Modeling: Abstraction, Structure, and Reduction

• Modeling can be applied to simulation models and other model types.
• All fields require raw data to be processed into information.
• Important universal features of modeling include abstraction and structure
• Abstraction and structure reduce and manage complexity.
• Modeling requires the ability to analyze a problem and extract essential features

Modeling Steps:

• Select and modify assumptions characterizing the system, then test them.
• Enrich and elaborate the model until a useful approximation results.

Supermarket Abstraction Elements:

• Customers entering and exiting.
• Checkout counters for payments.
• Shelves and aisles for displaying products.
• Inventory and restocking processes.

Supermarket Reduction examples:

• Customer management involving queuing and checkout.
• Inventory management including stocking, ordering, and pricing.
• Facility management covering floor layout, lighting, and temperature control.
• Employee management related to scheduling, training, and task assignment.

How to Model:

• Break down the system problem into simpler sub-problems.
• Clearly define the objectives.
• Seek analogies and consider specific numerical instances.
• Establish symbols and write down obvious aspects.
• Enrich a model if tractable and simplify if not.

Simplifying a System:

• Turn variables into constants.
• Eliminate or combine variables.
• Assume linearity and add stronger assumptions/restrictions.
• Restrict the system's boundaries.
• Enrichment involves doing the opposite of simplification techniques.

Elevator as an Example:

• To simplify modeling, convert floors or passenger weight into constants.
• Eliminate variables like passenger entry/exit times, and limit the system to the elevator itself.

Modeling Patient Flow in an Emergency Room:

• Break the problem into sub-problems like patient arrival, triage, treatment, and discharge.
• Set clear objectives such as minimizing wait times or maximizing resource use.
• Use analogies to queuing systems like banks or supermarkets.
• Establish symbols for entities like patients, staff, and rooms.
• Write down the obvious components that needs to be triaged before treatment.
• Iteratively simplify and enrich model for a close real-world approximation.

Examples of Systems to Simulate:

• Commercial systems like barber shops, banks, supermarkets, and gas stations.
• Transportation systems, including toll booths, traffic lights, ship loading, parking lots, and elevators.
• Business-to-business systems like machine repair shops.
• Social service systems , legislative systems, and health-care systems.

When to use Simulation:

• Desired process history over time.
• Need for system time compression.
• Real experimentation is impossible.
• An analytic solution does not exist.
• Mathematics are too complicated.
• When Education and training are needed

Simulation vs. Analytic Solutions:

• Simulation can verify hypothesized analytic models, test the accuracy of models with simplifying assumptions, and develop or suggest analytic models.
• Inventory management in a retail store can be modeled through simulation and analytic solutions.

Simulation and Analytic Solution:

• A real-life example of both simulation and an analytic solution being implemented could modelling and developing the inventory management system of a retail store.
• A simulation could study customer demand, inventory levels, and other factors.
• A metamodel is an analytic model using data from system simulations.

Metamodels can enhance the researcher's understanding by:

• Performing sensitivity analysis
• Answering "what-if" and inverse questions.
• An example of a metamodel application is modeling building energy consumption.
• Simulation data on energy usage under different conditions can be used to create a metamodel predicting consumption and allow to explore potential changes.

Supermarket Metamodel:

• Entities include: Customers, Products, Shelves, Checkout Counters, Inventory, Employees
• Attributes: Customer attributes include name, age, purchase history, loyalty points; product attributes consist of name, price, category, brand, quantity inventory attributes comprise stock levels, reorder points, lead times.
• Relationship examples: Customers interact with Check-out Counters making purchases.

Supermarket Metamodel Scenario:

• A supermarket implements a new loyalty program. The metamodel helps system designers and developers identify entities, understand relationships, develop conceptual models, and guide program design.

Simulation Study Progress:

• The simulation is a system study with simulation at its core.
• Problem definition involves defining the scope, objectives and boundaries of the study.
• System analysis and design identifies performance characteristics and parameters.

Progress of a Simulation Study Steps:

• Design the simulation model as a flowchart (model design).
• Construct the model by selecting a language, coding, and debugging for verifying.
• Validate the model by comparing simulation data to real system data.

Progress of a Simulation Study details:

• With modeling tasks completed, the researcher has a valid computer program for experiments.
• Attention is paid to the design and analysis of the Simulation experiments.
• The goal of the design is to ensure the experiment contains all the relevant information. The goal of the analysis is to extract the information from the experiment

Progress of a Simulation Study further info:

• Experimental design involves strategic planning and selecting the appropriate simulation experiment in accordance the objectives of the simulation study.
• Simulation requires running under design constraints.
• Statistical analysis involves analyzing and interpreting the analyzed data.

More information on the Progress of a Simulation Study:

• Decision making involves transforming model data into information that meets problem-defined objectives.
• Implementation involves using the model or results where metamodels may be used as decision-making tools.

Typical Simulation Study Goals:

• Better understanding of system processes, or determine functional relationships.
• Compared to parameter estimation and comparing other techniques involve selecting the best system.
• Optimize prediction and factor screening.

Good Simulation Qualities:

• Simple to understand and goal-oriented; adaptive.
• Robust. Easy to control and complete.
• Evolutionary, starting simple and becoming more complex.

Aspects learned regarding simulation modeling and experimentation include:

• When to use simulation
• Simulation vs. analytic solutions
• Simulation study objectives.
• The use of a simulation model in the context of the greater statistical experiment
• The simulation progress and steps involved.
• The crucial properties for a simulation to be considered effective