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Convex Analysisの二,三の進展について

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value--and at the same time fundamentally limited--in their ability to characterize system performance.We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.

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Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects

Call centers are an increasingly important part of today's business world, employing millions of agents across the globe and serving as a primary customer-facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research.

In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.

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The Modern Call Center: A Multi-Disciplinary Perspective on Operations Management Research

Personnel scheduling: A literature review

We present an iterative cutting plane method for minimizing staffing costs in a service system subject to satisfying acceptable service level requirements over multiple time periods. We assume that the service level cannot be easily computed, and instead is evaluated using simulation. The simulation uses the method of common random numbers, so that the same sequence of random phenomena is observed when evaluating different staffing plans. In other words, we solve a sample average approximation problem. We establish convergence of the cutting plane method on a given sample average approximation. We also establish both convergence, and the rate of convergence, of the solutions to the sample average approximation to solutions of the original problem as the sample size increases. The cutting plane method relies on the service level functions being concave in the number of servers. We show how to verify this requirement as our algorithm proceeds. A numerical example showcases the properties of our method, and sheds light on when the concavity requirement can be expected to hold.

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Call Center Staffing with Simulation and Cutting Plane Methods

We consider the problem of minimizing staffing costs in an inbound call center, while maintaining an acceptable level of service in multiple time periods. The problem is complicated by the fact that staffing level in one time period can affect the service levels in subsequent periods. Moreover, staff schedules typically take the form of shifts covering several periods. Interactions between staffing levels in different time periods, as well as the impact of shift requirements on the staffing levels and cost, should be considered in the planning. Traditional staffing methods based on stationary queueing formulas do not take this into account. We present a simulation-based analytic center cutting-plane method to solve a sample average approximation of the problem. We establish convergence of the method when the service-level functions are discrete pseudoconcave. An extensive numerical study of a moderately large call center shows that the method is robust and, in most of the test cases, outperforms traditional staffing heuristics that are based on analytical queueing methods.

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Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods

We study the problem of approximating a subgradient of a convex (or concave) discrete function that is evaluated via simulation. This problem arises, for instance, in optimization problems such as finding the minimal cost staff schedule in a call center subject to a service level constraint. There, subgradient information can be used to significantly reduce the search space. The problem of approximating subgradients is closely related to the one of approximating gradients and we suggest and compare how three existing methods for computing gradients via simulation, i. e., finite differences, the likelihood ratio method and infinitesimal perturbation analysis, can be applied to approximate subgradients when the variables are discrete. We provide a computational study to highlight the properties of each approach.

Júlíus Atlason

Papers

Call Center Staffing with Simulation and Cutting Plane Methods

Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods

Customer relations management: service operations: using simulation to approximate subgradients of convex performance measures in service systems