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The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

The Carbon Cycle

The Carbon Cycle

Carbon is the basis of all organic matter on Earth, and is recycled through the ecosystem in two primary processes: one in which carbon is exchanged among living organisms, and one in which carbon is cycled over long periods of time through fossilized organic remains, weathering of rocks, and volcanic activity. Human activities, including increased agricultural practices and the burning of fossil fuels, has greatly affected the balance of the natural carbon cycle.

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

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Related Experiment Video

Updated: Feb 2, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Bi-objective inventory allocation planning problem with supplier selection and carbon trading under uncertainty.

Kai Kang¹, Wei Pu¹, Yanfang Ma¹

¹School of Economics and Management, Hebei University of Technology, Tianjin, P. R. China.

|November 29, 2018

Summary

This study introduces a bi-objective inventory model integrating supplier selection and carbon trading to balance economic and environmental impacts. It demonstrates how carbon pricing influences inventory decisions under uncertainty.

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Area of Science:

Operations Research
Environmental Management
Supply Chain Management

Background:

Growing concern over businesses prioritizing economic gains over environmental and social impacts.
Need for integrated models addressing both economic efficiency and ecological footprint in supply chains.

Purpose of the Study:

To investigate a bi-objective inventory allocation planning problem incorporating supplier selection and carbon trading under uncertainty.
To analyze the impact of carbon emissions costs on overall inventory network costs.

Main Methods:

Development of a novel bi-objective model using normalized normal constraint method.
Application of differential evolution algorithm and uncertainty simulation for complex problem-solving.
Generation of Pareto frontier to illustrate trade-offs between economic and environmental objectives.

Main Results:

Demonstration of model effectiveness and practicability through a representative case study.
Analysis of how carbon cap and carbon credit price influence environmental objectives in inventory networks.
Validation of the proposed method against exact solutions for large-scale problems.

Conclusions:

The study provides a robust framework for sustainable inventory management by integrating economic and environmental considerations.
The model offers valuable insights for businesses navigating carbon regulations and seeking to minimize their ecological impact.