Advanced Engineering Management Science Review Flashcards

This set covers vocabulary and core concepts from the Advanced Engineering Management Science (AEMS) course, including optimization, linear programming, forecasting, and statistical process control.

Advanced Engineering Management Science (AEMS)

A field that integrates principles of engineering, management, and decision science to optimize complex systems and processes using scientific and mathematical approaches.

Decision Variables

The choices and options that need to be controlled or adjusted to achieve the objective in an optimization model.

Objective Function

The mathematical measure of what needs to be maximized (e.g., profit), minimized (e.g., cost), or optimized in a model.

Constraints

The conditions that must be fulfilled or satisfied in a problem, acting as the boundaries within which the decision variables must operate.

Parameter Estimation

The step in AEMS that involves determining constants through statistical analysis from historical data or expert judgment.

Model Validation

The process of testing model outputs against real-world observations to check assumptions, sensitivity, and errors.

Optimization Modelling

A branch of Management Science that attempts to find the 'best' solution to a problem from a set of possible solutions using mathematical equations.

Linear Programming (LP)

A method of depicting complex relationships by using functions where all relationships in the model are linear in nature.

Non-linear Programming

An optimization technique where either the objective function or any of the constraints are defined by non-linear relationships.

Continuous Variables

Decision variables that represent measurable physical quantities such as production amounts, hours worked, or money invested.

Binary Variables

Decision variables that represent 'yes/no' type choices (e.g., selecting a supplier or opening a facility), often denoted as $1$ or $0$.

Logical Dependency (Constraint)

A constraint used in Binary LP where one decision depends on another, such as $x_C \le x_B$, meaning project C can only be selected if project B is also selected.

Forecasting

Estimates of the occurrence, timing, or magnitude of uncertain future events based on historical data.

Time Series

A set of observations of a variable at regular intervals over time, such as days, months, quarters, or years.

Cyclical / Seasonal Effect

An evident pattern in a time series where similar variations occur during corresponding periods.

Random / Irregular Effect

Fluctuations in a time series where no similar patterns exist and the variable value is due to chance and unpredictable occurrences.

Timeseries Smoothing

A technique used to reduce fluctuations in data to separate the seasonal trend from random noise and draw insights about patterns.

Moving Average

A smoothing method obtained by summing and averaging values from a given number of periods repetitively, deleting the oldest value and adding the latest.

Exponential Smoothing

A weighted moving average method that gives more weight to recent data than older data, where weights decrease exponentially as data gets older.

Alpha ($\alpha$)

A smoothing constant between $0$ and $1$; a low value gives more weight to older values (stable conditions), while a high value weights recent values (changing conditions).

Mean Squared Error (MSE)

A measure of forecasting accuracy calculated using the formula $\sum \frac{e^2}{n}$, where $e$ is the error and $n$ is the number of data points.

Statistical Process Control (SPC)

A quality control method developed by Walter A. Shewhart in the 1920s that uses statistical methods to monitor and control a process.

Common Cause Variation

The natural and inherent variability that is always present in a process.

Special Cause Variation

Abnormal, assignable causes of variation in a process that must be investigated and eliminated.

Control Limits

Statistical boundaries (UCL and LCL) based on process data, used to distinguish between common and special cause variations.

Specification Limits

Process boundaries defined by customer requirements rather than statistical process data.

Control Chart

A graphical tool used in SPC to monitor variation, consisting of a Center Line (Process average), UCL, and LCL.

Moving Range (MR)

The absolute value of the difference between the current value and the previous value, calculated as $|Current Value - Previous Value|$.