Dynamic Pricing under a Static Calendar

Ma, Will; Simchi‐Levi, David; Zhao, Jinglong

doi:10.2139/ssrn.3251015

Cited by 6 publications

(9 citation statements)

References 30 publications

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“…The seminal work of Gallego and Van Ryzin (1994) shows that if the revenue function is concave, a static pricing policy loses at most 1/(2 min{C, λ * t}), where C is the number of units and λ * t represents the expected number of sales under the myopic price. The authors also show a universal guarantee of 1 − 1/e for any parameter regime, with both results relying on a concavity assumption on the revenue rate (see also Ma et al (2018)). Ma et al (2018) recently generalize these results for the same model without the concavity assumption, and also provide non-adaptive pricing policies for assortment optimization and non-stationary demand settings with constant factor performance guarantees.…”

Section: Literature Reviewmentioning

confidence: 88%

“…The authors also show a universal guarantee of 1 − 1/e for any parameter regime, with both results relying on a concavity assumption on the revenue rate (see also Ma et al (2018)). Ma et al (2018) recently generalize these results for the same model without the concavity assumption, and also provide non-adaptive pricing policies for assortment optimization and non-stationary demand settings with constant factor performance guarantees. showed that the 1 − 1/e guarantee and asymptotic optimality for static pricing also holds in the presence of strategic customers.…”

Section: Literature Reviewmentioning

confidence: 88%

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Static Pricing: Universal Guarantees for Reusable Resources

Besbes

Elmachtoub

Sun

2019

Preprint

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We consider a fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and upon arrival decide whether or not to purchase the service, depending on their willingness-to-pay and the current price. The service time during which the resource is used by the customer is stochastic and the firm may incur a service cost. This model represents various markets for reusable resources such as cloud computing, shared vehicles, rotable parts, and hotel rooms. In the present paper, we analyze this pricing problem when the firm attempts to maximize a weighted combination of three central metrics: profit, market share, and service level. Under Poisson arrivals, exponential service times, and standard assumptions on the willingness-to-pay distribution, we establish a series of results that characterize the performance of static pricing in such environments.In particular, while an optimal policy is fully dynamic in such a context, we prove that a static pricing policy simultaneously guarantees 78.9% of the profit, market share, and service level from the optimal policy. Notably, this result holds for any service rate and number of units the firm operates. In the special case where there are two units and the induced demand is linear, we also prove that the static policy guarantees 95.5% of the profit from the optimal policy. Our numerical findings on a large testbed of instances suggest that the latter result is quite indicative of the profit obtained by the static pricing policy across all parameters.

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Section: Literature Reviewmentioning

confidence: 88%

Section: Literature Reviewmentioning

confidence: 88%

Static Pricing: Universal Guarantees for Reusable Resources

Besbes

Elmachtoub

Sun

2019

Preprint

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“…In the special case where all of the patience levels equal 1, our problems reduce to the classical online stochastic matching/assortment problems where the firm only gets one chance to make an offering to each customer. Under stationary arrivals, the tight approximation ratio relative to the LP is 1 − 1/e in both of these cases (see Brubach et al (2017) and Ma et al (2018), respectively). Our work, and specifically our impossibility result, shows that both of these problems are substantially more challenging when there are multiple chances to interact with each customer.…”

Section: Contributionsmentioning

confidence: 98%

Multi-Stage and Multi-Customer Assortment Optimization With Inventory Constraints

Fata

Simchi‐Levi

2019

SSRN Journal

Self Cite

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We consider an assortment optimization problem where a customer chooses a single item from a sequence of sets shown to her, while limited inventories constrain the items offered to customers over time. In the special case where all of the assortments have size one, our problem captures the online stochastic matching with timeouts problem. For this problem, we derive a polynomial-time approximation algorithm which earns at least 1-ln(2-1/e), or 0.51, of the optimum. This improves upon the previous-best approximation ratio of 0.46, and furthermore, we show that it is tight. For the general assortment problem, we establish the first constant-factor approximation ratio of 0.09 for the case that different types of customers value items differently, and an approximation ratio of 0.15 for the case that different customers value each item the same. Our algorithms are based on rounding an LP relaxation for multi-stage assortment optimization, and improve upon previous randomized rounding schemes to derive the tight ratio of 1-ln(2-1/e).

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“…Other models. Some other problems that are indirectly related to us are (i) online bipartite stochastic matching [e.g., 17,4,39,42,33], (ii) online bipartite matching with stochastic rewards [e.g., 40,28,31] and (iii) online prophet inequality matching, with or without reusable resources [e.g., 3,19,11,20,38]. Finally, marginally related to us in terms of modeling is also the rich literature on stochastic i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Online Bipartite Matching with Reusable Resources

Delong¹,

Farhadi²,

Niazadeh³

et al. 2021

Preprint

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We study the classic online bipartite matching problem with a twist: offline nodes are reusable any number of times. Every offline node i becomes available d steps after it was assigned to. Nothing better than a 0.5-approximation, obtained by the trivial deterministic greedy algorithm, was known for this problem. We give the first approximation factor beating 0.5, namely a 0.505 approximation, by suitably adapting and interpreting the powerful technique of Online Correlated Selection.

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Dynamic Pricing under a Static Calendar

Cited by 6 publications

References 30 publications

Static Pricing: Universal Guarantees for Reusable Resources

Static Pricing: Universal Guarantees for Reusable Resources

Multi-Stage and Multi-Customer Assortment Optimization With Inventory Constraints

Online Bipartite Matching with Reusable Resources

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