Performance Analysis and Optimization of Inbound Call Centers

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.