Online Reusable Resource Allocations with Multi-class Arrivals

Huo, Tianming; Cheung, Wang Chi

doi:10.2139/ssrn.4320423

Cited by 2 publications

(2 citation statements)

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“…Chen et al (2017) considers a generalization of the model to allow advanced reservations. Assortment optimization problems of reusable resources have also been considered (Owen and Simchi-Levi 2018, Rusmevichientong et al 2020, Goyal et al 2020, Gong et al 2022, Zhang and Cheung 2022, Huo and Cheung 2022, Feng et al 2022.…”

Section: Literature Reviewmentioning

confidence: 99%

The Power of Static Pricing for Reusable Resources

Elmachtoub¹,

Shi²

2023

Preprint

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We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has an exponential distribution. This system is equivalent to the classical Erlang loss model. The objective is to maximize the steady-state revenue rate.Although an optimal policy is fully dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.2% of the revenue from the optimal dynamic policy. When there are multiple classes of customers that each have their own regular valuation distribution and service rate, we prove that static pricing guarantees 78.9% of the revenue of the optimal dynamic policy. In this case, the optimal policy grows exponentially large in the number of classes while the static policy requires only one price per class.

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Section: Literature Reviewmentioning

confidence: 99%

The Power of Static Pricing for Reusable Resources

Elmachtoub¹,

Shi²

2023

Preprint

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“…Goyal et al (2021), Feng et al(2021) study the problem when resources have large capacities. Several works consider different variations of the model we consider here(Rusmevichientong et al 2020, Dickerson et al 2018, Owen and Simchi-Levi 2018, Levi and Radovanović 2010, Feng et al 2020, Manshadi and Rodilitz 2022, Baek and Ma 2022, Baek and Wang 2023, Simchi-Levi et al 2022, Huo and Cheung 2022.…”

mentioning

confidence: 99%

Multiobjective Maximization of Monotone Submodular Functions with Cardinality Constraint

Udwani

2021

INFORMS Journal on Optimization

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We consider the problem of multiobjective maximization of monotone submodular functions subject to cardinality constraint, often formulated as [Formula: see text]. Although it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, it is known that when the number of objectives m grows as the cardinality k, that is, [Formula: see text], the problem is inapproximable (unless P = NP). On the other hand, when m is constant, there exists a a randomized [Formula: see text] approximation with runtime (number of queries to function oracle) the scales as [Formula: see text]. We focus on finding a fast algorithm that has (asymptotic) approximation guarantees even when m is super constant. First, through a continuous greedy based algorithm we give a [Formula: see text] approximation for [Formula: see text]. This demonstrates a steep transition from constant factor approximability to inapproximability around [Formula: see text]. Then using multiplicative-weight-updates (MWUs), we find a much faster [Formula: see text] time asymptotic [Formula: see text] approximation. Although these results are all randomized, we also give a simple deterministic [Formula: see text] approximation with runtime [Formula: see text]. Finally, we run synthetic experiments using Kronecker graphs and find that our MWU inspired heuristic outperforms existing heuristics.

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Online Reusable Resource Allocations with Multi-class Arrivals

Cited by 2 publications

References 0 publications

The Power of Static Pricing for Reusable Resources

The Power of Static Pricing for Reusable Resources

Multiobjective Maximization of Monotone Submodular Functions with Cardinality Constraint

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