Hill A.V. The Encyclopedia of Operations Management: A Field Manual and Glossary of Operations Management Terms and Concepts
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barter – Bass Model
The Encyclopedia of Operations Management Page 36
Barcodes provide many business benefits, including reducing transaction cost and providing information that
can be used to improve service levels, reduce stockouts, and reduce unnecessary inventory.
Barcodes come in many varieties. The 2D (two-dimensional) barcode is in the form of bars and spaces,
normally in a rectangular pattern. In contrast, a 3D (three-dimensional) barcode looks like a group of random
black boxes scattered across a white background. 3D barcodes are often used in environments where labels
cannot be easily attached to items.
A barcode reader (scanner, wand) is a device that scans a barcode to record the information.
The Wikipedia article on barcodes provides detailed information on types of barcodes and barcode standards.
See Automated Data Collection (ADC), Electronic Product Code (EPC), part number, Radio Frequency
Identification (RFID), Universal Product Code (UPC).
barter – The exchange of goods without using cash or any other financial medium.
For example, oil is sometimes bartered for military equipment in the Persian Gulf.
barriers-to-entry – See core competence, switching cost.
base stock system – See order-up-to level.
Bass Model – A well-known approach for modeling the sales pattern for the life cycle of a new product
introduction developed by Professor Frank Bass.
The demand for a new music title or any other type of new product follows a similar demand pattern through
its product life cycle, with early growth, maturity, and finally decline. The Bass Model (and its many extensions)
has inspired many academic research papers and has been used in many applications. The basic idea is that some
products take off right away due to the early adopters (the “innovators”) who immediately make purchases. The
“imitators” do not buy right away, but buy soon after they see others with the product. The model requires three
parameters:
m Total market potential, which is the total number of unit sales that we expect to sell over the life of the
product. This is the sum of the demand during the product life and is also the area under the curve.
p Innovation coefficient, which primarily affects the shape of the curve during the beginning of the life cycle.
This parameter is also called the external influence, or the advertising effect.
q Imitation coefficient, which primarily affects the shape of the curve after the peak of the product life cycle.
This parameter is also called the internal influence, or word-of-mouth effect.
In summary, m is the scale parameter and p and q are the shape parameters. With these three parameters, the
Bass Model can predict almost any realistic new product introduction demand pattern. The challenge is to
estimate m, p, and q for a new product introduction. The best approach for handling this problem is to predict m
based on marketing research and to select the p and q parameters based on experience with similar products.
The basic idea of the Bass Model (Bass 1969) is that the probability of an initial purchase made at time t is a
linear function of the proportion of the population that has already purchased the product. Define F(t) as the
fraction of the installed base through time t and
( ) ( )/
f
t dF t dt
as the rate of change in the installed base
fraction at time t. The fundamental model is given by
( )/(1 ( )) ( )
f
t F t p qF t
. Assuming that F(0) = 0
gives
1
( ) ( )
( ) 1 1 ( / )
p qt p q t
F t e q p e
and
2
2 ( ) ( )
( ) (( ) / ) 1 ( / )
p p q t p q t
f t p q p e q p e
. From this,
the cumulative sales through period t can be estimated as
( ) ( )S t mF t
and the rate of change in the installed
base at time t is
( )/ ( )dS t dt m
f
t
. The time of peak sales is
* ln( / ) / ( )t q p p q
. The Bass Model has been
extended in many ways, but those extensions are outside the scope of this encyclopedia. Mahajan, Muller, Eitan,
and Bass (1995) provided a summary of many of the extensions of the Bass Model.
Historical data can be used to estimate the parameters p and q. Define N(t) as the cumulative historical sales
through time t. Simple linear regression can now be run using the model
2
( ) ( ) ( )
y
t a bN t cN t
and then m,
p, and q can be estimated with these equations solved in this order
2
4 / ( 2 )m b b ac a
,
/
p
a m
, and
q cm
. The average value of p is around 0.03, but it is often less than 0.01. The value of q is typically in the
range (0.3, 0.5) with an average around 0.38.
The example below starts with the empirical data in the table and finds the optimal parameters m = 87,
p = 0.100, and q = 0.380. The graph for this curve is shown on the right.
ptg6843605
batch − bathtub curve
Page 37 The Encyclopedia of Operations Management
The logistic curve entry presents simpler models, such as the logistic, Richards Curve, and Gompertz Curve.
See adoption curve, all-time demand, forecasting, linear regression, logistic curve, network effect, product
life cycle management.
batch – See lotsize.
batch flow – See batch process.
batch picking – A warehousing term for an order picking method where multiple orders are picked by one picker in
one pass and then later separated by order.
See Automated Storage & Retrieval System (AS/RS), carousel, picking, wave picking, zone picking.
batch process – A system that produces a variety of products but produces them in groups of identical items.
Unlike a continuous process, a batch process is characterized by (1) a system that can make more than one
product or product type, (2) setups that are used to change the process to make a different product, and (3) work-
in-process inventory between steps in the process due to batchsizes and contention for capacity.
A batch process is often associated with a job-shop that has general purpose equipment arranged in a process
layout. In a process layout, the location of the equipment is not dictated by the product design but rather by
groups of similar general purpose equipment that share a common process technology or required skill.
Most batch processes require significant setup time and cost with each batch. In the lean perspective, setup
time is waste and reducing setup time and cost is often considered a strategic priority. If a system is dedicated to
producing only a single product, it has no setups or changeovers and is a continuous process.
Examples of batch processes include (1) apparel manufacturing, where each batch might be a different style
or size of shirt, (2) paint manufacturing, where different colors of paint are mixed in different batches, and (3)
bottle filling operations, where each batch is a different liquid (e.g., soft drink).
See batch-and-queue, continuous process, discrete manufacturing, job shop, sequence-dependent setup time,
setup, setup cost, setup time.
batch-and-queue – A negative term often used by promoters of lean manufacturing to criticize manufacturing
operations that have large lotsizes, large queues, long queue times, long cycle times, and high work-in-process.
One-piece flow is a better method because it eliminates batches, which reduces the average time in queue
and the average number in queue (assuming that no additional setup time is required).
See batch process, continuous flow, lean thinking, one-piece flow, overproduction, value added ratio.
batchsize – See lotsize.
bathtub curve – A U-shaped curve used in reliability theory and reliability engineering that shows a typical hazard
function with products more likely to fail either early or late in their useful lives.
-
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8 9 10 11 12
Sales (units)
Time Period
Bass Model
Time period
Predicted
sales
Predicted
cumulative sales
1 9 9
2 11 20
3 12 32
4 13 45
5 12 58
6 10 68
7 8 76
8 5 80
9 3 83
10 2 85
11 1 86
12 0 86
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Bayes’ Theorem
–
Bayes’ Theorem
The Encyclopedia of Operations Management Page 38
Reliability engineers have observed population failure rates as units age over time and have developed what
is known as the “bathtub curve.” As shown in the graph below
4
, the bathtub curve has three phases:
Infant failure period – The initial
region begins at time zero, when a
customer first begins to use the product.
This region is characterized by a high but
rapidly decreasing failure rate and is
known as the early failure, or infant
mortality period. Immediate failures are
sometimes called “dead on arrival,” or
DOA.
Intrinsic failure period – After the
infant mortality period has passed, the
failure rate levels off and remains roughly
constant for the majority of the useful life
of the product. This long period with a
fairly level failure rate is also known as the
intrinsic failure period, stable failure
period, or random failure period. The
constant failure rate level is called the intrinsic failure rate.
End of life wear out period – Finally, if units from the population remain in use long enough, the failure
rate begins to increase again as materials wear out and degradation failures occur at an increasing rate. This is
also known as the wear out failure period.
For example, a newly purchased light bulb will sometimes fail when you first install it (or very shortly
thereafter). However, if it survives the first few hours, it is likely to last for many months until it fails. Another
example is human life. The death rate of infants is relatively high, but if an infant makes it through the first
couple of weeks, the mortality rate does not increase very much until old age.
The Weibull distribution is a flexible life distribution model that can be used to characterize failure
distributions in all three phases of the bathtub curve. The basic Weibull distribution has two parameters, the
shape and scale parameters. The shape parameter enables it to be applied to any phase of the bathtub curve. A
shape parameter less than one models a failure rate that decreases with time, as in the infant mortality period. A
shape parameter equal to one models a constant failure rate, as in the normal life period. A shape parameter
greater than one models an increasing failure rate, as during wear-out. This distribution can be viewed in
different ways, including probability plots, survival plots, and failure rate versus time plots (the bathtub curve).
The bathtub curve can inform decisions regarding service parts. However, the need for service parts at the
end of the product life cycle is affected by retirement (removal) of the equipment in the field. Although the
bathtub curve suggests that the demand for service parts at the end of life might increase, this effect is mitigated
by the retirement of machines from the field, making it difficult to predict the demand for service parts at the end
of the product life cycle.
See maintenance, Mean Time Between Failure (MTBF), newsvendor model, Poisson distribution, product
life cycle management, reliability, service parts, Total Productive Maintenance (TPM), Weibull distribution.
Bayes’ Theorem
– An important probability theory concept that expresses the conditional probability of event A in
terms of the conditional and marginal probabilities of events A and B.
Bayes’ Theorem stated mathematically is
( | ) ( )
( | )
( )
P B A P A
P A B
P B
, where
( | )P A B
is the probability of
event A given event B,
( | )P B A
is the probability of event B given event A, and
( )P A
and
( )P B
are the
unconditional (marginal) probabilities of events A and B.
4
This bathtub curve is the sum of four Weibull curves
1
( ) exp( ( / ) )f t t t
with α = 0.5, 1, 3, and 10, β = 135, for t in
the range (1, 250).
ptg6843605
beer game − benchmarking
Page 39 The Encyclopedia of Operations Management
Red Green Blue
A popular example is the North American TV game show “Let’s Make a Deal,” which
gave contestants the option of selecting one of three doors (red, green, and blue), where only
one door had a prize hidden behind it. After the contestant selected a door, the game show
host opened another door where the prize was not hidden. The host then asked the
contestant if he or she wanted to select a different door. In this game context, many people
incorrectly conclude that the chances are 50-50 between the two unopened doors and that the
contestant has no reason to select a different door.
To better understand the probabilities involved in this game, define events R (the prize is behind the red
door), G (the prize is behind the green door), and B (the prize is behind the blue door). When the prize is
randomly assigned to a door, then P(R) = P(G) = P(B) = 1/3. To simplify exposition, assume that the contestant
has selected the red door and that the host has opened the blue door to show that the prize is not behind it (event
S
B
). Without any prior knowledge, the probability that the host will show the blue door is P(S
B
) = 1/2. If the
prize is actually behind the red door, the host is free to pick between the green and blue doors at random (i.e.,
P(S
B
|R) = 1/2). If the prize is actually behind the green door, the host must pick the blue door (i.e., P(S
B
|G) = 1).
If the prize is behind the blue door, the host must pick the green door (i.e., P(S
B
|B) = 0). Given that the host
showed the blue door, Bayes’ Theorem shows:
Probability of the prize behind the red door:
( | ) ( ) (1 / 2)·(1 / 3)
( | ) 1/3
( ) (1 / 2)
B
B
B
RP S P R
P R S
P S
Probability of the prize behind the green door:
( | ) ( ) 1·(1 / 3)
( | ) 2 / 3
( ) (1 / 2)
B
B
B
P S G P G
P G S
P S
Probability of the prize behind the blue door:
( | ) ( )
0·(1 / 3)
( | ) 0
( ) (1 / 2)
B b b
B
B
P S A P A
P S
P S
B
Therefore, in this situation, the contestant should always choose the green door. More generally, the
contestant should always change to the other door. Another way of looking at this problem is to understand that
the contestant had a 1/3 chance of being right in selecting the red door. When the blue door was shown to not
have the prize, the conditional probability of the red door having the prize is still 1/3, but the probability of the
green door having the prize is now 2/3. See http://en.wikipedia.org/wiki/Monty_Hall_problem for more details.
See decision tree.
beer game – A popular simulation game to help people understand the bullwhip problem in supply chains and learn
how to deal with the problem in practical ways.
The beer game was designed by Professor John Sterman (1992) at MIT to demonstrate the bullwhip in
supply chains. It emphasizes the importance of information flow along the supply chain and shows how humans
tend to overreact and overcompensate for small changes in demand, which results in magnified fluctuations in
demand that are passed down the supply chain.
The class is divided into teams of four players at each table. The four players include a retailer, warehouse,
distributor, and factory. The “products” are pennies, which represent cases of beer. Each player maintains an
inventory and keeps track of backorders. Players receive orders from suppliers after a one-week delay. The
instructor privately communicates the demand to the retailer, with a demand for four cases per week for the first
four weeks and eight cases per week for the remainder of the game.
The results of the game are fairly predictable, with nearly all teams falling into the trap of wild oscillations.
At the end of the game, the instructor asks the factory players to estimate the actual demand history. They
usually guess that demand varied widely throughout the game. Students are often surprised to learn that demand
was steady except for the initial jump. The teaching points of the game revolve around how the internal factors
drive the demand variations and about how this “bullwhip” can be managed.
See bullwhip effect.
benchmarking – Comparing products or processes to a standard to evaluate and improve performance.
Finding comparable numerical comparisons between two or more firms is very difficult because no two
organizations, processes, or products are truly comparable. Although knowing that two processes (or products)
have different performance might help an organization prioritize its improvement efforts, it does not help the
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Bernoulli distribution – beta distribution
The Encyclopedia of Operations Management Page 40
organization know how to improve. Real improvement only comes when a better process or product is
understood and that information is used by the organization to improve its processes and products.
Many consulting firms have moved away from the term “benchmarking” because it focused more on
comparing numbers (benchmarks) than on understanding and improving processes. Many of these consulting
firms then started to use the term “best practices” instead of benchmarking. However, due to the difficulty of
knowing if a process or product is truly the best, most consulting firms now use the term “leading practices.”
Product benchmarking compares product attributes and performance (e.g., speed and style) and process
benchmarking compares process metrics, such as cycle time and defect rates. Internal benchmarking sets the
standard by comparing products and processes in the same firm (e.g., another department, region, machine,
worker, etc.). In contrast, external benchmarking sets the standard based on products and processes from
another firm. Competitive benchmarking is a type of external benchmarking that sets the standard based on a
competitor’s products or processes. Of course, no competitor should be willing to share process information.
Informal benchmarking is done by finding a convenient benchmarking partner (often in a warm climate) who is
willing to share information. In contrast, formal benchmarking involves mapping processes, sharing process
maps, comparing numbers, etc.
Many professional trade organizations provide benchmarking services. For example, several quality awards,
such as the Deming Award in Japan, the European Quality Award in Europe, and the Malcolm Baldrige Award
in the U.S., serve as benchmarks for quality performance. The PRTM consulting firm and other firms provide
benchmarking consulting using the SCOR framework.
See balanced scorecard, best practices, entitlement, lean sigma, Malcolm Baldrige National Quality Award
(MBNQA), operations performance metrics, process improvement program, process map, SCOR Model, supplier
scorecard, Y-tree.
Bernoulli distribution – A discrete probability distribution that takes on a value of x = 1 (success) with probability
p and value of x = 0 (failure) with probability q = 1 – p.
Parameter: The probability of success, p.
Probability mass function: If X is a random variable with the Bernoulli distribution, then
( 1) 1 ( 0) 1P X P X p q
.
Statistics: The Bernoulli has range (0, 1), mean p, and variance p(1 – p).
Excel simulation: The inverse transform method can be used. If RAND() < p then X = 1; otherwise, X = 0.
In Excel, this is IF(RAND()<p,1,0).
Other distributions: The sum of n independent identically distributed Bernoulli random variables with
probability p has the binomial distribution with parameters n and p.
History: The Bernoulli distribution was named after Swiss mathematician Jacob Bernoulli (1654-1705).
See binomial distribution, negative binomial distribution, p-chart, probability distribution, probability mass
function.
best practices – A set of activities that has been demonstrated to produce very good results; the best-known
performing process, methodology, or technique.
The term “best practices” is often used in the context of a multi-divisional or multi-location firm that has
similar processes in many locations. A best practice is developed by some consensus process (such as the
nominal group technique) and then shared across the organizational boundaries.
For example, Wells Fargo (a large bank in North America) has similar processes in many locations. As a
result, Wells Fargo is always looking to identify, document, and implement the “best practice” for each process
throughout the system.
The challenge, of course, is to identify what is truly the best performing process in light of imperfect
information caused by differences in performance measures, process environments, process implementations, and
local organizational cultures. To be more accurate, many consulting firms now use the term “leading practice”
instead of best practice.
The concept of best practices is closely related to benchmarking and is also closely related to Frederick
Taylor’s (1911) notion of “one best method” for each process.
See benchmarking, scientific management.
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beta distribution
−
beta function
Page 41 The Encyclopedia of Operations Management
beta distribution
– A continuous probability distribution used for task times in the absence of data or for a random
proportion, such as the proportion of defective items.
Historically, the PERT literature recommended that task times be modeled with the beta distribution with
mean (a + 4m + b)/6 and variance (b a)
2
/36, where the range is (a, b) and m is the mode. The PERT entry
critically reviews this model.
Parameters: Shape parameters
0
and
0
.
Density and distribution functions: The beta density function for x > 0 is
1 1
( ) (1 ) / ( , )f x x x B
,
where
( , ) ( ) ( ) / ( )B
is the beta function and
( )
is the gamma function (not to be confused
with the gamma distribution). The beta distribution function has no closed form.
Statistics: The statistics for the beta
include range [0,1], mean
/( )
, variance
2
/(( ) ( 1))
, and mode
( 1) / ( 2)
if
1
and
1
; 0 and
1 if
1
and
1
; 0 if
1
and
1
or
1
and
1
; 1 if
1
and
1
;
1
or
1
and
1
; the mode does not
uniquely exist if
1
.
Graph: The graph on the right is the beta
probability density function (pdf) with
parameters (
,
) = (1.5, 5.0).
Parameter estimation: Law and Kelton
(2000) noted that finding the Maximum
Likelihood Estimates for the two parameters
requires solving equations involving the
digamma function with numeric methods (a
non-trivial task) or referencing a table, which may lack accuracy. The method of moments estimates the two
parameters based on the sample mean
x
and sample variance s
2
using
2 2
(1 ) /x x s x
and
2 2
(1 ) / 1x x s x
.
Excel: Excel provides the distribution function BETADIST(x, α, β) and the inverse function BETAINV(p,
α, β), but does not provide a beta density function. The beta density function in Excel is x^(α-1)*(1- x)^( β-
1)/EXP(GAMMALN(α)+GAMMALN(β)-GAMMALN(α+β)). For the beta distribution transformed to range
[A, B], use BETADIST(x, α, β, A, B). The gamma function is EXP(GAMMALN(α)). In Excel 2010, the beta
distribution related functions are renamed BETA.DIST and BETA.INV, but still use the same parameters.
Excel simulation: In an Excel simulation, beta random variates can be generated with the inverse transform
method using x = BETAINV(1-RAND(), α, β).
See beta function, gamma distribution, gamma function, probability density function, probability
distribution, Project Evaluation and Review Technique (PERT), Weibull distribution.
beta function
– An important function used in statistics; also known as the Euler integral.
The beta function is defined as
1
1 1
0
( , ) (1 )
x y
t
x y dt tt
for x > 0 and y > 0. The incomplete beta function
is
1 1
0
( ; , ) (1 )
x
a b
t
x a dtb t t
and the regularized incomplete beta function is
( , ) B( ; , ) / B( , )
x
I a b x a b a b
. The
beta and gamma functions are related by
B( , ) ( ) ( ) / ( )x y x y x y
. In Excel, B(x, y) can be computed using
EXP(GAMMALN(x) + GAMMALN(y) – GAMMALN(x+y)).
See beta distribution, gamma function, negative binomial distribution.
ptg6843605
beta test – bill of material (BOM)
The Encyclopedia of Operations Management Page 42
beta test – An external test of a pre-production product, typically used in the software development context.
A beta test is an evaluation of new software by a user under actual work conditions and is the final test before
release to the public. The purpose of a beta test is to verify that the product functions properly in actual customer
use. The term is often used in the context of software released to a limited population of users for evaluation
before the final release to customers. In contrast, the alpha test is the first test conducted by the developer in test
conditions.
See agile software development, pilot test, prototype.
bias – (1) In a statistics context: The difference between the expected value and the true value of a parameter. (2) In
a forecasting context: An average forecast error different from zero. (3) In an electrical engineering context: A
systematic deviation of a value from a reference value. (4) In a behavioral context: A point of view that prevents
impartial judgment on an issue.
See forecast bias, forecast error metrics.
bid rigging – A form of fraud where a contract is promised to one party even though for the sake of appearance
several other parties also present a bid.
This form of collusion is illegal in most countries. It is a form of price fixing often practiced where contracts
are determined by a request for bids, a common practice for government construction contracts. Bid rigging
almost always results in economic harm to the organization seeking the bids. In the U.S., price fixing, bid
rigging, and other forms of collusion are illegal and subject to criminal prosecution by the Antitrust Division of
the U.S. Department of Justice.
See antitrust laws, bribery, predatory pricing, price fixing.
big box store – A retailer that competes through stores with large footprints, high volumes, and economies of scale.
Examples of big box stores in North America include Home Depot, Walmart, OfficeMax, and Costco.
Carrefour is an example in western Europe. Historically, these big box stores have been built in the suburbs of
large metropolitan areas where land was less expensive.
See category killer, distribution channel, economy of scale.
bill of lading – A transportation/logistics term for a contract between the shipper and the carrier.
The bill of lading (BOL) serves many purposes, such as (1) providing a receipt for the goods delivered to the
carrier for shipment, (2) describing the goods, including the quantity and weight, (3) providing evidence of title,
(4) instructing the carrier on how the goods should be shipped, and (5) providing a receiving document for the
customer; sometimes abbreviated B/L.
See consignee, manifest, packing slip, purchasing, receiving, waybill.
bill of material (BOM) – Information about the assemblies, subassemblies, parts, components, ingredients, and
raw materials needed to make one unit of a product; also called bill of materials, bill, product structure, formula,
formulation, recipe, or ingredients list.
The item master (part master or product master) is a database that provides information for each part (item
number, stock keeping unit, material, or product code). A record in the item master may include the item
description, unit of measure, classification codes (e.g., ABC classification), make or buy code, accounting
method (LIFO or FIFO), leadtime, storage dimensions, on-hand inventory, on-order inventory, and supplier.
The BOM provides the following information for the relationships between items in the item master.
BOM structure – The hierarchical structure for how the product is fabricated or assembled through multiple
levels. In a database, this is a double-linked list that shows the “children” and the “parents” for each item.
Quantity per – The quantity of each component required to make one unit of the parent item.
Yield – Yield information is used to inflate production quantities to account for yield losses.
Effectivity date – This indicates when an item is to be used or removed from a BOM.
A simple multi-level BOM product structure for a toy car is shown below. The final product (Item 1, the car
assembly) is at level 0 of the BOM. Level 1 in this example has the body and the axle subassembly. Note that
plastic is used for both items 2 and 4, but is planned at level 3 rather than at level 2. If plastic were planned at
level 2, it would have to be planned again at level 3 when the gross requirements for item 4 were created. Each
item should be planned at its “low level code.”
ptg6843605
bill of material (BOM)
−
bill of material (BOM)
Page 43 The Encyclopedia of Operations Management
A single-level BOM shows only the immediate components needed to make the item, whereas a multi-level
BOM shows all items. An indented BOM is a listing of items where “child” items are intended (moved to the
right). The table below is a simple example of the indented bill of material for the above product structure.
Indented bill of material
Level Item Item number Unit of measure Make/buy
0 Car assembly 1 Each Make
..1 Body 2 Each Make
..1 Axle subassembly 3 Each Make
….2 Wheel 4 Each Make
….2 Axle 5 Each Make
……3 Plastic 6 ml Buy
……3 Wire 5 cm Buy
A BOM explosion shows all components in the BOM, whereas a where-used report (sometimes called a
BOM implosion) shows a list of the items that use an item. A single-level where-used report lists the parent
items and quantity per for an item. An indented where-used report lists the lowest-level items on the far left
side and indents the parent items one place to the right. Each higher-level parent is indented one additional place
to the right until the highest-level item (level 0) is reached. Single-level pegging is like a single-level where-
used report but it only points to higher-level items that have requirements. If a BOM has high commonality,
items are used by many parent items.
A planning bill of material, sometimes called a percentage BOM, super BOM, or pseudo BOM, can be
used to plan a family of products using percentages for each option. For example, in the example below, a car
manufacturer has historically sold 20% of its cars with radio A, 30% with radio B, and 50% with radio C. The
firm forecasts overall sales for cars and uses a planning BOM to
drive Materials Requirements Planning (MRP) to plan to have
about the right number of radios of each type in inventory when
needed. A Final Assembly Schedule (FAS) is then used to build
cars to customer order.
A BOM can define a product as it is designed (engineering
BOM), as it is built (manufacturing BOM), or as it is ordered
by customers (sales BOM).
The Master Production Scheduling (MPS) entry discusses several types of BOM structures and the Materials
Requirement Planning (MRP) entry explains how the BOM is used in the planning process.
See ABC classification, backflushing, bill of material implosion, Business Requirements Planning (BRP),
commonality, dependent demand, effectivity date, Engineering Change Order (ECO), Enterprise Resources
Planning (ERP), Final Assembly Schedule (FAS), formulation, low level code, Master Production Schedule
Wheel (Item 4)
2 per axle subassembly
Sim
p
le bill of material (
p
roduct structure) for a to
y
car
Body (Item 2)
1 per car assembly
Axle subassembly (Item 3)
2 per car assembly
Level
0
1
2
3
Axle (Item 5)
1 per axle subassembly
Plastic (Item 6)
1 ml per wheel
Wire (Item 5)
1 cm per axle
Car assembly
(Item 1)
Plastic (Item 6)
4 ml per body
Automobile
Radio A Radio B Radio C
20% 50%30%
Planning bill of material
ptg6843605
bill of material implosion
–
binomial distribution
The Encyclopedia of Operations Management Page 44
(MPS), Materials Requirements Planning (MRP), part number, pegging, phantom bill of material, product
family, routing, shop packet, VAT analysis, Warehouse Management System (WMS), where-used report, yield.
bill of material implosion
– A manufacturing term used to describe the process of indentifying the “parent” item
(or items) for an item in the bill of material; the opposite of a bill of material explosion; also called a where-used
report.
See bill of material (BOM), pegging, where-used report.
bill of resources
– A list of the machine time and labor time required to make one unit of a product.
The bill of resources should only include a few key resources (i.e., those resources that normally have the
tightest capacity constraints). Rough Cut Capacity Planning (RCCP) uses the bill of resources to convert the
Master Production Schedule (MPS) into a rough cut capacity plan.
See capacity, Master Production Schedule (MPS), Rough Cut Capacity Planning (RCCP), Theory of
Constraints (TOC).
bimodal distribution
– A statistics term for a
probability distribution with two identifiable
peaks (modes).
A bimodal distribution is usually caused
a mixture of two different unimodal
distributions. The example on the right
shows a histogram for the mixture of two
normally distributed random variables with
means 14 and 24. (This is a probability
mass function because the graph shows
frequencies for integer values.)
See probability distribution, probability
mass function.
bin
– See warehouse.
binary logistic regression
– See logistic
regression.
binomial distribution
– A discrete probability distribution used for the number of successes (or failures) in n
independent trials with probability p for success in each trial.
The binomial is a useful tool for quality control purposes.
Probability mass and cumulative distribution functions: The binomial probability mass function is
( ) (1 )
x n x
n
p x p p
x
, where
!
!( )!
n
x
n
x n
x
is the binomial
coefficient, which is the number of
combinations of n things taken x at a time.
The cumulative distribution function
(CDF) is then
0
( ) Pr( ) (1 )
x
i n i
i
n
F x X x p p
i
,
where
x
is the greatest integer less than
or equal to x.
Graph: The graph on the right is the
binomial probability mass function with
n = 20 trials of a fair coin (p = 0.5).
ptg6843605
Black belt − blue ocean strategy
Page 45 The Encyclopedia of Operations Management
Statistics: Range {0, 1, … , n}, mean np, variance np(1 − p), and mode
( 1)p n
or
( 1) 1p n
.
Excel: In Excel, the probability mass function is BINOMDIST(x, n, p, FALSE) and the probability
distribution function is BINOMDIST(x, n, p, TRUE). Excel does not have an inverse function for the binomial
distribution.
Excel simulation: An Excel simulation might use the inverse transform method to generate binomial
random variates using a direct search.
Relationships with other distributions: The Bernoulli distribution is Binomial(1, p). The binomial is the
sum of n Bernoulli random variables (i.e., if X
1
, X
2
, … , X
n
are n independent identically distributed Bernoulli
random variables with success probability p, the sum
1
n
i
i
Y X
is binomial). The normal distribution can be
used to approximate the binomial when
10np
and
(1 ) 10np p
. However, a continuity correction factor of
0.5 should be used, which means that P(X = x) for the binomial is estimated using F(X + 0.5) – F(X – 0.5) for the
normal. The normal approximation is particularly important for large values of n. The Poisson distribution can
be used to approximate the binomial with large n and small p (i.e., n ≥ 20 and p ≤ 0.05 or n ≥ 100 and np ≤ 10).
The binomial is a good approximation for the hypergeometric distribution when the size of the population is
much larger than the sample size.
See bar chart, Bernoulli distribution, combinations, hypergeometric distribution, normal distribution, p-
chart, Poisson distribution, probability distribution, probability mass function.
Black belt – See lean sigma.
blanket order – See blanket purchase order, purchase order (PO).
blanket purchase order – A contract with a supplier that specifies the price, minimum quantity, and maximum
quantity to be purchased over a time period (e.g., one year); sometimes called a blanket or standing order.
Blanket orders usually do not state specific quantities or dates for shipments. Instead, purchase orders
(releases) are placed “against” the blanket order to define the quantity and due date for a specific delivery. The
advantage of a blanket purchase order for both the customer and the supplier is that it locks in the price so it does
not need to be renegotiated very often. The supplier usually gives the customer a quantity discount for the
blanket order and may also be able to provide the customer with a reduced leadtime and better on-time
performance. Any company representative who knows the purchase order number can purchase items until the
value of the blanket order has been exceeded. Providing a blanket order to a supplier may reduce the leadtime
and improve on-time delivery.
See on-time delivery (OTD), purchase order (PO), purchasing, quantity discount.
blending problem – See linear programming (LP).
blind count – An inventory counting practice of not giving counters the current on-hand inventory balance.
With a blind count, the counter is given the item number and location but no information about the count
currently in the database. This approach avoids giving counters a reference point that might bias their counts.
See cycle counting.
blocking – The lean practice of not allowing a process to produce when an output storage area is full.
Examples of output storage areas include a container, cart, bin, or kanban square. A kanban square is
rectangular area on a table or floor marked with tape. Blocking is good for non-bottleneck processes because it
keeps them from overproducing (i.e., producing before the output is needed). Blocking avoids overproduction
and keeps the total work-in-process inventory down to a reasonable level. Blocking for a bottleneck process is
bad because it causes the system to lose valuable capacity. Remember that an hour lost on the bottleneck is an
hour lost for the entire system. Starving and blocking are often discussed in the same context.
See CONWIP, kanban, lean thinking, starving, Theory of Constraints (TOC), Work-in-Process (WIP)
inventory.
blow through – See phantom bill of material.
blue ocean strategy – A business strategy that finds new business opportunities in markets that are not already
crowded with competitors.