arriving higher-value proposals in an attempt to improve revenue. Our contribution lies in operationalizing this idea with the help of algorithms that utilize thresholds. Moreover, we show that if non-optimal thresholds are chosen, then those may lead to poor CRs. We provide a rigorous method by which an owner can decide the best approach in their context by analyzing the CRs of greedy algorithms and those proposed by us.

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Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-Dependent Competitive Ratios

Abstract: Resource Allocation and Pricing in the Absence of a Demand Forecast

Cited by 64 publications

References 31 publications

Competitive Online Optimization with Multiple Inventories: A Divide-and-Conquer Approach

Competitive Online Optimization with Multiple Inventories: A Divide-and-Conquer Approach

Using Predicted Weights for Ad Delivery

The Online Reservation Problem

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