Hill A.V. The Encyclopedia of Operations Management: A Field Manual and Glossary of Operations Management Terms and Concepts

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ptg6843605

future reality tree – game theory

The Encyclopedia of Operations Management Page 146

For example, a customer order begins with a salesperson who hands it off to order entry, but neglects to

include some information. The order entry person enters the sales order data into the information system, but

accidentally enters the promise date incorrectly. The manufacturing organization makes the product to the

customer’s requirements, but misses one important unusual customer need. The shipping people accidently ship

the product to the billing address rather than to the point of need. It is easy for information to get lost in this

process because each “silo” (department) has different goals and information systems. It is hard for any one

process to “own” this customer order because the process is too far from the voice of the customer.

The lean answer to this issue is to create organizations around value streams that are aligned with market

segments. A focus on value streams instead of silos reduces waste, cycle time, cost, and defects. In the

operations strategy literature, this is called a focused factory.

See Deming’s 14 points, focused factory, lean thinking, mass customization, order entry, value stream.

future reality tree – A theory of constraints term for a type of causal map used to show the relationships needed to

create the future state desirable effects.

See causal map, current reality tree, Theory of Constraints (TOC).

futures contract – An agreement to purchase or sell a commodity for delivery in the future with (1) a price

determined at initiation of the contract, (2) terms that obligate each party to fulfill the contract at the specified

price, (2) the purpose of assuming or shifting price risk, and may be satisfied by delivery or offset; also called

futures.

A futures contract is a standardized, transferable, exchange-traded contract that requires delivery of a

commodity, bond, currency, or stock index, at a specified price, on a specified future date. Unlike options,

futures convey an obligation to buy. The risk to the holder is unlimited, and because the payoff pattern is

symmetrical, the risk to the seller is unlimited. Money lost and gained by each party on a futures contract is

equal and opposite. In other words, futures trading is a zero sum game. Futures contracts are forward contracts,

meaning they represent pledges to make certain transactions at future dates. The exchange of assets occurs on

the date specified in the contract. Futures are distinguished from generic forward contracts in that they contain

standardized terms, trade on formal exchanges, are regulated by overseeing agencies, and are guaranteed by

clearinghouses. To insure that payment will occur, futures also have a margin requirement that must be settled

daily. Finally, by making an offsetting trade, taking delivery of goods, or arranging for an exchange of goods,

futures contracts can be closed. Hedgers often trade futures for the purpose of keeping price risk in check.

See commodity, forward buy, purchasing, zero sum game.

fuzzy front end – The process for determining customer needs or market opportunities, generating ideas for new

products, conducting necessary research on the needs, developing product concepts, and evaluating product

concepts up to the point that a decision is made to proceed with development.

This process is called the fuzzy front end because it is the most unstructured part of product development.

Preceding the more formal product development process, it generally consists of three tasks: strategic planning,

concept generation, and pre-technical evaluation. These activities are often chaotic, unpredictable, and

unstructured. In comparison, the subsequent new product development process is typically structured,

predictable, and formal, with prescribed sets of activities, questions to be answered, and decisions.

Adapted from www.pdma.org (April 18, 2011).

See New Product Development (NPD).

 G 

Gage R&R – See Gauge R&R.

gainsharing – An incentive program that provides financial benefits to employees based on improvements in

quality or productivity; also called pay for performance.

See Balanced Scorecard, human resources, job design, pay for skill, piece work.

game theory – A branch of mathematics that models the strategic interactions among competitors to determine the

optimal course of action.

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gamma distribution

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gamma distribution

Page 147 The Encyclopedia of Operations Management

Business can be viewed as a “game” between the competitors in a market. A decision (move) by one player

motivates a move by another player. Historically, game theory can be traced back to the Talmud and Sun Tzu’s

writings. John von Neumann and Oskar Morgenstern are credited with the mathematical development of

modern-day game theory in their book

Theory of Games and Economic Behavior

(Neumann & Morgenstern

1944). In the early 1950s, John Nash generalized these results and created the basis for the modern field of

mathematical game theory

. The most widely known example of game theory is the prisoners’ dilemma.

A major issue with game theory is the trade-off between realism and simplicity. The most common

assumptions in game theory are (1) rationality (i.e., people take actions likely to make them happier, and they

know what makes them happy) and (2) common knowledge (i.e., everyone else is trying to make themselves

happy, potentially at our expense).

See co-opetition (co-competition), prisoners’ dilemma, zero sum game.

gamma distribution – A continuous probability distribution often used to model task times and other variables

that have a left tail bounded by zero.

The gamma distribution has shape parameter α and scale parameter β. Important special cases of the gamma

distribution include the exponential, k-Erlang, and chi-square distributions. The k-Erlang is a special case of the

gamma with an integer shape parameter.

Gamma density and distribution functions:

The gamma density function is

1 /

( )

/ ( )

f x

x e

  

 

  





for

0x 

; ( ) 0f x  otherwise, where

( )

t e dt





 



 



is the gamma function. The gamma function does not

have a closed form when



is not an integer, which means that the gamma density and distribution functions

must be approximated numerically. The gamma function entry presents the VBA code for the gamma function.

Graph:

The graph below shows a gamma density function with a range of



parameters and scale

parameter



= 1. Note that if X is a gamma distributed random variable with shape α and scale 1, then βX is a

gamma distributed random variable with shape α and scale β.

Statistics:

Mean

 

 , variance

2 2

 



, mode

( 1)

 







and 0

otherwise, skewness



, and coefficient

of variation

 



Parameter estimation:

Many authors,

such as Fisher and Raman (2010), use the

method of moments to estimate

2 2

/x s





and

/s x





, where

and s are the

sample mean and standard deviation. Law

(2007) presented a maximum likelihood

estimation procedure that requires numerical

methods. Minka (2002, p. 2) claimed that

the approach in Law “can be quite slow,

requiring around 250 iterations if α = 10”

and presented an MLE approach that

converges in about four iterations. All MLE

approaches are based on the fact that the

MLE estimate for beta is

 

 .

Excel:

In Excel, the natural log of the gamma function is GAMMALN(



), which means that the gamma

function is EXP(GAMMALN(



)). The gamma density and distribution functions are GAMMADIST(x, α, β,

FALSE) and GAMMADIST(x, α, β, TRUE). The inverse distribution function is GAMMAINV(p, α, β). In

John Nash was awarded the Nobel Prize in Economics in 1994 and was the subject of the film A Beautiful Mind in 2001.

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gamma function – gamma function

The Encyclopedia of Operations Management Page 148

Excel 2010, the gamma distribution function is renamed GAMMA.DIST(x, α, β, TRUE), and the gamma inverse

function is renamed GAMMA.INV(p, α, β).

Excel errors: The GAMMADIST and GAMMAINV functions in Excel 2003 and Excel 2007 will return

#NUM for some combinations of input parameters. Knüsel (2005) stateed that the GAMMADIST function “can

have numerical problems just in the most important central part of the distribution.” Evidently, these problems

have been fixed in Excel 2010.

Excel simulation: An Excel simulation can generate gamma distributed random variates with the inverse

transform method using x = GAMMAINV(1-RAND(), α, β).

Partial expectation function:

( ) ( | 1, )

Gamma

H x F x



 

 

Related distributions: If ~ Gamma(1, )X



, then ~ Exponential( )X



, where



is the mean. If

~ Gamma( , )X k



, then ~ Erlang( , )X k



, where k is an integer. If ~ Gamma( / 2, 2)X k , then

~ Chi-squareX with k degrees of freedom. See Law (2007) for more details. The gamma, Weibull, and log-

normal distributions are special cases of the generalized gamma distribution (Wikipedia 2010). The gamma

converges to the normal distribution as the shape parameter (α) approaches infinity.

See beta distribution, chi-square distribution, Erlang distribution, exponential distribution, gamma function,

inverse transform method, negative binomial distribution, partial expectation, probability density function,

probability distribution.

gamma function – A mathematical extension of the factorial function to real and complex numbers.

The gamma function is

( )

t e dt





 



 



for





. When



is a non-negative integer, ! ( 1)





  .

Note that

(1 / 2)



 

. In Excel, the gamma function can be computed as exp(GAMMALN(x)).

The gamma function is used in several probability distributions, including the beta, F, gamma, chi-square,

and Weibull, and is also useful for evaluating ratios of factorials. The factorial of a positive integer n is defined

as ! ( 1) ( 2) 1n n n n      , where

0! 1

. The gamma function generalizes this to all non-negative real

numbers where ! ( 1)



  .

The gamma function provides a practical tool for evaluating ratios of factorials, such as n!/m!, that are

common in probability, statistics, and queuing theory. When n or m is large, the factorial results in integer

overflow problems. (The largest factorial that Excel can handle is 170!) Given that !/ ! ( 1) / ( 1)n m n m    ,

we know that ln( !/ !) ln( ( 1) / ( 1)) ln( ( 1)) ln( ( 1))n m n m n m           . Defining ( ) ln( ( ))GLN x x  , then

ln( !/ !) ( 1) ( 1)n m GLN n GLN m    and !/ ! exp( ( 1) ( 1))n m GLN n GLN m



   . This procedure can be done

in double precision and eliminates the risk of integer overflow problems. However, this procedure can have

rounding problems. This method is comparable to cancelling out common terms in the ratio n!/m! before doing

the division. In Excel, the function for the natural log of the gamma function is GAMMALN(x).

The following table illustrates this point in Excel. From basic algebra, we know that ( 1) !/ !y n n  is equal

1n 

. The table shows that for n = 2, 4, and 169, the factorial and gamma function approaches both provide

the correct values. However, for n > 170, the factorial method has integer overflow problems. In contrast, the

gamma function provides the correct answer within the limits of computer precision.

Table comparing the factorial approach to the gamma approach

Input

data

2 3 169 170 3000

Exact answer (n + 1) 3 4 170 171 3001

Factorial

approach

n! 2 6 4.2691E+304 7.2574E+306 Integer overflow

(n + 1)! 6 24 7.2574E+306 Integer overflow Integer overflow

y = (n + 1)!/n! 3 4 170 Integer overflow Integer overflow

Overflow problems No No No Yes Yes

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Gantt Chart

−

gate

Page 149 The Encyclopedia of Operations Management

Gamma function

approach

= gammaln(n + 1) 0.6931472 1.7917595 701.4372638 706.5730622 21,024.0248530

= gammaln(n + 2) 1.7917595 3.1780538 706.5730622 711.7147258 21,032.0315539

d = g

− g

1.0986123 1.3862944 5.1357984 5.1416636 8.0067008

y = exp(d) 3 4 170 ~171 ~3001

Overflow problems No No No No

Source: Professor Arthur V. Hill

The gamma function has no closed form, but accurate and efficient approximate numerical methods are

available. The following VBA code was written by this author based on the algorithm in Press et al. (2002).

This was tested in Excel and found to be identical to the Excel function GAMMALN() in every case tested.

Function gamma_ln(xx As Double) as double

Dim x As Double, y As Double, tmp As Double, ser As Double, j As Integer

Static cof(0 To 5) As Double

cof(0) = 76.1800917294715: cof(1) = -86.5053203294168

cof(2) = 24.0140982408309: cof(3) = -1.23173957245015

cof(4) = 1.20865097386618E-03: cof(5) = -5.395239384953E-06

x = xx: y = x: tmp = x + 5.5: tmp = tmp - (x + 0.5) * Log(tmp): ser = 1.00000000019001

For j = 0 To 5

ser = ser + cof(j) / (y + j + 1)

Next j

gamma_ln = -tmp + Log(2.506628274631 * ser / x)

End Function

According to Wikipedia, Stirling’s approximation is said to be good for large factorials. However, this

author’s implementation found that it had overflow problems for n > 170. The Wikipedia entry suggests Nemes

approximation as an alternative, where

 

1 1

ln ( ) ln(2 ) ln ln 1

2 12 0.1 /

z z z z

z z



     



 

 

 

. The author has

tested this approximation and found it to be very precise for all values of z. Interestingly, the average of the

gamma function approach and Nemes approach was consistently better than either approach in these tests.

See algorithm, beta distribution, beta function, chi-square distribution, combinations, error function,

factorial, gamma distribution, hypergeometric distribution, Student’s t distribution.

Gantt Chart – A graphical project planning tool that uses horizontal bars to show the start and end dates for each

task.



The simple Gantt Chart example on the right

shows the start and end dates for five tasks. Although

a Gantt Chart is a useful tool for communicating a

project schedule (plan), it does not usually show

precedence relationships between tasks and therefore is

not a good project planning tool for large projects.

Microsoft Project, the most popular project

planning software on the market today, uses Gantt

Charts to communicate project schedules. Unlike most

Gantt Charts, this software can use arrows to show

precedence relationships between tasks.

See bar chart, Critical Path Method (CPM), project management, waterfall scheduling.

gap model – See service quality.

gate – See project management, stage-gate process.

For n = 170, the Excel value was y ≈ 171.0000000000540; for n = 3000, y ≈ 3001.000000006510.

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gateway workcenter – gemba

The Encyclopedia of Operations Management Page 150

gateway workcenter – The location in a facility where a manufacturing order has its first operation.

See CONWIP, pacemaker.

GATT – See General Agreement on Tariffs and Trade (GATT).

gauge – An instrument used for measurement or testing; also spelled gage.

The word “gauge” is often spelled “gage,” but according to the New Merriam-Webster Pocket Dictionary

(G. & C. Merriam Co. 1971), “gauge” is the proper spelling.

An old management proverb says, “You cannot manage what you cannot measure.” This is particularly true

for managing process improvement. It is impossible to reduce variation in a process (and the products that are

produced by that process) without a reliable measurement system.

Many people assume that the term “gauge” is confined to mean a micrometer, but in the context of Gauge

R&R, the term “gauge” can mean any measurement device. In fact, “Gauge R&R” can be used for any

measurement tool and can even be used for surveys and other non-factory measurement tools. The following list

of common measurement and test equipment includes a broad range of measuring devices:

 Hand tools (calipers, micrometers, linear

scales)

 Gauges (pins, thread, custom gauges)

 Optical tools (comparators, profiles,

microscopes)

 Coordinate measuring machines

 Electronic measuring equipment (digital

displays, output)

 Weights, balances and scales

 Hardness testing equipment

 Surface plate methods and equipment

 Surface analyzers (optical flats, roughness

testers)

 Force measurement tools (torque wrenches,

tensiometers)

 Angle measurement tools (protractors, sine

bars, angle blocks)

 Color measurement tools (spectrophotometer,

color guides, light boxes)

 Gauge maintenance, handling, and storage

See Gauge R&R, manufacturing processes, Measurement System Analysis (MSA), metrology.

Gauge R&R – A statistical tool that measures the variation in measurements that arises from (a) measurement

device variability (repeatability) and (b) operator variability (reproducibility); also called Gage R&R.

The measurement system is a key part of understanding and improving process capability and Gauge R&R is

a key part of the measurement system. In many lean sigma and lean manufacturing applications, Measurement

System Analysis (MSA) is conducted in the Measure step of the DMAIC process. MSA is also a key part of the

Control step (the “C”) in DMAIC.

Gauge R&R measures two different types of variation in the measurement process:

• Repeatability – The ability of a device (gauge) to produce consistent results. It is a measure of the “within”

variability between repeated measurements for one device, with one operator, on one part.

• Reproducibility – The ability of the appraiser (operator) to produce consistent results. It is the variation

between different operators who measure the same part with the same device.

In addition, most Gauge R&R studies also measure the interaction between the gauge and the operator. For

example, out of several inspectors, one might have a tendency to read one gauge differently than others.

The two most common methods used for Gauge R&R are the (1) Average and Range method and (2)

Analysis of Variance (ANOVA). The Average and Range method, like many classical SPC methods, is based

on ranges, which are easy to calculate manually. ANOVA is more accurate, but the Range and Average method

is simpler and therefore has been more widely used. With the increased availability of statistical software tools

for ANOVA, it is likely that ANOVA-based Gauge R&R will become the method of choice in the future.

Although the most obvious application of Gauge R&R is for tools, it can be applied to any type of

measurements. For example, it can be applied to customer satisfaction and employee engagement surveys.

Some of the material above was adapted from e-mail correspondence with Gary Etheridge, Staff Engineer at

Seagate, and from the website for the Automotive Industry Action Group (www.aiag.org). DeMast and Trip

(2005) is a good reference on Gauge R&R.

See Analysis of Variance (ANOVA), Design of Experiments (DOE), DMAIC, gauge, lean sigma,

Measurement System Analysis (MSA), metrology, tooling.

gemba – A Japanese term for the actual place where “real” work takes place; sometimes spelled genba.

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gemba walk − geometric mean

Page 151 The Encyclopedia of Operations Management

The Japanese word “gemba” is frequently used for the shop floor or any place where value-adding work

actually occurs. The main idea communicated by the term is that improvement really only takes place with (1)

engagement of the people who work the process and (2) direct observation of the actual current conditions. For

example, standardized work cannot be documented in the manager’s office, but must be defined and revised in

the “gemba.” According to one source

, the more literal translation is the “actual spot” and was originally

adapted from law enforcement’s “scene of the crime.”

The Japanese characters are 現場 (from www.fredharriman.com/resources/documents/FHcom_Kaizen_

Terminology_03.pdf (January 27, 2009).

See 3Gs, checksheet, kaizen workshop, lean thinking, management by walking around, waste walk.

gemba walk – See waste walk.

General Agreement on Tariffs and Trade (GATT) – A set of rules created by the United Nations to promote

freer trade by limiting or eliminating tariffs and import quotas between signatory countries.

GATT is now supervised by the World Trade Organization (WTO), which expanded its scope from only

traded goods to include services and intellectual property rights.

See antitrust laws, purchasing, tariff.

genetic algorithm – A heuristic search procedure that finds solutions to optimization problems by generating an

initial solution and then permuting solutions until a stopping condition is found.

See heuristic, operations research (OR), optimization.

geometric decay – See all-time demand, geometric progression.

geometric mean – A measure of the central tendency appropriate for the product of two or more values.

The arithmetic mean (i.e., the average) is relevant for quantities that are added together and answers the

question, “If all quantities had the same value, what value is needed to achieve the same total?” In contrast, the

geometric mean is relevant for quantities that are multiplied together and answers the question, “If all quantities

had the same value, what value is needed to achieve the same product?”

Example 1 – The area of a rectangle can be found by multiplying the length (L) and the width (W). In other

words, A = LW. When L = 10 feet and H = 6 feet, the area is A = 60 square feet. What are the dimensions of a

square with L = W that has the same area? The answer is the geometric mean which is equal to

1/ 2 1/ 2

( ) (10 6) 60 7.746G LW    

feet. The arithmetic mean for this problem is (10+6)/2 = 8 feet and the

geometric mean is less than the arithmetic mean (i.e., 7.746 < 8 feet).

Example 2 – The volume of a room can be found by multiplying the length (L), depth (D), and height (H)

together. In other words, V = LDH. When L = 10 feet, D = 12 feet, and H = 8 feet, then V = 960 cubic feet.

What are the dimensions of a room that is a perfect cube with L = D = H that has the same volume? The answer

is the geometric mean, which is equal to

1/3 1/3 1/3

( ) (10 12 8) 960 9.87G LDH     

feet. The arithmetic mean

is (10+12+8)/3 = 10 feet and the geometric mean is less than the arithmetic mean (i.e., 9.87 < 10 feet).

Example 3 – The geometric mean is an appropriate measure of the central tendency when an average growth

rate is required. For example, suppose that in three successive years the return on an investment was 5%, 20%,

and −4%. The “average” rate of return for these three years can be found as the geometric mean G = (1.05 ·1.20 ·

0.96)

1/3

≈ 1.065. Therefore, the average rate of return (Compound Annual Growth Rate or CAGR) is 6.5%. To

prove this, we see that 1.065

≈ 1.05 · 1.20 · 0.96 = 1.2096. The arithmetic means for these three values is (1.05

+ 1.2 + 0.96)/3 = 1.07, which is more than the geometric mean.

The geometric mean is closely related to the CAGR. If sales grow from s

to s

over 1

n j i   years, the

CAGR during this period is

( / ) 1

j i

s s 

. For example, if sales grew from $10 to $16 million over a five-year

period, the CAGR during this period is (16/10)

1/5

– 1 = 0.10 or 10%.

The arithmetic mean is

n i





and the geometric mean is

1 2

( )

n n i

G x x x x



   

 

 

 



, where x

the i-th value and n is the number of values. The geometric mean is always less than or equal to the arithmetic

http://elsmar.com/Forums/showthread.php?t=30789, June 14, 2010.

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geometric progression – Global Data Synchronization Network (GDSN)

The Encyclopedia of Operations Management Page 152

mean (i.e.,

n n

G A

). The arithmetic and geometric means are equal (i.e.,

n n

G A



) only if x

= x

= … = x

. The

logarithm of the geometric mean is the arithmetic mean of the log transformed data (i.e.,

log( ) (1 / ) log( )

n i

G n x





Excel – Excel uses the function GEOMEAN(number1, number2,...) for the geometric mean. The CAGR can

be computed with the Excel function XIRR(values, dates).

See Compounded Annual Growth Rate (CAGR), forecast error metrics, geometric progression, Internal Rate

of Return (IRR), mean, skewness.

geometric progression – A sequence of terms in which each term is a constant factor times the previous one.

The n-th term in a geometric progression is

1n n

d d







(in recursive form) and

d d





(in closed form).

The



parameter is called the common ratio and is defined as

n n

d d







. The example below has d

= 100

and 0.8



 . In this example,

6 5

0.8 32.77 26.21d d



   

and

6 0

26.21d d



 

(values are rounded).

Term index n 0 1 2 3 4 5 6

Value d

100.00 80.00 64.00 51.20 40.96 32.77 26.21

Finite sum, S

80.00 144.00 195.20 236.16 268.93 295.14

When





, the sum of a geometric progression (a geometric series) has a closed-form expression. The

sum of the first n terms (after term 0) is

1 2 0 0 0

... ...

n n

S d d d d d d

  

       

. Multiplying both sides



yields

2 3 1

0 0 0

...

S d d d

   



   

, and then subtracting this new equation from the first one yields

0 0

n n

S S d d

  



  

, which simplifies to

(1 ) (1 )

S d



 

  

. Given that 1



 , it is clear that

1 0



  , which means it is possible to divide both sides by 1





, which yields

(1 ) / (1 )

S d



 

  

. At

the limit as

n 





and the infinite sum (after term 0) is

/(1 )S d









. In summary, the sum of an

infinite geometric progression (starting at n = 1) is

/(1 )S d









and the finite sum of the first n terms is

(1 ) / (1 )

S d



 

  

. The finite sum from terms m to n is then

, 0

( ) / ( 1)

n m

m n

S d

  





 

For the above example, the infinite sum is

/ (1 ) 100 0.8 / (1 0.2) 400S d

 



     

and the sum of the

first six terms (after term 0) is

6 6

6 0

(1 ) / (1 ) 100 0.8 (1 0.8 ) / (1 0.8) 295.14S d

  

        

The initial value (d

) is called the scale factor and the constant factor (



) is called the common ratio. The

sequence of values (d

, d

, …, d

) is called a geometric progression and the sum of a geometric progression

+ d

+ … + d

) is called a geometric series. The product of a geometric progression is

 

( 1)/2

0 1

d d d









if 0



 and d

> 0.

See all-time demand, exponential smoothing, geometric mean.

geometric series – See geometric progression.

Getting Things Done (GTD) – A philosophy for managing a personal task list, filing system, and e-mails in a

disciplined way; the name of a popular book on personal time management by David Allen (2001).

See the entry for the two-minute rule for what is probably Allen’s most famous principle.

See personal operations management, two-minute rule, two-second rule, tyranny of the urgent.

Global Data Synchronization Network (GDSN) – An initiative designed to overcome product data

inaccuracies and increase efficiencies among trading partners and their supply chains.

GDSN is a network of certified data pools that enable product information to be captured and exchanged in a

secure environment conforming to global standards. Different versions of product information in the supply

chain can cause serious business issues. Global Data Synchronization (GDS) ensures that trading partners

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always use the same version of the data. This empowers the supplier to manage the information flow in the

supply chain and not rely on the trading partner or other third parties to manipulate their data. The foundational

principles of GDS include:

 Product data is updated consistently between trading partners.

 Data is validated against standards and business rules.

 Trading partners classify their products in a common, standardized way.

 Trading partners have a single point of entry through their chosen data pool, reducing the cost of using

multiple vendors.

 The uniqueness of items is guaranteed through the GS1 Global Registry.

The standards body that governs the GDSN is GS1, an organization dedicated to the design and

implementation of global standards and solutions to improve the efficiency and visibility of supply and demand

chains globally and across sectors. The GS1 system of standards is the most widely used supply chain standards

system in the world and has been used for more than 30 years in multiple sectors and industries.

Global Positioning System (GPS) – A satellite-based technology that can be used to determine the current

latitude and longitude for a device.

GPS technology can be a very helpful tool for collecting information in a transportation system.

See logistics, telematics.

global sourcing – See sourcing.

goal tree – See Y-tree.

gold parts – A phrase used in the Theory of Constraints for parts that have passed through the bottleneck.

These parts are much more valuable because the organization has invested time in them from its most

valuable resource (the bottleneck).

See inspection, Theory of Constraints (TOC).

golden zone – See forward stocking area.

Goldratt – See Theory of Constraints (TOC).

Gompertz Curve – See logistic curve.

Good Manufacturing Practices (GMP) – Quality guidelines and general principles for producing and testing

products developed by the U.S. Food and Drug Administration (the FDA) covering pharmaceuticals, diagnostics,

foods, and medical devices; also called Current Good Manufacturing Practices (CGMP).

All guidelines follow the following basic principles:

• Manufacturing processes are clearly defined and controlled. All critical processes are validated to ensure

consistency and compliance with specifications.

• Manufacturing processes are controlled and any changes to the process are evaluated. Changes that have an

impact on the quality of the drug are validated as necessary.

• Instructions and procedures are written in clear and unambiguous language.

• Operators are trained to carry out and document procedures.

• Records are made manually or with instruments that demonstrate that all the steps required by the defined

procedures and instructions were, in fact, taken and that the quantity and quality of the drug was as expected.

Deviations are investigated and documented.

• Records of manufacture (including distribution) that enable the complete history of a batch to be traced are

retained in a comprehensible and accessible form.

• The distribution of the drugs minimizes any risk to their quality.

• A system is available for recalling any batch of drug from sale or supply.

• Complaints about marketed drugs are examined, the causes of quality defects are investigated, and

appropriate measures are taken with respect to the defective drugs and to prevent recurrence.

Adapted from http://en.wikipedia.org/wiki/Good_manufacturing_practice (March 19, 2011).

See process validation, quality management.

goodness-of-fit tests – See chi-square goodness of fit test, Kolmogorov-Smirnov test (KS test).

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goodwill – (1) In any business context: The value of a good relationship between a business and its customers. (2)

In a business acquisitions context: An intangible asset equal to the cost to acquire a business over the fair market

value of all other assets. (3) In an interpersonal context: A cheerful, friendly, kind attitude toward others.

In any business context, goodwill is the reputational capital of the firm. Goodwill is lost when the

company cannot fulfill its service promises, runs out of inventory, or has poor product or service quality. Lost

goodwill can lead to lost sales, lower margins, and loss of brand equity. Goodwill is very difficult to measure.

In a business acquisition context, goodwill is the difference between the fair market value of a company’s

assets (less its liabilities) and the market price or asking price for the overall company. In other words, goodwill

is the amount in excess of the firm’s book value that a purchaser would be willing to pay to acquire it. If a sale is

realized, the new owner of the company lists the difference between book value and the price paid as goodwill in

financial statements.

See Economic Value Added (EVA), financial performance metrics, quality management, safety stock, service

level, stockout.

GPS – See Global Positioning System (GPS).

gravity flow rack – See flow rack.

gravity model for competitive retail store location – A mathematical model for locating one or more new

retail stores relative to the competing stores in a region.

The basic concept of the gravity model is that the “gravitational pull” for a store on customers is directly

proportional to the size of the store and inversely proportional to the travel time squared. In other words,

customers will be attracted to larger close-by stores much more than they will be to smaller far-away stores. This

model is an application of Newton’s Law, which states that the gravitational pull between two planets is directly

proportional to their mass and inversely proportional to the square of the distance between them.

The goal is to find the best location for one or more new stores from a set of potential locations, assuming

that the new stores will have to compete for customers with the other stores in the region. The model allocates

the revenue in the market to each of the stores based on the “pull,” which is a function of store size (bigger is

better) and travel time (closer is much better). The model can be used to evaluate all reasonable alternatives and

select the store locations that maximize the total expected revenue.

The algorithm allocates all revenue in a region to the m stores. Store j is characterized by its size S

and by a

competitive index c

, which is used to adjust for weak and strong competitors in the market. The region has n

population areas (census blocks). The travel time from census block i to store j is t

. The “pull” for store j with

competitive index c

on census block i is directly proportional to the size of the store and inversely proportional

to the travel time to the ρ power. Pull, therefore, is defined as

ij j j ij

pull c S t





. The ρ parameter can be

determined empirically, but is usually close to ρ = 2.

The probability that a resident of census block i will shop at store j is the normalized pull, which is given by

pull





. Census block i has m

customers with average revenue per customer of r

. The expected

revenue for store j, therefore, is

ij i i

R p rm





. The best location for a store (or set of stores) can be found by

using the model to evaluate all reasonable alternative configurations and selecting the one that has the largest

expected revenue.

See center-of-gravity model for facility location, facility location, great circle distance, numeric-analytic

location model.

gray market – See gray market reseller.

gray market reseller – A broker that sells products through distribution channels other than those authorized or

intended by the manufacturer; spelled “grey” outside the United States

“Gray” with an “a” is used in America and “grey” with an “e” is used in England and everywhere else outside the U.S.

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Gray market resellers typically buy used equipment or clearance products on the open market and resell

them to end-user customers at prices lower than those desired by the manufacturer. These resellers sell outside

the normal distribution channels, typically have no relationship with the manufacturer, and typically provide no

aftersales service. In some cases, the warranty is no longer valid.

Gray market products are usually (but not always) legal and are usually (but not always) bought and sold at

prices lower than the prices set by the manufacturer or regulatory agency. These are often products that were

sold in one national market and then exported and sold in another national market at a lower price. For example,

a dealer might buy a car at a reduced price in one country and then sell it in another country at a lower price.

See the diversion entry for more information on the problems with this practice.

See broker, diversion.

great circle distance – The shortest distance between any two points on a sphere.

Given that the earth is approximately spherical, the great circle distance can be used to estimate the travel

distance between any two points defined by their latitude and longitude coordinates. Now that Global

Positioning Systems (GPS) and geographical databases are widely available, the great circle distance is a

practical means to estimate distances for a wide variety of logistics and transportation planning problems.

The Spherical Law of Cosines computes the great circle angle (a

) between the points i and j on the earth

using

acos(sin( )sin( ) cos( )cos( )cos( ))

ij i j i j j i

a x x x x y y  

, where (x

, y

) and (x

, y

) are the latitude and

longitude coordinates for the two points expressed in radians. Convert the great circle angle into a great circle

distance using

ij ij

d r a 

, where r is the average radius of the earth, which is r ≈ 3958.76 miles or r ≈ 6371.01

km. If latitude and longitude are expressed in hours, minutes, and seconds (h:m:s), convert them to decimal

degrees using decimal_degrees = h + m/60 + s/60/60, and then convert to radians using radians = π ·

decimal_degrees/180.

The Excel formula for the Spherical Law of Cosines is r*ACOS(SIN(x1)*SIN(x2)+

COS(x1)*COS(x2)*COS(y2-y1)) for earth radius r and coordinates (x1,y1) and (x2,y2) expressed in radians.

When using the arc cosine function (ACOS), the absolute value of the argument must be less than one. It is

useful, therefore, to implement this distance function in VBA to conduct this check. The following VBA code

developed by this author implements the Law of Cosines great circle distance function in VBA using a derived

arc cosine. It is important to use double precision for all variables in this code.

Global Const pi As Double = 3.14159265358979

Function distf(ByVal x1 As Double, ByVal y1 As Double,

ByVal x2 As Double, ByVal y2 As Double) As Double ' input lat/long data in decimal degrees

Const r_miles As Double = 3958.76 ' average radius of the earth in miles.

Dim a As Double

' convert decimal degrees to radians for lat/long coordinates (x1, y1) and (x2, y2).

x1 = CDbl(x1 * pi / 180): y1 = CDbl(y1 * pi / 180): x2 = CDbl(x2 * pi / 180): y2 = CDbl(y2 * pi / 180)

a = Sin(x1) * Sin(x2) + Cos(x1) * Cos(x2) * Cos(y2 - y1) ‘apply law of cosines

If a < -1 Then a = -1 ' the argument for the arc cosine cannot be less than -1.

If a > 1 Then a = 1 ' the argument for the arc cosine cannot be greater than 1.

distf = Atn(-a / Sqr(-a * a + 1)) + pi / 2 ' compute the arc cosine of a in radians.

distf = r_miles * distf ' convert radians to miles.

End Function

The above VBA code finds that the distance between Seattle (47:36:00,122:20:00) and Miami (25:45:00,

80:11:00) is 2732.473 miles and the distance between the Nashville International Airport (N 36°7.2’, W

86°40.2’) and the Los Angeles International Airport (N 33°56.4’, W 118°24.0’) is 1793.555 miles.

Love, Morris, and Wesolowsky (1988) suggest inflating intracity travel distances by a factor of roughly 1.18

to account for the fact that travel distances between intracity points is, on average, greater than the straight-line

distance due to road structures.

See facility location, gravity model for competitive retail store location, Manhattan square distance,

numeric-analytic location model.

green belt – See lean sigma.