## 28. Simulation

• Some complex systems can’t be modeled because of,

- random events

- changing operating conditions

- too many interactions

- exact solutions don’t exist

• Simulation is used to determine how these systems will behave

• Simulation typically involves developing a model that includes discrete stations and events that occur with some probable distribution.

• We can then examine the simulation results to evaluate the modeled system. Examples include,

- machine utilization

- down time

- etc.

• This is a very effective tool when considering the effect of a change, comparing decision options, or refining a design.

• Some simulation terms include,

System - the real collection of components

Model - a reasonable mathematically (simpler) representation of the system

State - the model undergoes discrete changes. A state is a ‘snapshot’ of the system

Entity - a part of the system (eg machine tool)

Attributes - the behavior of an entity

Event - something that changes the state of a machine

Activity - when an entity is going through some activity. (eg, press cycling)

Delay - a period of time with no activity

• Good approach to simulation,

1. Determine what the problem is

2. Set objectives for the simulation

3. Build a model and collect data

4. Enter the model into a simulation package

5. Verify the model then check for validity

6. Design experiments to achieve goals

7. Run simulations and collect results

8. Analyze and make decisions

### 28.1 Model Building

• If we are building a model for a plant floor layout, we will tend to have certain elements,

- material handling paths (transfer)

- buffers/waiting areas (delays)

- stock rooms (source)

- shipping rooms (destination)

- machine tools (activities)

• Some of these actions can be stated as exact. For example, a transfer time can be approximated and random (manual labor), or exact (synchronous line), or proportional to a distance.

• Some events will occur based on availability. For example, if there are parts in a buffer, a machine tool can be loaded and activity occurs.

• Some activities and events will be subject to probabilities. Consider that the operation time in a press may vary, and there is probability of scrapping a part.

• The random variations can be modeled as,

- discrete - for individual units

- continuous for variations

• Well known distributions include,

• This data may be found using data provided by the manufacturer, sampled in-house, etc.

### 28.2 Analysis

• To meet goals, simple tests may be devised. These tests should be formulated as hypotheses. We can then relate these to the simulation results using correlation.

• Simulation software will provide information such as,

- production rates

- machine usage

- buffer size

- work in process

### 28.3 Design of Experiments

• WHAT? combinations of individual parameters for process control are varied, and their effect on the output quality are measured. From this we determine the sensitivity of the process to each parameter.

• WHY? Because randomly varying individual parameters takes too long.

• e.g. A One-Factor-At-A-Time-Experiment

• The example shows how the number of samples grows quickly.

• A better approach is designed experiments

• e.g. DESIGNED EXPERIMENT for springs in last section

### 28.4 Running the Simulation

• When a simulation is first run it will be empty. If it is allowed to run for a while it will settle down to a steady state. We will typically want to,

- run the simulation for a long time

- or, delay the start of data collection

- or, preload the system will parts

### 28.5 Decision Making Strategy

• The general sequence of thought when making decisions is,

- purpose

- direction

- plans

- action

- results

• General properties of strategy include,

- time horizon

- impact

- concentration of effort

- patterns of decisions

- pervasiveness

• The levels of strategies include,

- corporate

- departmental/functional

• Decisions can be categorized,

hardware/fixed

- capacity

- facilities

- technology

- vertical integration

software/flexible

- workforce

- quality

- production planning/material control

- organization

• Typical criteria for making decisions might include,

- consistency

- harmony

- contribution