ABSTRACT
CONTENTS 13.1 Introduction to Simulation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803 13.2 Problems Domains and Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805
13.2.1 Manufacturing and Service Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806 13.2.2 Communication and Transportation Networks . . . . . . . . . . . . . . . . . . . . . . . 808 13.2.3 Asset Valuation and Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809 13.2.4 Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 13.2.5 Selecting Input Distributions and Processes . . . . . . . . . . . . . . . . . . . . . . . . 811
13.3 Random Variates Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812 13.3.1 Linear Congruential Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813 13.3.2 Lagged Fibonacci Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813 13.3.3 Generation of Discrete Random Variates . . . . . . . . . . . . . . . . . . . . . . . . . . 814
13.3.3.1 n-Outcome Random Variate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814 13.3.3.2 Poisson Random Variate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815
13.3.4 Generation of Continuous Random Variates . . . . . . . . . . . . . . . . . . . . . . . . 815 13.3.4.1 Inverse Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816 13.3.4.2 Acceptance-Rejection Method . . . . . . . . . . . . . . . . . . . . . . . . . . 817 13.3.4.3 Normal Random Variate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818 13.3.4.4 Chi-Square and Other Random Variates . . . . . . . . . . . . . . . . . . . . 821
13.3.5 Testing Random Variates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821 13.3.5.1 Testing for Independence of Random Numbers . . . . . . . . . . . . . . . 821 13.3.5.2 Testing for Correctness of Distribution . . . . . . . . . . . . . . . . . . . . 823
13.4 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 13.4.1 Techniques for Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 13.4.2 Techniques for Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827
13.5 Simulation Output Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828 13.5.1 Descriptive Output Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829
13.5.1.1 Designing Simulation Run by Properties of Estimators . . . . . . . . . 830 13.5.2 Inferential Output Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831
13.6 Variance Reduction Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832 13.6.1 Control Variates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 13.6.2 Antithetic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837 13.6.3 Stratified Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 840 13.6.4 Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842 13.6.5 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843
13.7 Rare-Event Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844 13.7.1 Methodologies for Rare-Event Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 845
13.8 Simulation for Dynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 848
13.8.1 Euler Method for Solving Differential Equations . . . . . . . . . . . . . . . . . . . . . 849 13.8.2 Evaluating Simulation Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852
13.8.2.1 Convergence Properties of Solutions . . . . . . . . . . . . . . . . . . . . . . 852 13.8.2.2 Error Analysis: Absolute Error Criterion . . . . . . . . . . . . . . . . . . . 853 13.8.2.3 Error Analysis: Mean Error Criterion . . . . . . . . . . . . . . . . . . . . . 855
13.8.3 Estimating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857 13.8.4 Geometric Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857
13.8.4.1 Method of Maximum Likelihood . . . . . . . . . . . . . . . . . . . . . . . . 858 13.8.4.2 Method of Quasi-Maximum Likelihood . . . . . . . . . . . . . . . . . . . . 860
13.9 Stochastic Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 860 13.9.1 Basic Kriging Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861 13.9.2 Additional Issues and Applications of Kriging . . . . . . . . . . . . . . . . . . . . . . . 862
13.10 Simulation-Based Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 13.10.1 Challenges of Simulation-Based Optimization . . . . . . . . . . . . . . . . . . . . . . . 865 13.10.2 Simulation Optimization Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . 868 13.10.3 Continuous Simulation-Based Optimization . . . . . . . . . . . . . . . . . . . . . . . . 869
13.10.3.1 Gradient-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870 13.10.4 Global Optimization Approach for Simulation-Based Optimization . . . . . . . . 871
13.10.4.1 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871 13.10.4.2 Tabu Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872 13.10.4.3 Scatter Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873 13.10.4.4 Evolutionary Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874 13.10.4.5 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 875
13.11 Future Challenges for Simulation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876 13.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 878 13.13 Annotated Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 878
13.13.1 Conferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 13.13.2 Simulation Journals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 13.13.3 Simulation Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882
ABSTRACT Simulation modeling and analysis is a powerful suite of techniques for addressing a broad array of decision analytical problems. In this chapter, we highlight the most important aspects of the topic, taking advantage of prior development of discrete and continuous stochastic models in this book. Beginning with discussing model building for simulation analysis relevant in various application areas, we review the fundamentals of simulation in terms of random variates generation, model validation, and simulation output analysis. We consider manufacturing and service systems, where we are concerned with the optimal layout and configuration of manufacturing operations or service delivery setup for best-performance characteristics, or sensitivity analysis from changes made in layout or changes appearing due to breakdowns. The second application domain we consider is that of communication and transportation networks, where flow of entities is on a fixed infrastructure designed to meet customer demand, while satisfying “physical” constraints of the system. Therefore, capability analysis is often the motivation of evaluating such systems for meeting demand as well as quality of service delivered to customers. We finally consider two example application domains in banking and finance, one in asset valuation and allocation and the other in risk management. In the second part of the chapter, we delve into specialized topics of interest for a simulation study, such as variance reduction techniques, rare-event simulation, and stochastic Kriging. For a more sophisticated use of simulation modeling and analysis, we develop
modeling approaches for simulation of dynamic systems. Acknowledging that many decision analytics problems extend to assessing better or the best configurations of systems or ways of performing tasks, the chapter presents simulation-based optimization methodologies and techniques to address optimal decision-making problems. While we have initiated the chapter with several specific application domains where simulation modeling and analysis is extensively utilized, the entire chapter is interspersed with examples for making a stronger context for an analyst to benefit from the topics covered.
