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Performance Analysis and Optimization of Inbound Call Centers


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April 2003

Beschreibung

Beschreibung

The material presented in this book is a result of my work in the field of call center management during the period 1999-2002. The focus is on the perfor­ mance analysis and optimization of inbound call centers. Since call arrivals and call-handling times are often random in inbound call centers, this thesis concentrates on the performance analysis and optimization using queueing models. This book describes mathematical methods and algorithms to relate the number of agents and telephone trunks of a given call center configuration to technical as well as economic performance measures. This book has been accepted as a PhD thesis in Business Administration at the Technical University of Clausthal, Germany. I am indebted to many people for their support during the process of writing this thesis. First of all, I would like to thank my advisor, Prof. Dr. Stefan Helber, for motivating my research to call center related problems. He gently pushed me in fruitful directions and encouraged me to strike a balance between mathematical results and economic implications. Many other helpful suggestions came from him, and his constructive comments on draft versions of this book are invaluable. I am thankful to him and to Prof. Dr. Rolf Schwinn for refereeing this thesis.

Inhaltsverzeichnis

1 Introduction.
2 Characterization of Inbound Call Centers.
2.1 What is an Inbound Call Center?.
2.2 Performance Measures and Objective Functions.
2.2.1 Technical Performance Measures.
2.2.2 Economic Performance Measures.
2.2.3 Objective Functions for Operational Planning.
2.3 Operational Personnel Planning in Inbound Call Centers.
2.3.1 Main Tasks of Operational Personnel Planning.
2.3.2 Call Forecasting.
2.3.3 Weekly Personnel Scheduling.
2.3.3.1 Current Planning Process in Practice.
2.3.3.2 Agent Requirements Planning.
2.3.3.3 Shift Scheduling and Rostering.
2.3.3.4 A Simultaneous Planning Approach.
3 Classification of Queueing Models of Inbound Call Centers.
3.1 Characteristics of Queueing Models of Call Centers.
3.2 Classification by Customers and Agents.
3.2.1 Arrival Process.
3.2.2 Waiting Behavior.
3.2.3 Distribution of Service Time.
3.2.4 Homogeneity of Customers and Agents.
3.3 Routing Decisions in Call Centers.
3.3.1 Overview.
3.3.2 Customer Selection.
3.3.3 Agent Selection.
3.4 Limitation of the Waiting Room.
3.5 Review of the Literature.
3.5.1 Overview.
3.5.2 Homogeneous Customers and Homogeneous Agents.
3.5.3 Heterogeneous Customers and Heterogeneous Agents.
3.5.3.1 Introduction of the M-Design.
3.5.3.2 The M-Design with Priority-Based Routing Policies.
3.5.3.3 Special Cases of the M-Design with Priority-Based Routing Policies.
4 Queueing Models of Call Centers with Homogeneous Customers and Homogeneous Agents.
4.1 Common Features.
4.2 The M /M/c and M /M/c/K Queueing Models with Patient Customers.
4.2.1 Description and Derivation of Performance Measures for the M /M/c/K Queueing Model.
4.2.2 Description and Derivation of Performance Measures for the M /M/c/00 Queueing Model.
4.2.3 Numerical Results.
4.2.3.1 Impact of the Number of Trunks.
4.2.3.2 Economies of Scale.
4.2.3.3 Impact of Talk Time.
4.2.3.4 Optimal Number of Agents and Trunks in Large Call Centers.
4.3 An M /M/c/K Queueing Model with Impatient Customers.
4.3.1 Model Description and Derivation of Performance Measures.
4.3.2 Numerical Results.
4.3.2.1 Impact of Customer Impatience: Reneging 8.
4.3.2.2 Impact of Customer Impatience: Balking 8.
4.3.2.3 Impact of Customer Impatience: Dependencies between Reneging and Balking 8.
4.3.2.4 Optimal Number of Agents and the Impact of the Number of Trunks 9.
4.4 Management Implications of the Numerical Results.
5 Queueing Model of a Call Center with two Classes of Customers and Skill-Based Routing.
5.1 Description of the Queueing System.
5.2 Description of the State Space.
5.2.1 Representation of the States.
5.2.2 Division and Size of the State Space.
5.3 Steady-State Equations.
5.3.1 Steady-State Equations for States with Waiting Aand B-Customers.
5.3.2 Steady-State Equations for States with Waiting Aand without Waiting B-Customers.
5.3.3 Steady-State Equations for States with Waiting Band without Waiting A-Customers.
5.3.4 Steady-State Equations for States without Waiting Customers.
5.4 Determination of Performance Measures.
5.4.1 Solution of the Steady-State Equations.
5.4.2 Derivation of Technical Performance Measures.
5.4.3 Validation of the Derivation for Special Cases.
5.5 Numerical Results.
5.5.1 Impact of Flexible Agents: Effects of Priority-Based Customer Selection and Pooling.
5.5.1.1 Impact of Priority-Based Customer Selection.
5.5.1.2 Comparison of Call Centers with Completely Crosstrained or Completely Specialized Agents.
5.5.1.3 Advantages of Adding Generalists Instead of Specialists.
5.5.2 Impact of the Processing Times of Generalists.
5.5.3 Impact of the Allocation of Trunks.
5.5.4 Impact of the Allocation of a Fixed Number of Agents.
5.5.4.1 Identically Distributed Processing Times for Specialists and Generalists.
5.5.4.2 Different Processing Times for Generalists and Specialists.
5.6 Management Implications of the Numerical Results.
6 Conclusions and Suggestions for Further Research.
A Algorithms for Call Center Models with Homogeneous Customers and Agents.
A.1 Computations for the M /M/c/K Model with Patient Customers.
A.2 Computations for the M /M/ c/00 Model with Patient Customers.
A.3 Computations for the M /M/c/K Model with Impatient Customers.
A.3.1 Computation of Steady-State Probabilities.
A.3.2 Computation of the Waiting Time Distributions.
B Appendix for the Queueing Model of a Call Center with two Classes of Customers and Skill-Based Routing.
B.1 Derivation of the Number of States.
B.2 Derivation of the Remaining Steady-State Equations.
B.2.1 Steady-State Equations for States with Waiting Aand without Waiting B-Customers.
B.2.2 Steady-State Equations for States with Waiting Band without Waiting A-Customers.
B.2.3 Steady-State Equations for States without Waiting Customers.
B.3 Algorithms Used for Performance Analysis.
B.3.1 Description of Data Structures and Algorithms.
B.3.2 Behavior of the Algorithm.
Glossary of Notation.
List of Figures.
List of Tables.
References.
EAN: 9783540008125
ISBN: 3540008128
Untertitel: 'Lecture Notes in Economics and Mathematical Systems'. Softcover reprint of the original 1st ed. 2003. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: April 2003
Seitenanzahl: 236 Seiten
Format: kartoniert
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