Industrial engineering (IE) is about how humans interact with different things—tools, technology, people, and processes. It is about the science, art, technology, and engineering 1-1
of making things more efficient. To accomplish this, formulas, equations, and calculations are very essential. There is an increasing surge in the demand for analytical reasoning in human endeavors. The analytical approach of IE is used to solve complex and important problems that mankind face. Life itself is about choices. The practice of IE is about making the right choices in a dynamic environment of competing alternatives. Be it in launching a space shuttle or executing project control, decisions must be made in an environment of risk and scarcity. Analytical techniques of IE help solve these problems by formulating both qualitative and quantitative components into an integrated model that can be optimized. IE computational techniques have a wide range of applications including the following:
• Transportation
• Manufacturing
• Engineering
• Technology
• Science
• Mathematics
• Electronics
• Environment
• Medicine
For example, the operational properties of Laplace transform and Z-transform are used to ease computational complexity in applications such as cash flow series analysis, queuing analysis, traffic flow modeling, and material handling moves. Similarly, statistical equations are used for forecasting, geometry formulas are used for facility layout prob- lems, and advanced algebraic computations are used in operations research optimization problems. The diverse capabilities of IE bring unique strengths in strategic management and organizational change and innovation. IE programs are mutually complementary with respect to the discipline’s competency in systems engineering by adding the research methods that blend engineering technology with management expertise to implement long-term strategies. Sustainability is essential for IE to help organizations achieve inte- grated solutions to emerging challenges, to help enhance the interface between technology and human resources, and to help decision-makers focus on systems thinking and process design that improve operational efficiency.
The appreciation and inclusion of qualitative aspects of a problem are what set IE apart from other technical disciplines. In this respect, IE is more human-centric than other engineering disciplines. Human-based decision-making is central to any technical undertaking. A pseudo-code of a typical mathematical formulation might look as follows:
Problem scenario: production planning
Desired objective: optimize product, service, or results Human resource options: H1, H2, H3, H4
Technology options: T1, T2, T3 Location options: L1, L2, L3, L4 Operational constraints: C1, C2, C3
Using the above problem framework, an organization can pursue cost reduction, profit maximization, or cost-avoidance goals. Superimposed upon the analytical framework are the common decision-making questions making up theeffectivenessequation presented below:
E=W5H, where the elements are expanded below:
• What
• Who
• Where
• Why
• When
• How
An excellent example of solving complex decision problems using analytical modeling is theBridges to Somewherepuzzle by Toczek (2009). The problem is paraphrased as follows:
The five residents of Hometown live in houses represented by the letters ‘A’ through
‘E’ as shown on the left side of Figure 1.1. The offices where they are working are represented by their matching letters on the island of Worktown. Because a river lies between Hometown and Worktown, the residents are unable to get to work.
They have in their budget enough funds to build two bridges that could connect Hometown to Worktown. The locations where these bridges could be built are indicated by the hashed 1×3 tiles. The two bridges can only be built in these approved areas. Once the bridges are built, the resident would then be able to commute to work. A commuter will always take the shortest path from home to work and can only travel in up, down, left, or right directions (no diagonals). Each tile represents a 1-km-by-km distance. As an example, if bridge number four were built, resident ‘E’ would have to travel 10 km to reach his workplace.
Decision required: Which two bridges should be built in order to minimize the total commuting distance of all residents?
If this problem is to be solved by non-seat-of-the-pants approach, then a mathemat- ical representation of the problem scenario must be developed. For this reason, IE and operations research often work hand-in-hand whereby one provides the comprehensive problem space and data requirements, whereas the other provides the analytical engine to solve the model. Equations help to link both sides of the decision-making partnership.
Many times, the qualitative formulation of a multifaceted problem is more difficult than the mathematical solution. A famous quote in this respect is echoed here:
The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new ques- tions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advances in science.
Albert Einstein
13
A
A
C
E D
Two One
Three
Four
B B
C D
E 12 11 10 9 8 7 6 5 4 3 2 1
Hometown Worktown
FIGURE 1.1 Bridge proposals connecting Hometown to Worktown. (Adapted from Toczek, J.
2009. Bridges to somewhere.ORMS Today, 36(4), 12.)
Einstein’s quote is in agreement with the very essence of IE, which embodies versatility and flexibility of practice beyond other engineering disciplines. The versatility of IE is evidenced by the fact that many of those trained as industrial engineers end up working in a variety of professional positions in science, technology, engineering, business, indus- try, government, and the military. In all of these professional roles, industrial engineers use fundamental calculations to design products and services and also to make business decisions. This book is designed primarily as a reference material for students and prac- ticing industrial engineers who may be unsure about the mathematical identity of the IE profession. Industrial engineers use analytical, computational, and experimental skills to accomplish integrated systems of people, materials, information, equipment, and energy.
IE is one unique discipline that factors in human behavioral aspects in the workplace.
Issues such as psychology, economics, health, sociology, and technology all have link- ages that are best expressed through analytical means. Therein lies the importance of IE calculations.
Many modern, complex computational processes that are most visibly associated with other disciplines do, indeed, have their roots in one form or another of the practice of IE dating back to the Industrial Revolution. Thus, having aHandbook of Industrial Engineering Equations, Formulas, and Calculationsis a fitting representation of the com- putationally rich history of the profession. The definition below aptly describes the wide span of IE practice.