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1. Pricing Strategies in Stochastic Systems with Customer Reneging

   Di, Jieqi; Andradóttir, Sigrún; Ayhan, Hayriye (June 2025, Proceedings of the IISE Annual Conference & Expo 2025)

   Gentry, E; Ju, F; Liu, X (Ed.)

   This research investigates optimal pricing strategies in a service-providing queueing system where customers may renege before service completion. Prices are quoted upon customer arrivals and the incoming customers join the system if their willingness to pay exceeds the quoted price. While waiting in line or during service, customers may get impatient and leave without service, incurring an abandonment cost. There is also a per-unit time per-customer holding cost. Our objective is to maximize the long-run average profit through optimal pricing policies. We model the problem as a Markov decision process and identify the optimal pricing using policy iteration. We also study the structure of the optimal pricing policy. Furthermore, we show that under mild assumptions, the optimal price increases as the number of customers in the system increases. When those assumptions do not hold, optimal price decreases and then increases as the number of customers in the system grows. 

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2. Pricing Strategies in Stochastic Systems with Customer Reneging

   Di, Jieqi; Andradóttir, Sigrún; Ayhan, Hayriye (June 2025, Proceedings of the IISE Annual Conference & Expo 2025)

   Gentry, E; Ju, F; Liu, X (Ed.)

   This research investigates optimal pricing strategies in a service-providing queueing system where customers may renege before service completion. Prices are quoted upon customer arrivals and the incoming customers join the system if their willingness to pay exceeds the quoted price. While waiting in line or during service, customers may get impatient and leave without service, incurring an abandonment cost. There is also a per-unit time per-customer holding cost. Our objective is to maximize the long-run average profit through optimal pricing policies. We model the problem as a Markov decision process and identify the optimal pricing using policy iteration. We also study the structure of the optimal pricing policy. Furthermore, we show that under mild assumptions, the optimal price increases as the number of customers in the system increases. When those assumptions do not hold, optimal price decreases and then increases as the number of customers in the system grows. 

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3. Managing Queues with Different Resource Requirements

   https://doi.org/10.1287/opre.2022.2284  

   Zychlinski, Noa; Chan, Carri W.; Dong, Jing (July 2022, Operations Research)

   Queueing models that are used to capture various service settings typically assume that customers require a single unit of resource (server) to be processed. However, there are many service settings where such an assumption may fail to capture the heterogeneity in resource requirements of different customers. We propose a multiserver queueing model with multiple customer classes in which customers from different classes may require different amounts of resources to be served. We study the optimal scheduling policy for such systems. To balance holding costs, service rates, resource requirement, and priority-induced idleness, we develop an index-based policy that we refer to as the idle-avoid [Formula: see text] rule. For a two-class two-server model, where policy-induced idleness can have a big impact on system performance, we characterize cases where the idle-avoid [Formula: see text] rule is optimal. In other cases, we establish a uniform performance bound on the amount of suboptimality incurred by the idle-avoid [Formula: see text] rule. For general multiclass multiserver queues, we establish the asymptotic optimality of the idle-avoid [Formula: see text] rule in the many-server regime. For long-time horizons, we show that the idle-avoid [Formula: see text] is throughput optimal. Our theoretical results, along with numerical experiments, provide support for the good and robust performance of the proposed policy. 

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4. Technical Note—Static Pricing: Universal Guarantees for Reusable Resources

   https://doi.org/10.1287/opre.2020.2054  

   Besbes, Omar; Elmachtoub, Adam N.; Sun, Yunjie (March 2022, Operations Research)

   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 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, although 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. Our proof technique relies on a judicious construction of a static price that is derived directly from the optimal dynamic pricing policy. In the special case in which 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 test bed 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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5. Blind Dynamic Resource Allocation in Closed Networks via Mirror Backpressure

   https://doi.org/10.1287/mnsc.2023.4934  

   Kanoria, Yash; Qian, Pengyu (September 2023, Management Science)

   We study the problem of maximizing payoff generated over a period of time in a general class of closed queueing networks with a finite, fixed number of supply units that circulate in the system. Demand arrives stochastically, and serving a demand unit (customer) causes a supply unit to relocate from the “origin” to the “destination” of the customer. The key challenge is to manage the distribution of supply in the network. We consider general controls including customer entry control, pricing, and assignment. Motivating applications include shared transportation platforms and scrip systems. Inspired by the mirror descent algorithm for optimization and the backpressure policy for network control, we introduce a rich family of mirror backpressure (MBP) control policies. The MBP policies are simple and practical and crucially do not need any statistical knowledge of the demand (customer) arrival rates (these rates are permitted to vary in time). Under mild conditions, we propose MBP policies that are provably near optimal. Specifically, our policies lose at most [Formula: see text] payoff per customer relative to the optimal policy that knows the demand arrival rates, where K is the number of supply units, T is the total number of customers over the time horizon, and η is the demand process’ average rate of change per customer arrival. An adaptation of MBP is found to perform well in numerical experiments based on data from NYC Cab. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Funding: Y. Kanoria was supported by the National Science Foundation’s Division of Civil, Mechanical, and Manufacturing Innovation [Grant CMMI-1653477]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4934 . 

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