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1. The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

   https://doi.org/10.1287/opre.2018.1839  

   Hochbaum, Dorit S. ; Rao, Xu ( September 2019 , Operations Research)

   The replenishment storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system, where each item has a given reorder size and cycle length. We consider the discrete RSP, where reorders can only take place at an integer time unit within the cycle. Discrete RSP was shown to be NP-hard for constant joint cycle length (the least common multiple of the length of all individual cycles). We show here that discrete RSP is weakly NP-hard for constant joint cycle length and prove that it is strongly NP-hard for nonconstant joint cycle length. For constant joint cycle-length discrete RSP, we further present a pseudopolynomial time algorithm that solves the problem optimally and the first known fully polynomial time approximation scheme (FPTAS) for the single-cycle RSP. The scheme is utilizing a new integer programming formulation of the problem that is introduced here. For the strongly NP-hard RSP with nonconstant joint cycle length, we provide a polynomial time approximation scheme (PTAS), which for any fixed [Formula: see text], provides a linear time [Formula: see text] approximate solution. The continuous RSP, where reorders can take place at any time within a cycle, seems (with our results) to bemore »easier than the respective discrete problem. We narrow the previously known complexity gap between the continuous and discrete versions of RSP for the multi-cycle RSP (with either constant or nonconstant cycle length) and the single-cycle RSP with constant cycle length and widen the gap for single-cycle RSP with nonconstant cycle length. For the multi-cycle case and constant joint cycle length, the complexity status of continuous RSP is open, whereas it is proved here that the discrete RSP is weakly NP-hard. Under our conjecture that the continuous RSP is easier than the discrete one, this implies that continuous RSP on multi-cycle and constant joint cycle length (currently of unknown complexity status) is at most weakly NP-hard.« less
2. 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, providemore »support for the good and robust performance of the proposed policy.« less
3. A Stochastic Analysis of Queues with Customer Choice and Delayed Information

   https://doi.org/10.1287/moor.2019.1024  

   Pender, Jamol ; Rand, Richard ; Wesson, Elizabeth ( August 2020 , Mathematics of Operations Research)

   Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] can be rigorously obtained as a functional law of large numbers limit of a stochastic queueing process, and we generalize their threshold analysis to arbitrary dimensions. Moreover, we prove amore »functional central limit theorem for the queue length process and show that the scaled queue length converges to a stochastic delay differential equation. Thus, our analysis sheds new insight on how delayed information can produce unexpected system dynamics.« less
4. Privacy-Preserving Dynamic Personalized Pricing with Demand Learning

   https://doi.org/10.1287/mnsc.2021.4129  

   Chen, Xi ; Simchi-Levi, David ; Wang, Yining ( October 2021 , Management Science)

   The prevalence of e-commerce has made customers’ detailed personal information readily accessible to retailers, and this information has been widely used in pricing decisions. When using personalized information, the question of how to protect the privacy of such information becomes a critical issue in practice. In this paper, we consider a dynamic pricing problem over T time periods with an unknown demand function of posted price and personalized information. At each time t, the retailer observes an arriving customer’s personal information and offers a price. The customer then makes the purchase decision, which will be utilized by the retailer to learn the underlying demand function. There is potentially a serious privacy concern during this process: a third-party agent might infer the personalized information and purchase decisions from price changes in the pricing system. Using the fundamental framework of differential privacy from computer science, we develop a privacy-preserving dynamic pricing policy, which tries to maximize the retailer revenue while avoiding information leakage of individual customer’s information and purchasing decisions. To this end, we first introduce a notion of anticipating [Formula: see text]-differential privacy that is tailored to the dynamic pricing problem. Our policy achieves both the privacy guarantee and the performancemore »guarantee in terms of regret. Roughly speaking, for d-dimensional personalized information, our algorithm achieves the expected regret at the order of [Formula: see text] when the customers’ information is adversarially chosen. For stochastic personalized information, the regret bound can be further improved to [Formula: see text]. This paper was accepted by J. George Shanthikumar, big data analytics.« less
5. Information Design in Service Systems and Online Markets

   Lingenbrink, David Alan ( January 2019 , ProQuest Dissertations & Theses A&I)

   In mechanism design, the firm has an advantage over its customers in its knowledge of the state of the system, which can affect the utilities of all players. This poses the question: how can the firm utilize that information (and not additional financial incentives) to persuade customers to take actions that lead to higher revenue (or other firm utility)? When the firm is constrained to "cheap talk," and cannot credibly commit to a manner of signaling, the firm cannot change customer behavior in a meaningful way. Instead, we allow firm to commit to how they will signal in advance. Customers can then trust the signals they receive and act on their realization. This thesis contains the work of three papers, each of which applies information design to service systems and online markets. We begin by examining how a firm could signal a queue's length to arriving, impatient customers in a service system. We show that the choice of an optimal signaling mechanism can be written as a infinite linear program and then show an intuitive form for its optimal solution. We show that with the optimal fixed price and optimal signaling, a firm can generate the same revenue as itmore »could with an observable queue and length-dependent variable prices. Next, we study demand and inventory signaling in online markets: customers make strategic purchasing decisions, knowing the price will decrease if an item does not sell out. The firm aims to convince customers to buy now at a higher price. We show that the optimal signaling mechanism is public, and sends all customers the same information. Finally, we consider customers whose ex ante utility is not simply their expected ex post utility, but instead a function of its distribution. We bound the number of signals needed for the firm to generate their optimal utility and provide a convex program reduction of the firm's problem.« less