Pricing and Capacity Rationing for Rentals with Uncertain Durations

Gans, Noah; Savin, Sergei

doi:10.1287/mnsc.1060.0651

Cited by 75 publications

(66 citation statements)

References 38 publications

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“…We prove the lemma by showing that if condition (19) is satisfied then λ * s > 0 and if it is not then λ * s = 0, i.e., there is no SU arrival and no profit is generated. Next, we analyze the expression…”

Section: Characterization Of the Profit Regions Of Static And Thrementioning

confidence: 96%

“…[19] analyzes a model similar to ours within the context of a generic rental management optimization problem. This work considers two type of customers, namely walk-in and contract users.…”

Section: Related Workmentioning

confidence: 99%

“…Contract users, on the other hand, have fixed prices and arrival rates which are analogous to our PUs. Different than our work, [19] focuses on determining structures of the optimal policy rather than providing a simple, near-optimal alternative as done here.…”

Section: Related Workmentioning

confidence: 99%

“…Proof: This lemma is obtained by applying Theorem 2 of [19] (see Section II). In order to apply results of [19] to our threshold model we assume that there are no walk-in users.…”

Section: Efficient Computation Of the Optimalmentioning

confidence: 99%

See 3 more Smart Citations

Spot Pricing of Secondary Spectrum Access in Wireless Cellular Networks

Mutlu

Alanyali

Starobinski

2009

IEEE/ACM Trans. Networking

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Abstract-Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this paper, we investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users. We first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, we investigate the design of efficient single pricing policies. We provide numerical and analytical evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of different pricing policies, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we prove that the profit region of threshold pricing is optimal and independent of the specific form of the demand function, and that it includes the profit region of static pricing. In addition, we show that the profit function of threshold pricing is unimodal in price. We determine a restricted interval in which the optimal threshold lies. These properties enable very efficient computation of the optimal threshold policy, which is far faster than that of the global optimal policy.

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Section: Characterization Of the Profit Regions Of Static And Thrementioning

confidence: 96%

“…[19] analyzes a model similar to ours within the context of a generic rental management optimization problem. This work considers two type of customers, namely walk-in and contract users.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…Proof: This lemma is obtained by applying Theorem 2 of [19] (see Section II). In order to apply results of [19] to our threshold model we assume that there are no walk-in users.…”

Section: Efficient Computation Of the Optimalmentioning

confidence: 99%

See 2 more Smart Citations

Spot Pricing of Secondary Spectrum Access in Wireless Cellular Networks

Mutlu

Alanyali

Starobinski

2009

IEEE/ACM Trans. Networking

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“…Extending this model to account for a compound Poisson arrival process, Papier and Thonemann (2008) conduct a stationary queueing analysis to obtain structural results for a fleet sizing problem and provide an approximation suitable for implementation. The use of the M/M/c/c or M/G/c/c queueing model as a basis for studying capacity management for rental systems further follows in Savin et al (2005), Gans andSavin (2007), Adelman (2008), Hampshire et al (2009), and Levi and Shi (2011). However, our work is different from this stream of research by our consideration of a discrete-time rental model with a finite rental season, random usage-based inventory loss, and an arbitrary demand model possessing the ability to capture any distributional characteristic.…”

Section: Literature Reviewmentioning

confidence: 99%

Managing Rentals with Usage-Based Loss

Slaugh

Biller

Tayur

2016

M&SOM

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Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different "recirculation" rules -i.e., which rental unit to choose to meet each demand -we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens.We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic.Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

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Optimal admission and pricing control problems in service industries with multiple servers and sideline profit

Son¹,

Ghamari²

2008

Appl Stoch Models Bus & Ind

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This paper deals with the problem of selecting profitable customer orders sequentially arriving at a company operating in service industries with multiple servers in which two classes of services are provided. The first class of service is designed to meet the particular needs of customers; and the company (1) makes a decision on whether to accept or to reject the order for this service (admission control) and (2) decides a price of the order and offers it to an arriving customer (pricing control). The second class of service is provided as a sideline, which prevents servers from being idle when the number of customer orders for the first class is less than the number of servers. This yields the sideline profit. A cost is paid to search for customer orders, which is called the search cost. In the context of search cost, the company has an option whether to conduct the search or not. In this paper, we discuss both admission control and pricing control problems within an identical framework as well as examine the structure of the optimal policies to maximize the total expected net profit gained over an infinite planning horizon. We show that when the sideline profit is large, the optimal policies may not be monotone in the number of customer orders in the system. OPTIMAL ADMISSION AND PRICING CONTROL PROBLEMS ‡ There exists a finite x )x , then z(x) = (>)a (see [26]). If F(w) is a uniform distribution on [a, b] with 0

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Pricing and Capacity Rationing for Rentals with Uncertain Durations

Cited by 75 publications

References 38 publications

Spot Pricing of Secondary Spectrum Access in Wireless Cellular Networks

Spot Pricing of Secondary Spectrum Access in Wireless Cellular Networks

Managing Rentals with Usage-Based Loss

Optimal admission and pricing control problems in service industries with multiple servers and sideline profit

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