A General Framework to Compare Announcement Accuracy: Static vs LES-based Announcement

Service providers often share delay information, in the form of delay announcements, with their customers. In practice, simple delay announcements, such as average waiting times or a weighted average of previously delayed customers, are often used. Our goal in this paper is to gain insight into when such announcements perform well. Specifically, we compare the accuracies of two announcements: (i) a static announcement that does not exploit real-time information about the state of the system and (ii) a dynamic announcement, specifically the last-to-enter-service (LES) announcement, which equals the delay of the last customer to have entered service at the time of the announcement. We propose a novel correlation-based approach that is theoretically appealing because it allows for a comparison of the accuracies of announcements across different queueing models, including multiclass models with a priority service discipline. It is also practically useful because estimating correlations is much easier than fitting an entire queueing model. Using a combination of queueing-theoretic analysis, real-life data analysis, and simulation, we analyze the performance of static and dynamic announcements and derive an appropriate weighted average of the two which we demonstrate has a superior performance using both simulation and data from a call center.

Does the Past Predict the Future? The Case of Delay Announcements in Service Systems

Motivated by the recent interest in making delay announcements in large service systems, such as call centers, we investigate the accuracy of announcing the waiting time of the Last customer to Enter Service (LES). In practice, customers typically respond to delay announcements by either balking or by becoming more or less impatient, and their response alters system performance. We study the accuracy of the LES announcement in single-class multi-server Markovian queueing models with announcement-dependent customer behavior. We show that, interestingly, even in this stylized setting, the LES announcement may not always be accurate. This motivates the need to study its accuracy carefully, and to determine conditions under which it is accurate. Since the direct analysis of the system with customer response is prohibitively difficult, we focus on many-server heavy-traffic analysis instead. We consider the quality-and-efficiency-driven (QED) and the efficiency-driven (ED) many-server heavy-traffic regimes and prove, under both regimes, that the LES prediction is asymptotically accurate if, and only if, asymptotic fluctuations in the queue length process are small as long as some regulatory conditions apply. This result provides an easy check for the accuracy of LES in practice. We supplement our theoretical results with an extensive simulation study to generate practical managerial insights

Staffing a Call Center with Uncertain Arrival Rate and Absenteeism

This paper proposes simple methods for staffing a single-class call center with uncertain arrival rate and uncertain staffing due to employee absenteeism. The arrival rate and the proportion of servers present are treated as random variables. The basic model is a multi-server queue with customer abandonment, allowing non-exponential service-time and time-to-abandon distributions. The goal is to maximize the expected net return, given throughput benefit and server, customer-abandonment and customer-waiting costs, but attention is also given to the standard deviation of the return. The approach is to approximate the performance and the net return, conditional on the random model-parameter vector, and then uncondition to get the desired results. Two recently-developed approximations are used for the conditional performance measures: first, a deterministic fluid approximation and, second, a numerical algorithm based on a purely Markovian birth-and-death model, having state-dependent death rates

Manufacturing and Supply Chain Flexibility: Building an Integrative Conceptual Model Through Systematic Literature Review and Bibliometric Analysis

The purpose of this study is twofold: first, to establish the current themes on the topic of manufacturing and supply chain flexibility (MSCF), assess their level of maturity in relation to each other, identify the emerging ones and reflect on how they can inform each other, and second, to develop a conceptual model of MSCF that links different themes connect and highlight future research opportunities. The study builds on a sample of 222 articles published from 1996 to 2018 in international, peer-reviewed journals. The analysis of the sample involves two complementary approaches: the co-word technique to identify the thematic clusters as well as their relative standing and a critical reflection on the papers to explain the intellectual content of these thematic clusters. The results of the co-word analysis show that MSCF is a dynamic topic with a rich and complex structure that comprises five thematic clusters. The value chain, capability and volatility clusters showed research topics that were taking a central role in the discussion on MSCF but were not mature yet. The SC purchasing practices and SC planning clusters involved work that was more focused and could be considered more mature. These clusters were then integrated in a framework that built on the competence–capability perspective and identified the major structural and infrastructural elements of MSCF as well as its antecedents and consequences. This paper proposes an integrative framework helping managers keep track the various decisions they need to make to increase flexibility from the viewpoint of the entire value chain

Pointwise Stationary Fluid Models for Stochastic Processing Networks

Generalizing earlier work on staffing and routing in telephone call centers, we consider a processing network model with large server pools and doubly stochastic input flows. In this model the processing of a job may involve several distinct operations. Alternative processing modes are also allowed. Given a finite planning horizon, attention is focused on the two-level problem of capacity choice and dynamic system control. A pointwise stationary fluid model (PSFM) is used to approximate system dynamics, which allows development of practical policies with a manageable computational burden. Earlier work in more restrictive settings suggests that our method is asymptotically optimal in a parameter regime of practical interest, but this paper contains no formal limit theory. Rather, it develops a PSFM calculus that is broadly accessible, with an emphasis on modeling and practical computation.admission control, dynamic routing, doubly stochastic arrivals, approximation, pointwise stationary, fluid models, abandonments, stochastic networks

Optimal Flexibility Configurations in Newsvendor Networks: Going Beyond Chaining and Pairing

We study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment. The resources differ by their level of flexibility, where "level-k flexibility" refers to the ability to process k different product types. We present an exact set-theoretic methodology to analyze newsvendor networks with multiple products and parallel resources. This simple approach is sufficiently powerful to prove that (i) flexibility exhibits decreasing returns and (ii) the optimal portfolio will invest in at most two, adjacent levels of flexibility in symmetric systems, and to characterize (iii) the optimal flexibility configuration for asymmetric systems as well. The optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature. For example, although chaining is not optimal in our setting, the gap is small and the inclusion of scale economies quickly favors chaining over pairing. We also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty.inventory production, stochastic models, programming, linear, applications, queues, networks, flexibility, newsvendor networks