More About Simulation

MORE ABOUT SIMULATION THE ART OF MODELING  The art of modeling may be applied to simulation models and also to all the many other types of models.  As we have seen previously, every field of human endeavor requires us to process raw data into information. In any modeling effort, abstraction...

MORE ABOUT SIMULATION THE ART OF MODELING  The art of modeling may be applied to simulation models and also to all the many other types of models.  As we have seen previously, every field of human endeavor requires us to process raw data into information. In any modeling effort, abstraction and structure are important universal features. These two related concepts are involved in the reduction and management of complexity.  Modeling is an art which requires the ability to: 1. Analyze a problem 2. Abstract from it its essential features 3. Select and modify basic assumptions – and test them! – that characterize the system 4. Then, enrich and elaborate until a useful approximation results. Provide a real-life example of a system that could be modeled and simulated? Supermarket? traffic patterns in a city? MORE ABOUT MODELING & SIMULATION 2 SUPERMARKET Abstraction: Customers entering and exiting the supermarket Checkout counters where customers pay for their items Shelves and aisles where products are displayed Inventory management and restocking processes Reduction: Customer management (e.g., queuing, checkout) Inventory management (e.g., stocking, ordering, pricing) Facility management (e.g., floor layout, lighting, temperature control) Employee management (e.g., scheduling, training, task assignment) MORE ABOUT MODELING & SIMULATION 3 HOW TO MODEL SOME GUIDELINES To simplify: Factor the system problem into simpler problems 1. make variables into constants 2. eliminate or combine variables Establish a clear statement of the objectives 3. assume linearity Seek analogies 4. add stronger assumptions and Consider a specific numerical instance of restrictions the problem 5. restrict the boundaries of the system Establish some symbols Write down the obvious To enrich, do the opposite. If a tractable model is obtained, enrich it. otherwise, simplify. MORE ABOUT MODELING & SIMULATION 4 ELEVATOR To simplify the model, the modeler could make variables like the number of floors or the average passenger weight into constants, eliminate variables like the time it takes for passengers to enter and exit, and restrict the boundaries of the system to only include the elevator itself, ignoring external factors. MORE ABOUT MODELING & SIMULATION 5 PATIENTS FLOW IN THE EMERGENCY ROOM  Factor the problem into simpler sub-problems, such as patient arrival, triage, treatment, and discharge.  Establish clear objectives, such as minimizing patient wait times or maximizing resource utilization.  Seek analogies to other queuing systems, such as a bank or a supermarket checkout line.  Consider a specific instance, such as a hospital with a known number of beds and typical patient arrival rates.  Establish symbols for the various entities (patients, staff, rooms, etc.) and processes.  Write down the obvious, such as the fact that patients must be triaged before treatment.  Iteratively simplify and enrich the model to achieve a useful approximation of the real system. MORE ABOUT MODELING & SIMULATION 6  Commercial – barber shop, bank, supermarket, gas station. Transportation – toll booth, traffic light, ship EXAMPLES OF loading / unloading, parking lot, elevators, CitiBike. SYSTEMS TO Business to business – machine repair shop, SIMULATE inspection stations, secretarial pools. Social service: judicial system, legislative systems (bills waiting for processing), health- care systems, foster care / family court. MORE ABOUT SIMULATION 7 WHEN TO SIMULATE: SIMULATION VS. OTHER TECHNIQUES MORE ABOUT SIMULATION 8  Real vs. Simulation? WHEN TO USE SIMULATION? Analytic vs. Simulation? Consider using simulation when: It is desired to observe a simulated history of the process over a period of An analytic solution does not exist. time. Time compression may be required for The mathematics involved in the systems with long time frames. analytic solution are more complicated than simulation. “Real” physical experimentation is impossible, e.g., nonexistent system, An education and training tool is disruptive system, destructive testing. desired. MORE ABOUT SIMULATION 9 SIMULATION VS. ANALYTIC SOLUTION Which is better? Simulation has been used to verify hypothesized analytic models Why must we choose between them? Both Simulation has been used to test the techniques have accuracy of analytic models in which been used together. several simplifying assumptions had been made Simulation has been used to develop, and even suggest the form of, analytic models. MORE ABOUT SIMULATION 10 SIMULATION + ANALYTIC SOLUTION A real-life example where both simulation and an analytic solution could be used is modeling the inventory management system of a retail store. An analytic solution could be developed to optimize the ordering and stocking of certain products based on historical demand data. However, simulation could also be used to study the dynamic interactions between customer demand, inventory levels, and other factors over time, allowing the modeler to explore more complex scenarios that may not be easily captured in an analytic solution. MORE ABOUT SIMULATION 11 SIMULATION + ANALYTIC SOLUTION  THE METAMODEL A Metamodel is an analytic model that is developed using data generated from the simulation of the system of interest.  Metamodels have been used to o carry out sensitivity analysis, o answer “what-if” questions, o answer inverse questions o enhance the researcher’s understanding of the processes that move the system MORE ABOUT SIMULATION 12 SIMULATION + ANALYTIC SOLUTION  THE METAMODEL A real-life example could be modeling the energy consumption of a building. Simulation could be used to generate data on the building's energy usage under various conditions (e.g., occupancy, weather, HVAC settings). This data could then be used to develop a metamodel that predicts the building's energy consumption, allowing the building's managers to quickly explore the impact of potential changes without the need to re-run the full simulation. MORE ABOUT SIMULATION 13  SUPERMARKET METAMODEL  Entities: Customers Products Shelves Checkout Counters Inventory Employees  Attributes: Customer attributes: name, age, purchase history, loyalty points Product attributes: name, price, category, brand, quantity in stock Shelf attributes: location, capacity, product placement Checkout counter attributes: number of lanes, staffing, processing speed Inventory attributes: stock levels, reorder points, lead times Employee attributes: name, role, shift schedule, training  Relationships: Customers interact with Checkout Counters to make purchases Products are displayed on Shelves 14 Inventory tracks the quantities of Products Employees are assigned to Checkout Counters and manage Inventory  SUPERMARKET METAMODEL  Imagine a supermarket that wants to implement a new loyalty program for its customers. The metamodel would help the supermarket designers and developers to: 1. Identify the relevant entities (Customers, Loyalty Program, Rewards, etc.) and their attributes. 2. Understand the relationships between these entities (e.g., Customers can enroll in the Loyalty Program and earn Rewards). 3. Develop a conceptual model of the loyalty program system based on the metamodel. 4. Use the metamodel to guide the design and implementation of the loyalty program, ensuring it aligns with the overall supermarket system. 15 ABOUT THE SIMULATION STUDY MORE ABOUT SIMULATION 16 PROGRESS OF A SIMULATION STUDY Simulation is actually a full-scale system study with simulation at its core.  Problem definition: Define the scope and objectives of the simulation study. Identify the boundaries of the system under study. Eliminate that which is exogenous to it.  System analysis and design: Investigate the system under study. Identify the performance characteristics, i.e., SIMULATION the measures of effectiveness of the system. Identify the input variables relevant to the objectives of the investigation. Collect and analyze data. Where possible, fit the data to theoretical probability distributions. Identify the parameters of the processes involved, along with possible design points for the simulation experiment. MORE ABOUT SIMULATION 17 PROGRESS OF A SIMULATION STUDY  Model design: Design the simulation model. This will likely be a flowchart or some other type of abstract model. Test for validity, if at all possible, e.g., face validity, expert walk-throughs, etc.  Model building: Construct the simulation model. This step includes selecting an appropriate computer programming language, writing the code for the simulation program, verifying (debugging) the simulation program.  Model validation. Is the model a good approximation to the real system? The simulation model is validated by one or more a number of appropriate techniques, e.g., face validity, comparing simulation-generated data to real data from a similar system, etc. MORE ABOUT SIMULATION 18 PROGRESS OF A SIMULATION STUDY Once the modeling-related tasks are completed, the researcher will have a valid model (i.e., the computer program) with which to experiment. Simulation is an experimental methodology. As with any statistical experiment, careful attention must be paid to the design and analysis of simulation experiments. The goal of the design is to ensure that the experiment contains as much relevant information as possible subject, of course, to certain feasibility constraints (e.g., cost). The goal of the analysis is to extract as much information from the experiment as possible. MORE ABOUT SIMULATION 19 PROGRESS OF A SIMULATION STUDY  Experimental design: Strategic Planning. Guided by and depending upon the objectives of the simulation study — e.g., optimization, estimation, prediction — the simulation experiment is designed. Tactical concerns, e.g., run length, number of replications, variance reduction techniques, are decided.  Simulation: Run the simulation experiment under the design constraints previously decided upon.  Statistical analysis: Analysis and interpretation. Drawing inferences. Further statistical analysis, beyond the explicit definition and testing of a mathematical metamodel, may be required by the decision maker. MORE ABOUT SIMULATION 20 PROGRESS OF A SIMULATION STUDY  Decision making: Data generated by the simulation model have been transformed into information by the analysis phases. In a well- designed study, these results meet the objectives delineated in the problem definition phase. Use the results of the simulation study in making decisions.  Implementation: Putting the model and/or results to use. A simulation metamodel may continue to be used as a decision-making tool long after the simulation model itself is “put to bed.” MORE ABOUT SIMULATION 21  Better understanding of system processes Parameter estimation Some typical goals of Comparing alternative systems a simulation study Selecting the best system Ranking alternative systems Prediction Optimization Factor screening Determining functional relationships MORE ABOUT SIMULATION 22  Simple to understand by the user Goal or purpose directed Robust, in that it does not give absurd answers WHAT MAKES A GOOD Easy for the user to control and manipulate SIMULATION? Complete on important issues Adaptive, easy to modify or update Evolutionary - starts out simple and becomes 23 MORE ABOUT SIMULATION more complex CONCLUSION In this lecture we have learned some of the most critical aspects about simulation modeling and experimentation:  When to use simulation  Simulation vs. analytic solutions  The simulation model in the context of the greater statistical experiment  The steps in the progress of a simulation study  Objectives of a simulation study  What makes a good simulation MORE ABOUT SIMULATION 24