Hybrid Simulation/Analytic Models for Military Supply Chain Performance Analysis

1. CELDi Center for Engineering Logistics & Distribution Hybrid Simulation/Analytic Models for Military Supply Chain Performance Analysis Research Program Review ASC PA 03-2418 9/15/03

2. Researcher Manuel D. Rossetti, Ph. D., P.E. Associate Professor Department of Industrial Engineering University of Arkansas

3. Research Team

4. Project Description • Hybrid models combine simulation and analytic models, improving computational efficiency • Use hybrid simulation/analytic models to efficiently predict the resulting performance of various logistical planning scenarios • Check the predicted results for accuracy and precision • Goal: To examine the feasibility of utilizing hybrid simulation/analytic techniques within logistical performance analysis in order to speed up the execution of logistical planning while maintaining the accuracy and precision of the performance predictions

5. Project Progress *** Completed *** Scheduled

6. Military Model Network Review (Fall 2002) • Multi-indenture, multi-echelon (MIME) spare parts inventory system conceptualized as a stochastic processing network • Hybrid simulation/analytic models consists of: • Operational/production components – use constraining resources to perform operations on units of work that flow through the system • Transportation components – involved in the movement of work within the system • Storage components – hold intermediate work products to gain efficiency in the use of timing of operational and transportation • Components constitute a queuing system, or more generally, a stochastic processing network

7. Military Supply Chain Incurred flight hours cause parts to fail 1. Aircraft are assigned sorties to fly 2. (Fall 2002) 3. Failed parts are sent for repair Base 5. Spare part from inventory replaces failed part on aircraft Inventory Warehouses D I D-level I-level O-level O 4. Repaired parts go into inventory

8. Analytical Approach Analytical models of queuing and inventory systems, useful in analyzing and predicting logistic system performance, face two challenges: • The inability to adequately represent complex routing and scheduling • Detailed mathematical representations cause difficulty to compute theoretical results Discrete event simulation can address these problems while being more amenable to address the requirements of real world logistical planners.

9. Combining Analytical and Simulation Models Analytic model Numerical output Inputs Military supply chain system Results used for problem solving Discrete-event simulation model

10. Combining Analytical and Simulation Models Major Research Questions: • What types of single station approximations are the most appropriate? • How can better, more robust, single station approximations be developed? • How can the single station approximations be combined to model logistical networks? • How can the analytical methods be properly combined with simulation techniques in the most appropriate manner? • What is the accuracy and precision of these techniques?

11. Performance Metric Identification (Fall 2002) Based on Whitt (1993), the following metrics will be used to evaluate the validity of the queuing station simulation: • E[W] - Expected Waiting Time • E[B] - Expected Number of Busy Servers • E[Q] - Expected Queue Length • E[N] - Expected Number of Customers in the System • E[T] - Expected Time in System Absolute Difference & Relative Percentage Error are used as Performance Metrics of the approximations. Additional metrics for the logistical network level are being investigated.

12. Literature Review (Fall 2002 - Spring 2003) • Topics covered: • Advantages and disadvantages of hybrid simulation • Applications of hybrid simulations • Analytical methods including: • Whitt’s 1983 QNA model • Whitt’s 1993 model • Springer and Maken’s model • Neural network methods • 52 pieces of literature reviewed

13. Literature Review Highlights • Analytical modeling is used for steady-state systems, while simulations are for systems with dynamic variability (Kaplan 2001) • Hybrid simulations trade reduced variance and improved efficiency for decreased flexibility (Frost and Shanumgan 1986) • Hybrid simulations have been used in less than truckload transportation networks (Simao and Powell 1992), data communication networks (Frost and Shanumgan), and to reduce variation in mean time to failure rates (Shahabuddin 1988) • Whitt’s (1983) QNA software approximates the congestion for a network of queues

14. Hybrid/Simulation Model Development (Summer 2003) • Decompose logistical network into subcomponents • Apply the modeling technique which is most appropriate to each subcomponent • Build simulation models to mimic appropriate subcomponents • Compare performance metrics of the simulation model to analytic single station queue processes (Whitt 1993)

15. Single Station Approximations • Build single station models that will serve as the underlying analytical approximations within the network • Begin with single station queues based on Whitt’s 1993 approximations • Models built in Arena 7.0 • Single station models are flexible; can simulate different distributions • Expand single station processes into an entire logistical network

16. Neural Networks • Research will investigate the use of neural networks to improve the approximations of underlying analytical models • Neural networks can be trained on observations from simulations and analytical approximations to predict queuing metrics • May eventually approximate metrics for queues with no known analytic approximation • Can “correct” for discrepancies in an approximate queuing model WANA - Based on analytic approximation WSIM - Based on observations from simulation E[W] - Base on neural network WANA Neural Network E[W] WSIM

17. Logistic Network Approximations To integrate the analytical models with simulation, given the network topology, demand characterization, and resource configuration, the basic method is to: 1) Randomly generate snapshots of demand at an instant in time, 2) Simulate the routing and resource scheduling allocation, and load assignment for each of the demands generated, 3) Load or reject each demand based on the routing and scheduling analysis, 4) Update the state of the network prior to evaluating each demand, 5) Exhaust the list of potential demands in the snapshot, 6) Model the performance of the state of the network at the network, delivery, and resource levels, 7) Summarize the performance measures over multiple snapshots, and 8) Report statistics from the modeled network.

18. Prototype Software Development (Summer 2003 – Fall 2003) • This task is currently just beginning • The purpose of this task will be to develop software that encapsulates the hybrid modeling ideas examined during the research • Implement the approximations • Single station • Network • Implement the combined analytic/simulation approach • Provide for testing and experimentation

19. Verification, Validation, & Testing (Summer 2003 – Fall 2003) • Compare metrics captured from the simulation models to approximations presented in Whitt (1993) • Metrics compared include: • E[W] - Expected Waiting Time • E[B] - Expected Number of Busy Servers • E[Q] - Expected Queue Length • E[T] - Expected Time in System • Additional system wide metrics will be compared • Validated models can be modified to simulate different approximations

20. Model Documentation and Final Report (Fall 2003 – Spring 2004) • Present documentation of hybrid models • Present data on the accuracy and precision of the models • Compare the hybrid models to pure simulation models to assess the efficiency of hybrid models • Use performance metrics and compared efficiency to assess the feasibility of utilizing hybrid techniques within a logistical performance analysis in order to speed up the execution of logistical planning

21. Questions?