Description
Share a 800-word minimum synopsis of the strategic marketing concepts discussed in the three articles attached not including introduction and conclusion.
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The
Good
BetterBest
Approach to
Prıcing
RAFI
MOHAMMED
Founder, Culture of Profit
or decades the auto insurance industry
operated on a simple assumption:
Consumers are highly price-sensitive,
and most will buy the least-expensive
plan they can find. But in the early 2000s
Allstate conducted some research that
caused it to revisit that assumption. Price
does matter, it learned, but there’s more to
the story: Many drivers worry about being
hit with premium hikes if they’re in an accident. And drivers
with clean records want to be rewarded.
Armed with those insights, in 2005 Allstate launched Your
Choice Auto. The program relied heavily on modifications to a
feature in the company’s standard policy (which it continued
selling) called accident forgiveness, in which drivers who went
five years without accident claims would have no premium
increase after their first accident. It introduced a Value plan,
priced 5% below Standard, that didn’t include accident forgiveness. A new Gold plan, priced 5% to 7% above Standard,
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Art by Dan Saelinger
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offered immediate forgiveness (no five-year wait) along with a
deductible rewards feature in which repair costs borne by the
driver would decline by $100 for every year of accident-free
driving. And at the highest end, a new Platinum plan (15% above
Standard) also included forgiveness for multiple crashes and
a safe-driving bonus under which credits were issued for each
accident-free six months.
Consumers were enthusiastic: By 2008 Allstate had sold
3.9 million Your Choice policies and was selling 100,000 new ones
each month. A decade later the pricing plan remains attractive: In
2017, 10% of customers chose the Value plan, and 23% chose Gold
or Platinum. The company has no doubt that Your Choice drove
significant incremental growth. “There were a lot of skeptical
people in the company,” recalls Floyd Yager, one of Allstate’s
senior vice presidents. “But we demonstrated that car insurance
doesn’t have to be about being the lowest-price game.”
Your Choice is a classic example of Good-Better-Best
(G-B-B) pricing. There’s nothing new about the concept of
adding or subtracting product features to create variably priced
bundles targeted to customers of varying economic means or
those who value features differently. It’s been nearly 100 years
since Alfred Sloan introduced a “price ladder” to differentiate
Chevrolets and Buicks from Oldsmobiles and Cadillacs, creating “a car for every purse and purpose” and powering General
Motors to overtake Ford. In the modern era, G-B-B pricing is
evident in many product categories. Gas stations sell regular,
plus, and super fuel. American Express offers a range of credit
cards, including green, gold, platinum, and black, with varying
benefits and annual fees. Cable TV providers market basic,
extended, and premium packages. Car washes typically offer
several options, separated by services such as waxing
and undercoating.
► Idea in Brief
► THE PROBLEM
Companies often crimp profits
by using discounts to attract
price-sensitive consumers and by
failing to give high-end customers
reasons to spend more.
► THE SOLUTION
A multitiered offering (typically with
three options) can use a strippeddown product to attract new
customers, the existing product to
keep current customers happy, and
a feature-laden premium version
to increase spending by customers
who want more.
► THE IMPLEMENTATION
Key steps include identifying
“fence” attributes that will
prevent current customers from
trading down from the existing
offering; carefully choosing
features and names to create
clear differentiation and value;
and setting prices using feedback
from in-house experts and,
when possible, drawing on
market research.
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Yet many companies and industries haven’t adopted tiered
pricing—and there’s little rhyme or reason to which have, which
haven’t, and why. G-B-B is a strategy every company should
consider. In my consulting work, I routinely see it used to
simultaneously attract new high-spending customers and price-
conscious ones, dramatically boosting revenue and profits.
(Disclosure: Among my clients is Harvard Business Publishing,
the publisher of this magazine.)
Although G-B-B is conceptually simple, implementation can
be tricky. If new offerings aren’t constructed and priced correctly,
existing customers will trade down, hurting profits. In this article
I outline why G-B-B can benefit many firms. Then I present a stepby-step guide to devising, testing, and launching the strategy in a
way that boosts profits and reduces the threat of cannibalization.
Capitalizing on G-B-B
G-B-B’s benefits come from three approaches: offensive plays
aimed at generating new growth and revenue, defensive
plays meant to counter or forestall moves by competitors,
and behavioral plays that draw on principles of consumer
psychology, whatever the competitive landscape.
Going on the offensive. Offensive plays can help brands
grow revenue in at least four ways. First, companies can dramatically lift margins by creating a high-end Best version that
persuades existing customers to spend more or attracts a new
cohort of high spenders. In my work with companies, managers
consistently underestimate customers’ willingness to spend
and the number of customers who might upgrade to Best, even
at prices that were previously unthinkable. Across a range of
industries, it’s not unusual to observe up to 40% of sales landing
on the Best option.
For example, visitors at Six Flags amusement parks can buy
one of three Flash Passes (Regular, Gold, and Platinum add-on
options to the standard admission ticket, with prices varying by
day and location) to bypass lines and thus enjoy more rides. The
Gold Pass, which costs as much as $80 a day on popular weekends, reduces waits by up to 50%; the Platinum Pass, which can
reach $135, reduces them by up to 90%. “It’s amazing, actually,
how many people pay for this,” then-CFO John Duffey told analysts shortly after the new passes were rolled out, in 2011. Many
Flash Pass purchasers are existing customers who decide to
upgrade, but some are new customers who had previously been
put off by the notoriously long lines for rides.
Second, and at the other end of the spectrum, a low-priced
Good offering can make a product accessible to price-sensitive
or dormant customers for whom the existing product line
(which typically then becomes a Better offering) is out of reach.
And it can limit the need for discounts or sales on the existing
A low-priced Good offering can make a product accessible to
price-sensitive or dormant customers, and it can limit the need
for discounts or sales on the existing offering.
product or service—a crucial advantage, because frequent sales
can erode long-term pricing power.
Uber has shown continued creativity and success with its
Good versions. The company began in 2010 as a black-car luxury
service, and it still offers several high-end options. But in 2014,
hoping to lure price-sensitive riders, it launched uberPOOL,
in which riders share a car with strangers going in the same
general direction. Unlike the traditional uberX service (in which
riders have a midsize sedan to themselves and go directly to
their destination), uberPOOL trips involve multiple pickups and
drop-offs of other passengers, so there’s additional travel time;
in exchange, the service is priced as much as 50% below uberX.
UberPOOL now accounts for 20% of all Uber rides—and in some
cities it accounts for more than half of all trips. The company has
begun experimenting with Express POOL, which costs 30% to
50% less than uberPOOL and requires riders to walk a few blocks
to a central pickup location. Uber’s story shows that even after
implementing a G-B-B strategy, companies should continue
exploring innovations that might lead to new, lower-priced
versions of Good.
A third way that G-B-B can increase revenue is through a
new Best offering that boosts the entire brand. In 2015 Patrón
Spirits debuted a line of Roca Patrón tequilas made by the
tahona process, which uses a two-ton wheel hand-cut from
volcanic stone to extract juice from cooked agave. The result is
a sweeter, earthier, more complex spirit than tequila produced
by automated means. Even at $69-plus a bottle, Roca Patrón has
exceeded sales expectations: It is projected to sell 60,000 cases
in 2018, which would make it the world’s seventh-best-selling
premium tequila brand.
And the benefits go beyond that revenue: Sales of lower-
priced Patrón tequilas have risen sharply. Lee Applbaum,
Patrón’s chief marketing officer, cites research showing that
Roca has boosted perceptions of the overall Patrón line as
artisan-crafted (from 60% of consumers surveyed to 64%),
made by a small-batch producer (47% to 58%), and fitting an
image people want to convey (59% to 65%). “The details of
the expensive and laborious way that Roca Patrón tequilas are
manufactured create a brand halo that reinforces important
attributes…for the entire Patrón line,” he says.
Fourth, a lower-priced Good version can spark ancillary
revenue from related or complementary goods and services.
Consider Apple’s SE phone, which sells for just $349 (roughly a
third as much as the iPhone X). Every SE sale stimulates additional revenue through purchases on iTunes and the App Store,
payments for iCloud storage space, and sales of cases, chargers,
and other accessories.
Playing defense. Sometimes G-B-B isn’t about aggressively
seeking new revenue—it’s about protecting a brand’s exposed
flank. When faced with a low-cost rival, many companies’ kneejerk response is to drop prices, but that’s often a mistake. When
the price holds firm, 15% of sales, say, might be lost to a low-cost
competitor, but 85% of customers are still paying full price—
whereas if the price is cut, 100% of customers will be paying less.
Another common response to cheaper rivals is to launch a “fighter
brand”—a discounted product with entirely new branding.
Classic examples include Procter & Gamble’s Luvs diapers and
Intel’s Celeron computer chip. (See “Should You Launch a Fighter
Brand?” HBR, October 2009.) That may work well, but the
resources needed to create a new brand can be enormous.
In many cases, creating a new Good product is a better
defensive strategy. Two of my B2B clients (in financial services
and industrial parts) held significant market share and enjoyed
healthy profit margins when new entrants began offering
inferior products at rock-bottom prices. Customers seized on
the disruptive entry as an invitation to negotiate, threatening
to defect from my clients unless granted a discount. Although
reluctant to lose any market share, both clients resisted the
impulse to discount their core offering. Instead, they quickly
rolled out cheaper Good versions that closely matched the new
entrants’ stripped-down products. When offered those options, most customers backed off their demands for a discount
and continued buying their existing offering at full price; they
had been bluffing and weren’t actually willing to trade down
to a lesser product. Implementing a Good version calls such
bluffs—something a straight discount can’t do.
A caveat: This defensive maneuver can have mixed results. In
2015 Town Sports International, a chain of fitness centers whose
memberships averaged $40 to $90 a month, began losing customers to competitors such as Planet Fitness, whose monthly fees are
as low as $10. To fight back, TSI retained its existing membership
plan and prices while launching a new plan—priced as low as
$19.99 a month—that excluded or restricted some benefits, such
as towel service and access to fitness classes. This staunched the
membership decline: TSI gained 64,000 new customers in 2015.
But the stock price plummeted, same-club revenues fell, and the
CEO resigned. Still, the new Good membership may have been
the best possible response in a tough environment. By steering
clear of a simple discount or a price war, TSI ensured that many
members continued to pay their existing monthly fees, and the
company avoided a devaluation of its primary offering.
Drawing on consumer psychology. Some G-B-B strategies
aren’t specifically aimed at luring new customers or defending
against competitive threats; they’re more-general responses to
consumer psychology.
For instance, companies often jam multiple features and
attributes into a single product, but this can confuse and overwhelm customers. A G-B-B plan helps potential buyers focus
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on and understand features and think about which ones they
value—and how much they’re willing to pay for them. (See the
exhibit “Helping Customers Understand Good-Better-Best.”)
An educational software company I worked with found that
customers didn’t really grasp its myriad product features. So it
tested a G-B-B model that unbundled those features, creating a
Good offering (its core software), a Better one (the core software
plus new electronic exercises), and a Best one (the core software
and exercises plus one-on-one tutoring). Customer research
showed that the three-tiered model helped people differentiate the company from competitors—and indicated that half of
potential customers would pay a premium for Better or Best.
(Because of a sudden leadership change, however, the G-B-B
model was never implemented.)
G-B-B can also shift customers from a binary “buy/don’t buy”
mentality to consideration of incremental value and spending. This can work in two ways. First, customers prefer having
choices to feeling under an ultimatum, so three differently
priced options can give them a sense of empowerment. Allstate
CEO Thomas Wilson has identified this as a key benefit of the
Your Choice policies, explaining that they moved people away
from simply comparing Allstate’s prices with those of competitors. “If people [have] a choice in the conversation, they are not
likely to switch [to a competitor] for $25 or $50,” he said in a July
2005 quarterly call.
Second, when faced with multiple options, customers tend
to decide more quickly whether they are going to buy something, using their remaining time to focus on what. Having
made that mental shift, they typically treat the Good version as
a sunk cost, which makes them more amenable to upgrading.
Salespeople exploit this tendency all the time: For example,
instead of detailing all the features of a $1,200 appliance, they
emphasize that “for only $200 more” than the entry-level $1,000
unit, a buyer gets lots of extra bells and whistles. Rental car
companies highlight the full-size sedan you could be driving for
$12 a day more than the price of a subcompact.
Companies can also use G-B-B to exploit the so-called
Goldilocks effect: people’s propensity to choose the middle option in a set of three. In his book Priceless, William Poundstone
recounts how Williams-Sonoma reaped unexpected benefits
after launching a fancy bread machine priced at $429. That highend model flopped—but sales of the $279 model (previously the
highest-priced unit) nearly doubled.
A final argument for considering G-B-B relates to the real
politik of instituting change. The simplicity of the G-B-B strategy
makes it highly compelling to senior executives. For change to
occur at any organization, top management must be committed,
deploying political capital to sell others on the shift. Because
managers have experienced G-B-B as consumers, they can
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quickly understand its appeal. In my consulting work, I often
suggest other pricing strategies but wind up helping implement
G-B-B because it’s the option managers find the easiest to understand, explain, and get behind.
Brainstorming About
Tiers and Features
When considering a G-B-B pricing structure, the first step is
to decide how many product versions to offer. As the name
implies, the most common approach is three. In general,
companies with a single existing product will designate it (or
something close to it) as Better, adding features to create Best
and subtracting them for Good. But if taking away features
to create a Good offering isn’t feasible, companies can forgo
that option and simply offer Better and Best.
Companies with complex products or a long buying cycle
may be able to justify more versions. But too much choice is
risky. In a well-documented study by Sheena Iyengar and
Mark Lepper, researchers offered samples of jam to shoppers
in an upscale grocery store. When presented with six flavors,
30% of tasters made a purchase. When 24 options were on the
table, only 3% opted to buy. Researchers believe that when
consumers have too many options, they become confused or
paralyzed with indecision—a phenomenon the psychologist
Barry Schwartz explored in The Paradox of Choice.
If a company is set on many offerings, it can be useful to
group them in a way that turns consumers’ decision making into
a two-step process. New York’s Metropolitan Museum of Art
offers seven memberships. To minimize confusion, it divides
them into two categories: Members Count plans ($80 to $600)
for people joining primarily because they want to visit the
museum, and Patron Circle memberships ($1,500 to $25,000) for
those whose primary goal is philanthropic. Grouping memberships in such a way guides people toward a general category;
once there, they can examine the G-B-B options in each.
After a company has gotten a sense of how many tiers to
offer, managers can brainstorm about the features to include
in each. Sometimes the decisions are obvious, but many of the
best G-B-B plans draw on unexpected features, as Six Flags did
when manipulating wait times to create a consumer benefit for
its Flash Passes.
To help companies consider a wide array of potential features
and benefits, I use a tool called the Value Barometer, which lists
13 common product attributes that can be added, dropped, or
varied to create different perceptions of value. (See the exhibit
“Pump Up the Value.”) Companies typically begin by identifying
features of the current offering that vary or would be easy to
Pump Up
the Value
A crucial step in devising Good-Better-Best bundles
is choosing attributes to add, drop, or vary to create
different perceptions of value. Adding and dropping are
straightforward; the creativity is in varying attributes that
span your G-B-B offerings. The chart below can help you
find nonobvious ways to create Good and Best variations
on an existing (Better) offering.
G-B-B Value Barometer
ATTRIBUTE
GOOD
BEST
Volume
Low
Unlimited
Service
Basic
High-end
Experience
Regular
Over-the-top
Time period
Off-peak
Peak
Waiting time
Standard
None
Speed
Slow
Fast
Brand
Generic
Differentiated
Warranty
Limited
Extended
Number of
restrictions
High
None
Relationship
Distant
Close
Certainty
Low
Guaranteed
Flexibility
Low
High
Skill level
Basic
Experienced
Examples
Volume: Netflix prices its streaming service according to the number
of devices on which content can be simultaneously viewed.
Service: The Princeton Review offers three SAT prep options, ranging from
“self-paced” (primarily do-it-yourself online exercises) to private tutoring.
Experience: The band Earth, Wind & Fire offers a “fantasy” package that gives
concertgoers a personal meet-and-greet and photo ops with the musicians.
Time period: Season passes at Sundance Mountain Resort come in two versions:
unlimited and discounted midweek.
Waiting time: Massachusetts General Hospital offers a concierge option
that provides 24/7 phone access to doctors; many concierge practices also
guarantee same- or next-day appointments.
Speed: Federal Express offers a variety of next-day delivery options in
major cities, often including 8:30 am, 10:30 am, and 3:30 pm.
Brand: 90+ Cellars buys excess inventory from highly rated wineries and sells it
under its own label, without revealing the wineries’ names.
Warranty: DieHard auto batteries have warranties ranging from
18 months (gold) to 4 years (platinum).
Number of restrictions: Many airlines offer “basic economy” tickets that
are nonrefundable and allow no advance seat assignments.
Relationship: Memberships to the Boston Symphony Orchestra vary in such things as access to
intimate gatherings with musicians, invitations to rehearsals, and behind-the-scenes lectures.
Certainty: Many heating oil companies offer homeowners the option of paying market
rates (which fluctuate) or, for a premium, locking in a rate for the season.
Flexibility: TV networks typically sell up to 85% of their ad spots in advance, reserving the rest
for advertisers, such as movie studios, willing to pay a premium for last-minute availability.
Skill level: Equinox Fitness rates and prices its personal trainers according to
how far they have advanced in its training institute.
vary, but the tool’s real power is its ability to help firms come up
with out-of-the-box options that could be increased, decreased,
or tweaked.
Once the brainstorming is complete, a company can begin
analyzing the potential features it has identified. Three questions are key: Does the feature have mass appeal or low appeal?
How would adding or subtracting it affect the cost of producing
the good or offering the service? And is it a “fence” attribute—
one that constitutes a barrier preventing existing customers
from crossing over to something cheaper?
Many managers start by focusing on the Best option, because of its obvious potential for revenue growth (and because
imagining new high-end features is fun). But they should begin
by identifying and analyzing fence attributes—often the most
challenging task in G-B-B implementation.
The goal of adding a Good offering is to pick up new budget-
minded customers without losing revenue from existing ones.
(In a perfect world, not a single customer would move from
Better to Good.) Indeed, one of the biggest risks of shifting to
G-B-B is that existing customers will migrate to the new lower-
priced offering, cannibalizing revenue and margins. Fence
attributes prevent this, by making the downgrade a difficult,
unpleasant, or painful choice.
Examples of fence attributes abound. In cable television,
ESPN, CNN, and HGTV are always included in “extended basic”
(the Better offering) because many existing viewers highly value
at least one of those channels, and losing access makes the idea
of trading down to basic (the Good offering) anathema. Hotels
offer discounted “no cancellation” reservations; the lack of flexibility creates a fence for many travelers. During a recent tour,
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the Rolling Stones sold seats for just $85, but those seats came
with a catch: Concertgoers wouldn’t learn their location until
arriving at the arena. That was a significant fence for many fans,
who would rather stay home than sit in a poor location. And
paperback versions of books previously published in hardcover
utilize an obvious fence: They appeal only to readers who don’t
mind waiting a year or more for the book. Companies seeking to
implement Good offers must find similarly effective fences.
Defining and Pricing Bundles
To choose the fence attributes that will separate their Good and
Better offerings, companies should look for features that have
both wide and deep appeal (meaning that most customers want
them and consider them vitally important) and are somewhat
costly to produce. The combination of high appeal and high
cost means that if the feature is part of the Better but not the
Good offering, relatively few people accustomed to Better (that
is, existing customers) will consider Good—but those willing
to do without the feature can enjoy a significant discount. For
instance, when the New York Times launched its digital subscriptions, in 2011, it moved to a G-B-B model in which the physical
paper (which many subscribers were loath to discontinue, and
which is costly to print and deliver) served as a fence attribute.
That fence is effective enough to support a hefty price differential: An all-access digital subscription currently costs $324 a year,
whereas adding print delivery brings the price to $481 and up,
depending on location.
The same qualities—appeal and cost—that help companies
choose fence features will also guide them toward features that
belong in Best. Those should similarly appeal to a wide segment
of buyers, but ideally they will cost relatively little to include so
that the company can keep high margins on Best.
When Southwest Airlines created the Business Select
package as its Best offering, about a decade ago, it identified
high-appeal/low-cost items such as priority boarding, extra
frequent-flier miles, and free cocktails as amenities worth
including. Bundling those relatively inexpensive amenities
in a premium package delivered $73 million in incremental
revenue in the offering’s first full year.
High-appeal/low-cost Best features are often less about
the actual product and more about the customer experience.
For instance, quicker delivery time can be part of a Best offer.
And in some industries, guarantees or warranties can deliver
high perceived customer value at little cost, depending on the
hurdles that must be overcome to redeem the guarantee or on
the expected utilization rate. For example, the length of the
warranty is the major differentiator between Good, Better,
and Best versions of car batteries—products that behave fairly
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Helping Customers
Understand Good-Better-Best
Once a company has
created a multitiered
offering, it needs to help
customers understand
the various options. This
comparison grid, from a
website design and hosting
firm, is effective for three
reasons, as described in the
following annotations.
1
1.
L imiting the use of features
available with the Good option
(pages, bandwidth, and storage)
creates a “fence” separating the
truly price-sensitive from those
willing to pay more.
predictably. But some products, such as tutoring services and
weight loss programs, require customer involvement to achieve
success. Because of that uncertainty, companies generally aren’t
willing to guarantee them, even as part of Best packages and
even if consumers would highly value guarantees.
When devising Best bundles, companies need to be realistic
about the attributes they can include. During brainstorming, it’s
natural to dream big—but as dreaming turns to planning, vigilance is needed to weed out features that may be difficult to execute well or that could delay the launch. It’s also important to be
judicious about the number of attributes. It’s tempting to throw
all the latest and greatest features into Best, but this can result in
unnecessary complexity and an unrealistically high price.
After completing the cost-benefit analysis of the various
features, it’s time to design and assign tentative prices to the
G-B-B bundles. Two rules of thumb for design: To ensure sharp
distinctions between offerings, no more than four attributes
114 HARVARD BUSINESS REVIEW SEPTEMBER–OCTOBER 2018
2
3
2.
T here’s a nice consistency and
progression between packages:
Customers don’t lose anything
as they move up in price, and
each level has three or four key
differentiators.
3.
The packages have been
intelligently named. In particular,
“Business” clearly communicates
the type of customer who should
choose the premium option. The
80% price difference between
that package and “Advanced”
signals the company’s belief
that business customers—who
typically have greater needs and
are less price-sensitive—will be
willing to pay significantly more.
should differ between Good and Better and between Better and
Best. And it’s important to maintain a consistent progression
of benefits from Good to Better to Best—beneficial features in
Good should be retained in the higher-priced offerings so that
every step up the ladder is a clear improvement.
Some rules of thumb can similarly help with pricing.
Companies should pay close attention to the price gaps between
Good and Better and between Better and Best. In my consulting,
I strongly advise against setting a Good price that’s more than
25% below Better, and I recommend that the Best price should
not exceed Better by more than 50%. Although customers’
perceived value must be the North Star, companies must also
consider how many customers might opt for Good, Better, and
Best and what the margins of each package will be. As a starting
point—before conducting customer research—many companies
estimate that 10% to 20% of revenue will come from Good, 25%
to 50% from Better, and 30% to 60% from Best. The actual mix
The Good-Better-Best Approach to Pricing
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will depend on how many attributes vary between versions, the
degree of differentiation achieved, and the price spread.
It’s never too early to think about names for the G-B-B options;
those are essential in helping consumers quickly identify which
version best meets their needs. Lisa Krassner, the chief member
and visitor services officer at the Metropolitan Museum of Art,
says that the very clear names of the three Members Count
options, each delineating a particular benefit—With Early Views,
With Evening Hours, and With Opening Nights—have been key
to the offerings’ success.
biased, particularly by the composition of the customer sample
that responds. Still, especially for companies desiring strong
quantitative evidence before bringing a G-B-B strategy to
market, positive results from a well-designed conjoint analysis
can provide comfort and affirmation.
Once research has helped a company finalize feature and
pricing decisions, it’s time to launch the G-B-B offerings. Early
results should be watched carefully and adjustments made as
needed. Compared with other product attributes, pricing is
often easy to alter on the fly.
Bringing in Research
MOST COMPANIES COULD implement some form of G-B-B. Every
company already offers the equivalent of a Better offering,
and even if some firms can’t implement both Good and Best,
many could gain new customers, additional revenue, or both
by adding either a Good or a Best to their lineup.
The companies with the biggest challenges in designing a
full G-B-B lineup are those whose products have few distinct
features and/or features that can’t easily be modified, making
it hard to identify effective fence attributes and move down market with a Good bundle. In other cases, executives may be too
fearful of cannibalization (or skeptical about the effectiveness
of fences to limit it) to sign off on a Good offering. (Some B2B
companies that decide against explicitly marketing a Good product may devise a compromise: quietly offering a Good version
to budget-constrained clients on a case-by-case basis, with the
goal of establishing new customers or saving existing ones and
upselling them in the future.) Even if a Good option is not viable
in any form, exploring a G-B-B strategy may prompt companies
to introduce a Best offering, which can deliver new revenue.
As strategies go, shifting to G-B-B pricing may seem simplistic, but many companies have discovered that it’s more powerful
than it appears at first blush. Jim Roth, a senior vice president at
Dell EMC, was in a fast-food restaurant at Chicago’s O’Hare airport when he realized that the bundled value meals on the menu
board made it easier for him to order. That caused him to reflect
on his own company’s pricing and bundles. Dell EMC ultimately
created Good, Better, and Best versions of its deployment
support for B2B customers—and found that customers buying
those bundles generally spent three times as much as they had
previously spent on that type of after-purchase support. Dell
EMC thus joined the many other firms who have recognized that
G-B-B could help them serve their customers better—and boost
HBR Reprint R1805H
their bottom line.
Many companies conduct formal research to see whether their
intuitive sense of what customers want is on target. The timing
and scope will depend partly on organizational culture: Some
data-driven companies do several rounds of testing, starting
soon after the brainstorming step, while other companies wait
until they’ve created tentative G-B-B bundles and prices. (Still
others proceed without any formal research.) Regardless of
timing, companies can draw on three sources of data:
Expert judgment. Experienced executives, salespeople, and
other frontline employees have a good understanding of customers and their needs. They’ve watched people balk at prices,
and they often have a sense of when customers would pay more.
When setting G-B-B prices, companies should collect and factor
in the views of these in-house experts. Although that may feel
unscientific, my experience with clients shows that in-house
expert judgments often reliably predict data gathered during
more-formal testing—and many companies design and implement effective G-B-B strategies using only those judgments to
drive bundle and pricing decisions.
General market research. Basic insights can be gained by
asking customers to respond to potential features and prices in
quantitative or qualitative surveys (the questions can be added to
existing post-purchase satisfaction surveys). Simplicity is crucial:
A survey item might say, “We’re excited to roll out this premium
feature for $79. Would you be interested in making this purchase,
and why or why not?” Modifying the questions to test customers’
interest in a discounted Good product instead can yield insights
into fence attributes and the risk of cannibalization.
Conjoint analysis. This common research technique
involves giving subjects a series of binary product choices,
each with different features and prices, and asking which they
prefer. It can be a powerful tool: If the choices are constructed
well and enough data is gathered, researchers can gain a clear
sense of which attributes or features customers want, how much
they will pay for each, and which are fence attributes. It isn’t
foolproof: As with any market research, results can be flawed or
RAFI MOHAMMED is the founder of Culture of Profit, a consultancy that
helps companies develop and improve their pricing strategies, and the
author of The Art of Pricing: How to Find the Hidden Profits to Grow Your
Business (Crown Business, 2005) and The 1% Windfall: How Successful
Companies Use Price to Profit and Grow (HarperBusiness, 2010).
SEPTEMBER–OCTOBER 2018 HARVARD BUSINESS REVIEW 115
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PRICING
A Survey of 1,700
Companies Reveals
Common B2B Pricing
Mistakes
by Ron Kermisch and David Burns
JUNE 07, 2018
GLASSHOUSE IMAGES/GETTY IMAGES
Poor pricing practices are insidious — they damage a company’s economics but can go unnoticed for
years. Consider the case of a major industrial goods manufacturer that was struggling with low profit
margins, relative both to competitors and to its own historical performance. It traced much of the
cause to a mismatch between its sales incentives and pricing strategy. The manufacturer was
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2
compensating sales representatives based solely on how much revenue they generated. Reps thus
had little motivation to hit or exceed price targets on any given deal, and most were closing deals at
the lowest permissible margin.
Like this manufacturer, many business-to-business (B2B) companies have a major opportunity to
improve their standing on price. To help companies understand the state of pricing capabilities and
how they figure into performance, Bain & Company conducted a global survey of sales leaders, vice
presidents of pricing, CEOs, CMOs, and other executives at more than 1,700 B2B companies. We
gathered their self-rating of 42 pricing capabilities and outcomes.
Roughly 85% of respondents believe their pricing decisions could improve. On average, large
capability gaps exist in price and discount structure, sales incentives, use of tools and tracking, and
structure of cross-functional pricing teams and forums.
What Pricing Leaders Do Differently
To understand which capabilities matter most, we studied a subset of top-performing companies, as
defined by increased market share, self-described excellent pricing decisions, and execution of
regular price increases. While different pricing capabilities may be important for a particular
situation, the analysis showed that top performers exceed their peers primarily in three areas. Top
performers are more likely to:
• employ truly tailored pricing at the individual customer and product level
• align the incentives for frontline sales staff with the pricing strategy, encouraging prudent pricing
through an appropriate balance of fixed and variable compensation
• invest in ongoing development of capabilities among the sales and pricing teams through training
and tools
Our analysis also revealed just how much excelling across multiple pricing capabilities pays off.
Among the companies that excel in all three areas, 78% are top performers, versus just 18% of
companies that excel in none of the three. Let’s explore why these three areas have such a strong
effect on pricing effectiveness.
Pricing to the Average Is Always Wrong
One-size-fits-all pricing actually fits no one. Yet it is not unusual for sales executives to admit that
their ability to tailor prices at the customer and transaction level is rudimentary, or that they are not
even aware of how much margin they make on deals.
By contrast, more-advanced companies tailor their pricing carefully for each combination of
customer and product, continually working to maximize total margin. They bring data and business
intelligence to bear on three variables for setting target prices:
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3
• the attributes and benefits that each customer truly values, and how much value is created for
them
• the alternatives and competitive intensity in the industry
• the true profitability of the transaction after accounting for leakage in areas such as rebates, freight,
terms, and inventory holding
One North American manufacturer with margins that were highly dependent on raw material pricing
suffered from an undisciplined approach to pricing. A diagnosis allocated costs at the product and
customer level to determine true profitability. That diagnosis, which showed the manufacturer was
undercharging in many cases, provided the support needed to raise prices where appropriate in
subsequent contract negotiations, leading to an average 4% increase from that opportunity alone.
The company designated an executive to be accountable for related profit margin opportunities and
to track the status and effect of each price increase. As a result, the company improved earnings
before interest, taxes, depreciation, and amortization by 7 percentage points.
Bad Incentives Undercut the Best Pricing Strategies
Managers often criticize sales reps for losing a deal, but rarely for pricing a deal too low, so reps learn
to concede on price in order to close the deal. Moreover, companies rarely reward sales reps for
exceeding price targets, which means few reps take risks to push for a higher price. Misaligned
incentives push deals down to the minimum allowed price.
The antidote is to align compensation with strategic goals. Incentive plans benefit from following a
few principles:
• Clarify the objectives — be they revenue growth, share gains, margin gains, or others — and the
behaviors that will help meet the objectives.
• Make it foolproof. Help sales reps understand the payout calculation, simplify the quota structures
and supplemental incentives, and make the upside for outperformance meaningful.
• Ensure transparency. Sales reps should easily see the effect of a deal’s price on their personal
compensation.
• Track the results through regular reviews that flag areas where frontline staff might game the
system.
Returning to the case of the industrial goods manufacturer described earlier, the company also
overhauled its incentive program to balance revenue and profit. It created a pricing tool to make the
commission on each deal visible to sales reps — for instance, “If I raise the price by $2,000, I earn an
extra $700.” Sure enough, reps began to close higher-margin sales. These changes led to a 7%
increase in prices, which added almost 1 percentage point as part of a 3.5-percentage-point
improvement in margin overall.
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4
Training and Tools — Often Afterthoughts — Can Have a Big Payoff
Top-performing firms invest in building the capabilities of the pricing team through training and
forums to share best practices. This runs counter to the norm at many B2B sales organizations, which
give little or no formal training on price realization.
Further, most companies can raise their game by adopting pricing software tools. Based on the
performance of historical deals, software solutions — whether in-house or from a provider such as
Vendavo or Price f(x) — can provide frontline reps with real-time pricing feedback based on the
characteristics of a deal under way. Using dedicated pricing software is associated with much
stronger pricing decision making, our survey analysis shows. Yet despite the proven value of pricing
software, only 26% of survey companies use it.
The value of developing capabilities became evident to a specialty chemical producer with lackluster
margins. The company had hundreds of different products, each with different competitors,
substitutes, and customer bases. Product and sales staff could not explain their pricing decisions, and
often resorted to a rule of thumb summed up by one product manager as, “I estimate I can raise the
price by four cents per pound.” Not surprisingly, she had raised prices by four cents per pound for
four straight years, leaving money on the table.
By analyzing the various products and their markets, the chemical producer found pricing
opportunities that enabled it to increase earnings before interest and taxes by 35% within two years.
Just as important, the company set out to raise its game on pricing capabilities. It created forums for
sharing best practices, trained product managers in doing fundamental pricing analysis, and trained
salespeople on how to have better pricing discussions with their customers. New dashboards
monitored progress toward pricing goals and flagged places where sales reps might be getting too
aggressive, or weren’t getting aggressive enough. Finally, the CEO reinforced these measures by
demanding that the product and sales teams report on pricing actions taken, as well as results, so that
effective pricing remained a high priority. The company established itself as a pricing leader in its
markets and continued to optimize margins, both by raising prices and, in selective cases, by
lowering prices to drive the right balance of price versus volume gains.
Regardless of a company’s starting point in pricing, there is significant value in building out the
capabilities highlighted by our survey analysis. The three areas discussed here have proved to be the
most important for upgrading tools, resources, and behaviors. That said, companies in almost all
industries have underinvested generally across pricing. The episodic “pricing project” approach
leaves companies well short of full potential. With meaningful margin upside at stake, managers
cannot afford to continue pricing by rules of thumb or by taking a one-size-fits-all approach to pricing
across entire segments of their business.
Ron Kermisch is a partner with Bain & Company’s Customer Strategy & Marketing practice.
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5
David Burns is a partner with Bain & Company’s Customer Strategy & Marketing practice.
COPYRIGHT © 2018 HARVARD BUSINESS SCHOOL PUBLISHING CORPORATION. ALL RIGHTS RESERVED.
6
Copyright 2018 Harvard Business Publishing. All Rights Reserved. Additional restrictions
may apply including the use of this content as assigned course material. Please consult your
institution’s librarian about any restrictions that might apply under the license with your
institution. For more information and teaching resources from Harvard Business Publishing
including Harvard Business School Cases, eLearning products, and business simulations
please visit hbsp.harvard.edu.
AI Communications 32 (2019) 15–29
DOI 10.3233/AIC-180603
IOS Press
15
Automated repricing and ordering strategies
in competitive markets
Rainer Schlosser ∗ , Carsten Walther, Martin Boissier and Matthias Uflacker
Hasso Plattner Institute, University or Potsdam, Potsdam, Germany
E-mails: Rainer.Schlosser@hpi.de, Carsten.Walther@hpi.de, Martin.Boissier@hpi.de, Matthias.Uflacker@hpi.de
Abstract. Merchants on modern e-commerce platforms face a highly competitive environment. They compete against each other
using automated dynamic pricing and ordering strategies. Successfully managing both inventory levels as well as offer prices
is a challenging task as (i) demand is uncertain, (ii) competitors strategically interact, and (iii) optimized pricing and ordering
decisions are mutually dependent. We show how to derive optimized data-driven pricing and ordering strategies which are based
on demand learning techniques and efficient dynamic optimization models. We verify the superior performance of our selfadaptive strategies by comparing them to different rule-based as well as data-driven strategies in duopoly and oligopoly settings.
Further, to study and to optimize joint dynamic ordering and pricing strategies on online marketplaces, we built an interactive
simulation platform. To be both flexible and scalable, the platform has a microservice-based architecture and allows handling
dozens of competing merchants and streams of consumers with configurable characteristics.
Keywords: Dynamic pricing, inventory management, demand learning, oligopoly competition, e-commerce
1. Introduction
Online markets have become highly dynamic and
competitive. Merchants automatically adjust prices to
react to changing market situations, cf. [1]. Similarly,
they can flexibly reorder items considering (i) estimated demand, (ii) delivery times, (iii) ordering costs,
and (iv) inventory holding costs.
Computing well-performing pricing and ordering
strategies is challenging as demand is uncertain and
markets are steadily changing (cf. [2–4]). What is
more, pricing and ordering strategies mutually affect
each other [5].
As testing is potentially hazardous when done in
production, simulating the performance of automated
ordering and pricing strategies is crucial. Nevertheless,
there is a distinct lack of simulation platforms which
allow evaluating data-driven strategies under various
competitive setups. Existing platforms, e.g., [6,7], are
limited in their capabilities: Simulations run (i) on a
single machine, (ii) offer a limited set of consumer behaviors, (iii) simulate solely short sales horizons, and
(iv) price updates or orders are restricted to predefined
discrete points in time.
* Corresponding author. E-mail: Rainer.Schlosser@hpi.de.
Resembling production marketplaces such as Amazon or eBay [8,9], we built a continuous time framework to simulate dynamic pricing and ordering under competition. The setup allows for customers with
heterogeneous buying behaviors. Further, the competitors’ offers include multiple dimensions such as price
and product quality.
Our platform supports large numbers of merchants
to compete simultaneously. Each merchant can run his
preferred ordering and repricing strategy to order products and adjust prices on the marketplace, respectively.
Market situations steadily change due to the strategic
interaction of competing merchants’ price reactions.
Simulating random streams of interested customers allows generating realized sales events and the firms’
sales revenues. The firms’ inventory levels, their holding costs as well as their ordering costs depend on their
ordering strategies and can be easily evaluated. By visualizing price evolutions, inventory levels, and profits over time, the user can easily study the complex interplay of ordering and repricing strategies and, most
importantly, compare short and long-term profits.
The platform logs each interaction such as orders,
price updates, stock-outs, new offers, sales, etc. This
historic data – which is defined as partially observable
as sales are typically private knowledge – is requested
and numerically analyzed by data-driven merchants.
0921-7126/19/$35.00 © 2019 – IOS Press and the authors. All rights reserved
16
R. Schlosser et al. / Repricing and ordering under competition
Our system supports self-adapting learning strategies.
Various state-of-the-art machine learning approaches
can be applied to quantify how demand (i.e., sales
probabilities) is affected by a merchant’s pricing decisions.
In addition, merchants are able to develop own optimization models [10–12] which are calibrated by estimated sales probabilities to compute optimized datadriven pricing and ordering strategies. In this context,
it is even possible to learn competitors’ strategies in
order to take anticipated price reactions into account.
Our framework also allows controlling and measuring the influence of (i) the customers’ buying behavior, (ii) price adjustment frequencies, as well as
(iii) the exit or entry of competitors on a strategy’s performance. In addition, different demand learning techniques and optimization approaches can be compared
regarding their accuracy and efficiency.
In this paper, we make the following contributions:
• We present a platform to simulate competing pricing and ordering strategies.
• We show how to estimate demand from partially
observable market data.
• We derive effective data-driven dynamic pricing
and ordering strategies.
• We evaluate the complex interplay of various
strategies in duopoly and oligopoly scenarios.
• We verify that our data-driven strategy outperforms different rule-based strategies.
This paper is organized as follows. In Section 2,
we discuss related work. In Section 3, we describe the
main components of our platform. In Section 4, we
introduce our stochastic dynamic optimization model.
We show how to estimate demand from historical market data and how to compute optimized pricing and ordering decisions. In Section 5, we present performance
evaluations of our data-driven strategy derived. In Section 6, we provide implementation details for our merchants. Conclusions are summarized in the final Section 7.
2. Related work
Inventory control problems and dynamic pricing
problems have been extensively studied for decades,
cf., e.g., [13,14] for pure ordering or [15,16] for pure
pricing problems. Joint dynamic pricing and ordering
problems are reviewed in the survey by [17]. Solu-
tions are proposed for different problem scenarios, if
demand is known, cf. [10,18], or [19].
Scenarios with uncertain demand are less well studied. Future demand must be estimated from market observations. Typical approaches are to investigate specific classes of parameterized demand distributions and
propose methods to find parameters, so that the demand distribution fits the experienced sales best, cf.
[20]. [21] propose Bayesian-based approaches for ordering and pricing problems with uncertain demand.
Adida and Perakis study this problem in a multiproduct scenario without backordering [22].
Further, in recent literature there are approaches
to also incorporate competition. The surveys [4] and
[23] provide an overview of the dynamic pricing
problem under competition for single-product and
multi-product scenarios. Finite time horizon settings
have been studied, e.g., by [24]. Data-driven repricing
strategies for infinite horizon oligopolies are derived in
[12]. In [3], the authors consider joint pricing and inventory control in a duopoly.
The combined problem of joint ordering and pricing,
demand learning, and oligopoly competition is highly
challenging; usually heuristics have to be used. For analyzing and evaluating the complex interplay of datadriven and rule-based ordering and pricing strategies
under competition, simulation platforms, cf. [25], can
be used. For testing and evaluating merchant strategies,
we use the platform Price Wars (cf. Section 3), a framework to simulate dynamic pricing competition on online marketplaces. The platform has advantages over
other solutions (e.g., [26–28]) as (i) its continuous time
model makes the platform similar to real online marketplaces like Amazon and (ii) users are unrestricted
in their choice and implementation of merchant strategies.
3. Platform description
The platform used for this project is called Price
Wars, an open source platform for dynamic pricing research [9,29]. The simulation platform is built with
a microservice-based architecture for scalability and
flexibility. Each service implements one business artifact, whereby services can be scaled out for large simulations. By having separated services, additional components can be added during running simulations at
any time.
Merchants update their products’ prices based on
the current market situation which they can request at
R. Schlosser et al. / Repricing and ordering under competition
17
Fig. 1. Depiction of the platform’s components and their interaction in a dynamic pricing scenario with inventory replenishment.
any time. Arbitrary strategies, e.g., rule-based or datadriven strategies, can be applied. Data of observed market situations as well as a merchant’s sales data can be
used to estimate sales probabilities (for current market
situations) using various machine learning techniques
(e.g., logistic regression, boosted trees [30], reinforcement learning [31], or neural networks). Merchants can
be easily added to the simulation or updated as long as
they conform to the HTTP/REST interface of the platform (cf. Section 6).
The centre of the simulation is the marketplace
which manages all product offers, cf. Fig. 1. The marketplace is the access point for the consumer component which creates a random stream of interested customers. Any customer choice behavior can be defined.
The decision whether a customer buys a product and
which offer is chosen, is probabilistically modelled and
can depend on all parameters of the current market situation.
The event store logs platform events (price adjustments, sales, etc.) and provides CSV files for datadriven merchants. The producer provides products ordered by the merchants.
The merchants regularly request current market situations and decide on price updates and orders. For optimized well-matched pricing and ordering decisions,
they can apply demand learning to estimate sales probabilities to be used in (dynamic) optimization models. We applied efficient dynamic programming techniques, which are described in the following sections.
The HTML-based front end, see Fig. 9 in the Appendix, enables the user to configure (i) the customer
behavior, (ii) the merchants’ strategy setup, as well as
(iii) all cost parameters (fixed/variable ordering costs,
holding cost rates [32]). The front end also allows observing prices (see Fig. 2), inventories (see Fig. 3), and
profits over time. The competing strategies’ short-term
and long-term performances are measured by different KPIs, including realized profits, revenues, holding
costs, ordering costs, etc.
Fig. 2. Example of three competitors’ prices over time.
Fig. 3. Example of competitors’ inventory levels over time.
4. Computation of pricing and ordering strategies
under competition
In this section, we show how to derive optimized
data-driven strategies. In Section 4.1, we introduce our
stochastic dynamic pricing and ordering model. In Section 4.2, we show how a firm’s observable historical
market data can be used to estimate sales probabilities
under competition. In Section 4.3, we propose an ef-
18
R. Schlosser et al. / Repricing and ordering under competition
ficient mechanism to compute optimized joint pricing
and ordering decisions.
4.1. Model description
We consider the situation in which a firm seeks to
sell a durable good over time. The time horizon is not
restricted. We assume that (i) demand is uncertain and
has to be estimated from historical data, (ii) prices can
be adjusted over time, and (iii) items can be reproduced
or reordered. Further, we assume several competitors
for our products. In our model, we include substitution
effects in demand as customers might compare prices
of competitors. The goal is to derive data-driven pricing and ordering decisions to maximize expected discounted long-term profits.
If a sale takes place shipping costs c have to be paid,
c 0. Moreover, we consider inventory holding costs.
We assume that each unsold item leads to holding costs
of l per unit of time (e.g., one hour or one day), l 0.
We also include discounting in the model. For one unit
of time, we use the discount factor δ, 0 0, given by α =
ln(δ −1 ). A list of variables and parameters is given in
the Appendix, cf. Table 6.
Due to customer choice, the demand for a firm’s
product particularly will depend on a firm’s offer
price a and the current competitors’ prices p =
(p (1) , . . . , p (K) ), where K is the number of competitors at a certain point in time. W.l.o.g, we assume time
homogeneous demand. To this end, the sales intensity
of a firm (i.e., the average demand within one unit of
time in case of stable prices) is denoted by λ, a 0,
p (k) 0, k = 1, . . . , K,
λ(a, p)
(1)
Our firm’s random inventory level at time t is denoted by Nt , t 0. If all items are sold, we let
λ(·, ·) = 0 (no back orders). If a firm does not offer
items, we let its offer price a := 0. Items can be ordered at any time t, t 0. The number of items ordered at time t are denoted by bt . Ordered products
are assumed to be delivered, e.g., with a delay of one
unit of time, i.e., in time t + 1 the inventory level Nt+1
raises by bt . The set of admissible order quantities is
denoted by B. Ordering costs C(b) are paid in advance
and characterized by fixed and variable cost parameters
cfix , cvar 0, b ∈ B, C(0) = 0,
C(b) := cfix · 1{b>0} + cvar · b
(2)
Prices can also be updated at continuous points in
time t, t 0. The set of admissible prices is denoted
by A. However, prices cannot be adjusted infinitely
often. As in real life, we assume a certain limit for
the number of updates processed within a certain time
frame.
We call strategies (at , bt ) admissible if they belong
to the class of Markovian feedback policies, i.e., pricing decisions at 0 and ordering decisions bt 0
may depend the current inventory level Nt and the current competitor prices pt .
To account for ordering costs, by Zt , we denote the
(random) number of positive orders (cf. 1{bs >0} ) initiated up to time t, t s 0, Z0 := 0. By Xt ,
we denote the random number of sales up to time t,
t 0, X0 := 0. A firm’s profits are characterized by its
sales and orders which are connected to the inventory
process Nt and the order process Zt . Given a pricing
and ordering strategy (at , bt ), a firm’s random accumulated future profits (i.e., sales revenues minus holding
costs minus order costs) from time t on (discounted on
time t) amount to, t 0,
Gt :=
t
∞
−
e−α·(u−t) · (au− − c) dXu
∞
e−α·(u−t) · l · Nu du
t
−
∞
e−α·(u−t) · C(bu− ) dZu
(3)
t
The objective is to determine a non-anticipating
feedback pricing and ordering policy that maximizes
the expected discounted total profit E(Gt |Nt , pt ), cf.
(1)–(3), conditioned on the current inventory level Nt
and the current market situation pt at time t.
4.2. Estimation of sales probabilities
The goal of this section is to estimate sales probabilities from historical market data. As in real-life applications, in our framework, merchants cannot continuously track markets over time. Typically, merchants
have to request the marketplace to observe the current
market situation. Then, based on the current market situation a price adjustment is sent back according to a
certain repricing rule or strategy. Each merchant can
also observe his/her realized sales as private knowledge.
Typically, firms observe market situations shortly
before they adjust their prices. Prices are kept constant
R. Schlosser et al. / Repricing and ordering under competition
Table 1
Illustration of observable and private data of a firm: Competitors’
offer prices p at discrete points in time t (j ) and number of sales
between t (j ) and t (j +1) at price at (j ) , j = 0, 1, . . . , J − 1
t (j )
t (j +1)
0
0.0
1
2
3
…
J −1
1.4
2.5
2.8
…
j
t (J −1)
p
(1)
t (j )
p
(2)
t (j )
…
p
(K)
t (j )
yt (j )
at (j )
1.4
4
15
11
13
…
/
2.5
2.8
4.0
…
t (J )
12
8
5
…
…
10
12
15
…
…
11
9
9
…
…
13
13
11
…
…
…
…
…
…
…
17
16
/
…
…
until the next price update, i.e., a market request, takes
place. A firm seeks to quantify how the numbers of observed sales within different time intervals are affected
by the relation of a firm’s offer price and the competitors’ prices.
In the following, we assume that a firm has historical data for J time intervals. Observable data includes offer prices at (j ) , competitor prices pt (j ) at times
t (j ) , and realized sales yt (j ) , i.e., the number of products sold within the time intervals (t (j ) , t (j +1) ), j =
0, . . . , J − 1, see Table 1.
A firm that plans to set a price at time t for the length
of, e.g., h units of time, seeks to estimate sales probabilities for the time frame (t, t + h) given the current market prices p observed at time t. The own offer price a can be chosen from a set A of admissible
prices. In this context, a firm seeks to derive an estimation of the (true) conditional sales probabilities, h > 0,
i = 0, 1, . . . , t 0, a, p (k) ∈ A, k = 1, . . . , K,
Pt,t+h (i, a|p)
(4)
There are several approaches to estimate sales probabilities, cf. (4), from data sets as described in Table 1,
see e.g., [12]. Common approaches are, e.g., least
squares, logistic regression, gradient boosted trees
(e.g., XGBoost [30]), neural networks, etc.
In the following, we illustrate a simple way to estimate demand. To explain the dependent variable yt (j ) ,
j = 0, . . . , J − 1, we can use, e.g., a robust least
squares regression model (LS model). Using the LS
model, we aim to specify average expected sales for a
time span of length h conditioned on initial (not necessarily stable) market prices p,
a, p (k) ∈ A, k =
1, . . . , K, h 0,
:= x(h, a, p)
λ̃(h, a|p;
β)
β
(5)
where β = (β1 , . . . , βM ) is the unknown parameter
vector that is associated to the vector x = (x1 , . . . , xM )
19
of M explanatory variables. The regressors x(h, a, p)
can be a function of offer price a and market prices p.
∗ ) can be
The optimal coefficients β∗ = (β1∗ , . . . , βM
easily obtained using standard methods.
:= λ̃(h, a|p;
The resulting intensities λ̃∗ (h, a|p)
∗
β ), cf. (5), can be used to estimate P , cf. (4): For
h units of time, we let the estimated sales probabil be Poisson distributed with rate
ities P̃t,t+h (·, a|p)
λ̃∗ (h, a|p),
a ∈ A, h 0, t 0, i = 0, 1, . . . , i.e.,
P̃t,t+h (i, at |pt ) :=
λ̃∗ (h, at |pt )i
i!
∗ (h,a |p
t t )
· e−λ̃
(6)
To illustrate the approach, in the following definition, we give simple examples of explanatory variables x.
Definition 4.1. We define the following regressors
(k)
xm , m = 1, . . . , 7, for given data at (j ) , pt (j ) ∈ A,
k = 1, . . . , Kt (j ) , h(j ) := t (j +1) − t (j ) , t (j ) 0,
j = 0, . . . , J − 1:
(i) constant / intercept
x1 h(j ) , at (j ) , pt (j ) = 1
(ii) own price at time t (j )
x2 h(j ) , at (j ) , pt (j ) := at (j )
(iii) rank of own price a within prices p at time t (j )
x3 h(j ) , at (j ) , pt (j ) := rank(at (j ) , pt (j ) )
(j )
(iv) price gap between at
and best competitor
x4 h(j ) , at (j ) , pt (j )
:= at (j ) −
min
k=1,…,Kt (j )
(k)
pt (j )
(v) number of competitors at time t (j )
x5 h(j ) , at (j ) , pt (j ) := Kt (j )
(vi) availability of our product at time t (j )
x6 h(j ) , at (j ) , pt (j ) := 1{Nt (j ) >0}
= 1{at (j ) =0}
20
R. Schlosser et al. / Repricing and ordering under competition
(vii) interval length h(j )
x7 h(j ) , at (j ) , pt (j ) := h(j )
Our framework allows to measure the impact of a
firm’s offer price in the presence of competitors’ market prices. Note, also non-linear versions of explanatory variables can be used. In this general framework,
further explanatory variables can be easily defined to
capture the impact of additional effects, such as time,
product quality, etc.
Note, the quality of estimations of sales probabilities (for the entire range of prices or for prices that often occur during the competition) can be analyzed and
compared for different demand learning techniques. As
the true sales probabilities are characterized by the defined customer behavior and the competing merchant’s
strategies they can be determined using, e.g., Monte
Carlo simulations, cf. [12].
In general, regression results are better if prices are
more randomized, cf. [33]. In this context, our platform can also be used to study the impact of a selection bias caused by a firm’s strategy as well as the competitors’ strategies. Moreover, the impact of various effects of the model can be studied, such as distribution
and length of reaction times, customer arrival intensity,
customers’ buying behavior, or number of competitors,
etc.
Finally, the (estimated) conditional probabilities (4)
and (6) are affected by both, the customer behavior as
well as the strategic interplay of competitors’ price adjustments. Recall, a firm’s demand learning does neither anticipate competitors’ strategies nor their reaction times. The estimated probabilities (6), however,
allow to indirectly measure the average impact of competitors’ price adjustments and, thus, account for the
fact that market situations may change between two
price adjustments of a firm.
Our platform allows to test and to validate different
demand learning approaches in different competitive
markets. In addition, components of the demand estimation can be further improved (exploration phases,
sampling, feature selection, etc.). While not focus of
this paper, further issues, such as missing variables, IIA
assumption, unobservable demand shocks, etc., can be
addressed, cf. to recent literature, e.g., [34] or [35]. To
this end, our model can be used to study to which extent such effects influence the quality of different demand learning approaches.
The goal of the next section is to derive effective
ordering and pricing decisions that are based on esti-
mated conditional probabilities for current market situations, cf. (6). Further, we seek to account for holding
costs, ordering costs, and discounting.
4.3. Dynamic model and solution approach
There are two major problems to derive applicable
pricing strategies in competitive markets: (i) as demand
is affected by many parameters (e.g., dozens of competitors’ prices) a model’s state space explodes and the
problem becomes intractable, and (ii) in general, as
competitors’ strategies are not known, their price adjustments cannot be effectively anticipated.
Our approach deals with both problems. Most importantly, instead of computing complete feedback
strategies, we compute prices for one period only based
on the current market situation that occurs during a
sales process. To compute controls for single time periods, in general, the current state as well as potential future states have to be considered. As price reactions of
competitors occur with a certain delay the short-term
evolution of the market can be well approximated by
the current market situation. The long-term evolution
of the market, however, can hardly be predicted. Our
approach is motivated by the fact that the optimal price
for one period mostly depends on the current state and
is much less affected by specific potential states in the
future, see [36] for finite horizon pure pricing problems.
For a current state, we manage problem (i) as follows: We roughly approximate future market situations
by using sticky prices. While the degree of inaccuracy
is acceptable, we gain a structure that makes it possible to circumvent the curse of dimensionality, cf. problem (i), as the states of our dynamic system (i.e., the
market situation) are not coupled and can be decomposed. Thus, for single states decisions can be computed independently, which makes it possible to consider current market situations only.
The second key idea is to compensate the model’s
inaccuracy as well as the lack of price anticipations,
cf. problem (i), by frequent price adjustments, which
in turn are possible as the model’s simplicity allows for
fast re-computations.
Due to price adjustments, exits, or entries of firms, in
general, market situations are not stable. In our model,
we consider (estimated) conditional sales probabilities,
cf. (6), a 0, h > 0, t 0, i = 0, 1, . . . ,
P̃ (h) (i, a|p)
:= P̃t,t+h (i, a|p)
(7)
R. Schlosser et al. / Repricing and ordering under competition
for selling i items within the time span (t, t + h) at
price a under the condition that at time t the market
situation is p (and may change within the period due
to competitors’ price reactions). Note, following our
assumptions, in (7) demand is time homogeneous, i.e.,
considering the interval (t, t +h) only the period length
h matters. However, time-dependent sales probabilities
are also possible (e.g., seasonal and cyclic effects).
W.l.o.g., in the following, we consider a firm with an
average price adjustment delay of h = 1. As described
in the beginning of this section, we use a simplified dynamic programming approach based on a discrete time
model. In this context, a firm’s random accumulated
future profits Gt , cf. (3), from time t on (discounted on
time t) amount to, t = 0, 1, 2, . . . ,
Gt :=
∞
δ s−t
s=t
·
(as (Ns , ps ) − c) · (Xs+1 − Xs )
−l · Ns − C(bs (Ns , ps ))
= max
⎧
⎨
a∈A,b∈B ⎩
i=0,…,Nmax
pected general long-term market trends (decay of average prices, product attractiveness, etc.). For the time
being, we let z := 1. The set of admissible prices A
and order quantities B can be chosen arbitrarily.
and ordering
The optimal joint pricing a ∗ (n, p)
n = 0, . . . , Nmax , p (k) 0, k =
strategy b∗ (n, p),
1, . . . , K, is given by the arg max of (9). If optimal
prices or ordering quantities are not uniquely determined, we choose the largest numbers.
The solution of the system of equations (9) can be
derived using standard methods like value iteration or
policy iteration. Alternatively, the system can also be
solved using a (nonlinear) solver. Note, the number of
variables and constraints is Nmax + 1.
Value iteration does not need a solver to approximate the value function. For a given “large” number T ,
we use the terminal condition
:= 0
VT (n, p)
(8)
In a given state (n, p)
at time t, the best expected
discounted future profits E(Gt |Nt = n, pt = p),
cf.
(8), are independent of time and described by the value
n = 0, 1, . . . , N , p (k) 0, k =
function V ∗ (n, p),
1, . . . , K.
If a period’s (random) demand is i items and b items
are ordered (with delivery delay), the transition of the
current inventory level n to the next period’s level is
given by n → max(n − i, 0) + b. To avoid an unbounded state space, we use the upper limit Nmax ,
which – if chosen sufficiently large – does not af b∗ (n, p)),
which
fect the optimal solution (a ∗ (n, p),
is characterized by the associated Hamilton-JacobiBellman equation, n = 0, . . . , Nmax , p (k) 0, k =
1, . . . , K,
V ∗ (n, p)
21
P̃ (1) (i, a|p)
⎞⎫
(a − c) · min(i, n) − l · n − C(b) ⎬
· ⎝ + z · δ · V ∗ (min((n − i)+ + b, ⎠
⎭
Nmax ), p)
(9)
⎛
where z, z 0, is an additional penalty/discount parameter which allows (i) to control the speed of sales
of the feedback policy, and (ii) to account for ex-
(10)
for all numbers n and market situations p.
Using the
recursion, t = 0, 1, . . . , T − 1, n = 0, . . . , Nmax ,
p (k) 0, k = 1, . . . , K,
=
Vt (n, p)
⎧
⎨
max
a∈A,b∈B ⎩
P̃ (1) (i, a|p)
i=0,…,Nmax
⎞⎫
(a − c) · min(i, n) − l · n
⎪
⎪
⎜ − C(b)
⎟⎬
⎜
⎟
·⎝
+ z · δ · Vt+1 (min((n − i)+ ⎠⎪
⎪
⎭
+ b, Nmax ), p)
(11)
⎛
we can compute the values Vt (n, p),
t = 0, 1, . . . , T −
1. The number of iteration steps T can be chosen such
that the approximation error between V and V ∗ is sufficiently small. The approximation error can be estimated via the discount factor δ.
Finally, the associated (optimal) strategies a0 (n, p)
n = 0, . . . , N , are given by the arg max
and b0 (n, p),
of (11) at the last recursion step, cf. t = 0.
Note, due to the size of the state space it is not pos for all states p in adsible to compute prices at (n, p)
vance. The following algorithm, however, circumvents
the curse of dimensionality and allows to derive viable
heuristic joint pricing and ordering strategies in competitive markets with a large number of competitors.
Algorithm 4.1. We define the following pricing and
ordering heuristic:
22
R. Schlosser et al. / Repricing and ordering under competition
Step 1: For every period t observe the new state,
i.e., the current inventory level Nt and
the current market situation pt . Compute
the probabilities P̃ (1) (i, a|pt ) for all i =
0, 1, . . . , Nt , a ∈ A.
Step 2: Solve either (9) for V ∗ (Nt , pt ) and a ∗ (Nt ,
pt ), b∗ (Nt , pt ), or use T recursion steps to
compute the specific value V0 (Nt , pt ), cf.
(10)–(11), and obtain the associated offer
price a0 (Nt , pt ) and the ordering decision
b0 (Nt , pt ).
The key idea is to just compute decisions for single market situations and to regularly refresh them in
response to changing market situations. Due to the
small dimensionality of the state space, a single recomputation is very fast. Further, our solution is scalable as the algorithm’s complexity does neither increase with the number of competitors, the number of
offer dimensions, nor the number of explanatory variables.
Remark 4.1. The recomputations of Algorithm 4.1
can be sped up as follows:
(i) Typically, it is sufficient to consider a small
subset of admissible prices A and order quantities B. Suitable subsets can be derived from
and b∗ (n,
previous computations for a ∗ (n, p)
p).
(ii) The computation of decisions via (11) can
be dramatically accelerated by using suitable
starting values v(n), n = 0, 1, . . . , Nmax , for
:= v(n),
the terminal condition VT (n, p)
cf. (10). Suitable starting values can be derived from previous computations, i.e., v(n) :=
V0 (n, p ) for market situations p similar to p.
(iii) Further, if the computation time shall be below
a certain time limit (e.g., 0.1 seconds) the number of recursion steps, cf. (11), can either be
chosen sufficiently small or the recursive approximation is stopped accordingly.
(iv) Reaction times are a competitive advantage.
However, the number of market requests is often limited. Our framework allows balancing
the accuracy of solutions and the required computation time. The number of price updates
processed can be effectively controlled.
5. Numerical examples and evaluation
The platform allows simulating strategic interaction of rule-based and data-driven strategies in differ-
ent market scenarios characterized by product portfolios, customer behaviors, oligopoly settings, and cost
definitions. In Section 5.1, we describe our setup
and give examples of rule-based merchants. In Section 5.2, we study how our data-driven strategy performs in duopoly setups. In Section 5.3, we evaluate an
oligopoly scenario.
5.1. Merchant description and simulation setup
Our merchant implementation with the proposed
optimization model is called data-driven merchant.
A new training on all training data is processed every
minute. The period length is four seconds. Further, we
let Nmax = 40, T = 40, A := {0.1, 0.2, . . . , 100},
B := {0, 1, 2, . . . , Nmax }, and δ = 0.9999.
Besides our data-driven merchant, we consider the
following two rule-based merchants. The cheapest
merchant always undercuts the cheapest competitor by
a configurable amount (here, 0.30). Only if the cheapest competitor price is higher than the upper price
bound of 30, the cheapest merchant sets a price of 30
instead. If no competitor offer is available, the cheapest
merchant sets the price to the upper price bound. The
merchant makes a new order when the inventory level
falls below six items. In that case, the merchant orders
as many items as needed to refill the inventory to 20
items. Price updates are made every four seconds.
The second rule-based merchant, called two bound
merchant, undercuts the competitor with the lowest
price by 0.30, similar to the cheapest merchant. However, the merchant has an upper and lower price bound.
If the cheapest competitor’s offer price is below the
lower price bound of 17, the two bound merchant sets
the price to the upper price bound, 30. Moreover, if no
competitor offers are available or all competitor prices
are above the upper price bound, the price is also set to
the upper price bound. This merchant makes a new order if the inventory level falls below four items. In that
case, the merchant orders as many items as needed to
refill the inventory to 15 items. Price updates are also
made every four seconds.
Consumers are configured to visit the marketplace
at an average rate of 100 consumers per minute.
The time between arriving consumers is exponentially
distributed with a mean of 0.6 seconds. They dismiss offers costing 80 or more. Assume the remaining J offers o = (o1 , o2 , . . . , oJ ) have prices p =
(p1 , p2 , . . . , pJ ). The maximal price in p is denoted
by pmax , the sum of these prices is denoted by psum .
An arriving consumer buys one item from the remain-
R. Schlosser et al. / Repricing and ordering under competition
23
ing offers j at random with the probability distribution,
j = 1, . . . , J ,
P (Buy from oj ) =
pmax + 1 − pj
J · (pmax + 1) − psum
(12)
If there are no offers with prices below 80 (willingness to pay), the consumer leaves the marketplace
without buying anything.
Simulations have a duration of 15 minutes. Ordering
costs are defined by cfix = 10 and cvar = 15. Holding
costs are three per minute per item for all merchants.
That corresponds to l = 3/(60s/4s) = 0.2 for the
data-driven merchant. If not mentioned otherwise, the
following simulations are run with the configuration
listed here.
5.2. Duopoly simulation
In this section, we investigate the profitability of the
proposed merchant in different duopoly scenarios. Our
data-driven merchant competes with each of the two
rule-based merchants. In the last duopoly scenario, two
data-driven merchants with the same strategy compete
with each other. In the simulations, the competitors’
strategies are mutually not observable.
5.2.1. Data-driven merchant vs. cheapest merchant
We simulated a duopoly between the data-driven and
cheapest merchant for 15 minutes. Figure 4 shows how
both merchants’ prices undercut each other. The datadriven merchant does not reduce the price below 20;
the price is raised to 25–30. The increased price has
lower sales probabilities but a higher profit margin.
Surprisingly, we observe that the cheapest merchant
increases the price sometimes. When the data-driven
merchant is out of stock, there is no competitor offer
for the cheapest merchant to undercut. When this is the
case, the cheapest merchant uses a default price. The
final performance results of this simulation are shown
in Table 2. The data-driven merchant has overall more
ordering and holding costs. However, profits are higher
as costs are overcompensated by higher revenues compared to the cheapest merchant.
5.2.2. Data-driven merchant vs. two bound merchant
In a second setup, we study the competition between
the data-driven merchant and the two bound merchant.
Compared to the cheapest merchant, we used a different ordering policy. The two bound merchant restocks
to 25 items (instead of 15) and makes a new order
Fig. 4. Screenshot of the Price Wars simulation: Price trajectories in
a duopoly of our data-driven merchant and the cheapest merchant.
Dots in the chart are price updates and bars are sales events. Configurations are listed in Section 5.1 and Section 5.2.1.
Table 2
Performance results of a duopoly with our data-driven merchant and
the cheapest merchant. Configuration as described in Section 5.1 and
Section 5.2.1
Merchant
Data-Driven
Cheapest
Profit
Revenue
Holding
Ordering
7 285.78
5 796.11
20 599.00
17 165.10
588.22
418.99
12 725.00
10 950.00
whenever the inventory level falls below 7 items (instead of 4). This reduces the risk of having stock-outs.
The data-driven merchant expects the most profit
from undercutting the competitor. This results in both
merchants undercutting each other as shown in Fig. 5.
The two bound merchant is programmed to raise the
price if it falls below a certain threshold (price 17).
However, the data-driven merchant was the first to increase the price in this simulation (if prices are below 20). The performance results are shown in Table 3.
Both merchants made less profit compared to the previous setting, see Section 5.2.1.
5.2.3. Data-driven merchant against itself
The third setup analyzes the competition between
two identical instances of our data-driven merchant.
The price chart in Fig. 6 shows again the typical zigzag pattern of two merchants undercutting each other
and periodically pushing the price up to restore the
price level and, in turn, to increase profit margins. The
24
R. Schlosser et al. / Repricing and ordering under competition
Fig. 5. Screenshot of the Price Wars simulation: Price trajectories in
a duopoly of our data-driven merchant and the two bound merchant.
The two bound merchant restocks the inventory to 25 and reorders if
the inventory falls below 7 instead of four items to reduce the number
of stock-outs. All other parameters are as defined in Section 5.1 and
Section 5.2.2.
Table 3
Simulation results of a duopoly with our data-driven merchant and
the two bound merchant. The two bound merchant holds more items
in the inventory to reduce the number of stock-outs. The two bound
merchant restocks the inventory to 25 instead of 15 items and reorders if the inventory falls below 7 instead of 4 items to reduce the
number of stock-outs. Other parameters as described in Section 5.1
and Section 5.2.2
Merchant
Data-Driven
Two Bound
Profit
Revenue
Holding
Ordering
5 858.79
5 230.10
18 984.00
16 952.70
595.20
527.60
12 530.0
11 195.0
competition between two data-driven merchants happens at a higher price level (around 32–51) compared
to the previous simulation (around 20–26). This results
in an overall higher profit for both competing merchants. The automated data-driven strategies suggest to
order new items whenever the inventory level falls below six items and restock the inventory to around 28
items.
Results of this simulation are shown in Table 4. We
observe that performance results are overall similar but
not entirely symmetric. Merchants do not gather the
same sales events which may result in different pricing and ordering policies. Further, as price reactions of
both merchants have the same frequency and occur al-
Fig. 6. Screenshot of the Price Wars simulation: Price trajectories
in a duopoly of two identically configured data-driven merchants.
Parameters as described in Section 5.1 and Section 5.2.3.
Table 4
Simulation results of a duopoly with two (symmetric) data-driven
merchants. Configurations as described in Section 5.1 and Section 5.2.3; simulation duration of 30 minutes
Merchant
Data-Driven
Data-Driven 2
Profit
Revenue
Holding
Ordering
17 361.30
15 650.58
30 936.0
27 282.0
804.69
721.41
12 770.0
10 910.0
most equidistantly, the mutual price reaction times can
be uneven. Hence, the percentage of time a merchant
has the most recent price update can be skewed, which
leads to different results. To circumvent this issue, reaction times can randomized, cf. [37]. This makes it
also harder to anticipate price reaction times in order
to choose the timing of price updates strategically.
5.3. Oligopoly simulation
This section illustrates how our data-driven merchant performs in an oligopoly. We simulated the competition between the data-driven merchant, the cheapest merchant, and the two bound merchant. The evolution of pricing and ordering decisions during the
simulation are depicted in Figs 7 and 8. Again, the
data-driven merchant learns the advantage of undercutting competitors’ offers. However, this creates a high
price competition and average price levels decrease.
With shrinking profit margins, it becomes unprofitable
R. Schlosser et al. / Repricing and ordering under competition
25
Table 5
Simulation results of an oligopoly scenario with the data-driven,
the cheapest, and a two bound merchant. The data-driven merchant
made the most profit. The cheapest merchant made the most revenue.
Configurations as described in Section 5.1 and Section 5.3; simulation duration of 30 minutes
Merchant
Data-Driven
Cheapest
Two Bound
Fig. 7. Screenshot of the Price Wars simulation: Price trajectories in an oligopoly scenario on the platform. Our data-driven merchant competes with two rule-based merchants. Configurations as
described in Section 5.1 and Section 5.3; simulation duration of 30
minutes.
Profit
Revenue
Holding
Ordering
5 944.13
5 386.90
5 038.63
21 938.00
23 770.80
20 148.30
943.87
903.89
644.67
15 050.00
17 480.00
14 465.00
to set the price below competitors’ prices. The datadriven merchant pushes the price up in such a situation.
This motivates the competitors to also increase their
offer prices.
Table 5 shows the results of a 30 minutes competition between the three merchants. The data-driven merchant outperformed all competitors. Our data-driven
merchant made around 10% more profit than the
cheapest merchant and 18% more than the two bound
merchant. Interestingly, our merchant did not make the
most revenue (the cheapest merchant did). The cheapest merchant sold the most items but with low profit
per item. Our merchant made the most profit by saving a lot of order cost compared to the cheapest merchant. The data-driven merchant orders on average
more items than the competitors. This results in higher
holding costs but saves on fixed order cost.
We find that fully automated data-driven strategies –
combined with efficient dynamic programming optimization techniques – clearly outperform rule-based
strategies after a sufficiently large data set has been
gathered for demand learning. It can also be studied
to which extent jointly optimized pricing and ordering
strategies outperform different combinations of single
ordering and pricing benchmark strategies.
Moreover, the platform can be used to study shortterm as well as long-term performance of self-adapting
strategies that iteratively improve over time.
6. Merchant implementation details
Fig. 8. Screenshot of the Price Wars simulation: Inventory levels over
time in an oligopoly scenario on the platform. Our data-driven merchant competes with two rule-based merchants. Configurations as
described in Section 5.1 and Section 5.3; simulation duration of 30
minutes. Note, while the simulation of sales is in continuous time,
the plot grid is discrete.
Merchants on the platform can be written in any
language as long as they comply with the platform’s
REST APIs. We decided to implement our merchant
in the Python programming language [38] for the following reasons. Python has great library support for
numerical computing. These libraries allow a concise
and efficient implementation without reinventing the
wheel. Our platform offers a Python implementation
26
R. Schlosser et al. / Repricing and ordering under competition
of the RESTful API for the merchant to communicate
with the platform’s services. Lastly, it is possible to
quickly create prototypes in Python.
Our merchant consists of four components. The
main loop is the central component. It regularly checks
the marketplace for open offers, updates prices, and orders items from the producer. After enough time has
passed, the merchant requests new market and sales
data from the event log and provides it to the demand
learning component to analyze demand.
The merchant makes ordering and pricing decisions
based on policies that are computed by the policy
component. The policy component contains the dynamic programming approach. The merchant provides
all arguments that are necessary for the policy creation and sales probabilities are requested from the demand learning component. The dynamic programming
function is the computational most expensive part of
the merchant. An efficient implementation reduces the
time needed for a pricing and ordering decision. We
create a vector that has the dimensions inventory levels, ordering decisions, pricing decisions, and demand.
The expected profit is calculated for each possible situation and decision that occur in this vector. The expected profits are used to find the most profitable decisions and to create the ordering and pricing policy.
We use fast and vectorized array operations from the
Numpy library [39] to compute the policies. Python
is a high-level programming language and has a lot
of computational overhead [40]. Numpy provides data
structures and functions implemented in the C programming language to overcome Python’s overhead
for numeric computations.
The merchant’s demand learning component is responsible for estimating sales probabilities and for
bringing market and sales data into a form that can be
used for training. The module uses linear regression
to learn and predict the demand. We use the scikitlearn library [41] for a reliable and fast linear regression implementation. As an additional benefit, it is
easy to change between regression algorithms using
scikit-learn. The demand learning is implemented in a
way that makes it easy to add new or change existing
explanatory variables. Only a single function (named
extract_features) must be changed to add new
explanatory variables.
The merchant server receives sales events from the
marketplace and triggers the appropriate action. In our
case, the merchants prints a message to notify the user
whenever an item was sold. Moreover, the server receives configuration updates from the platform frontend and applies them.
7. Conclusion and future work
In this work, we presented a distributed and scalable
platform resembling real-world e-commerce applications. Both practitioners and researchers can investigate the strategic interaction of various adaptive datadriven pricing and ordering strategies and develop, test,
and evaluate their own approaches.
Further, we have proposed a data-driven approach
to derive effective pricing and ordering strategies. We
combine private sales data with partially observable
data of the competitors’ offers to efficiently predict
sales probabilities in competitive markets. Using estimated sales probabilities, we have set up a dynamic
model including discounting, ordering costs, and holding costs. Our strategies are even applicable if the number of competitors’ products is large. Our solution approach is characterized by a simplified frequently updated dynamic programming model, in which only current market situations have to be considered.
Our framework can be easily extended in several
ways: (i) further offer dimensions (quality, ratings,
shipping time, etc.), (ii) the consideration of perishable products, and (iii) substitution effects between different products. While the simulation platform allows
taking these extensions into account, the presented optimization model has to be adapted. To address markets with multiple offer dimensions (cf. [42]) the demand learning component needs to be extended. In our
setting, additional characteristic explanatory variables
can be easily defined. The consideration of perishable
products requires finite horizon models. Such models
can be solved using recursive dynamic programming
techniques. In multi-product models, the state space as
well as the action space can be enormous. To manage
this complexity, relaxation approaches and decomposition techniques can be used. The demand learning
component has to be extended such that substitution
effects are taken into account, e.g., [43].
R. Schlosser et al. / Repricing and ordering under competition
27
Appenidx. Notation table and additional figures
Table 6
List of variables and parameters
Symbol
a
p
δ
t
B
cvar
λ(a, p)
Nt
Zt
y
Description
Symbol
Offer price
Competitors’ prices
Discount factor for future profits
Time
Set of admissible order quantities
Variable order costs
Mean sales for one period with stable prices
Random inventory level at the time t
Number of orders made until time t
Dependent variable (number of sales)
λ̃(h, a|p)
n
V ∗ (n, p)
T
Number of explanatory variables
Weights vector for linear regression
Estimated mean sales for a time span h
Inventory level
Value function
Number of periods/recursion steps
a ∗ (n, p)
Optimal pricing decision
M
β
A
K
l
b
cfix
C(b)
Pt,t+h (i, a|p)
Xt
Gt
x(h, a, p)
h
β∗
P̃ (h) (i, a|p)
Nmax
Vt (n, p)
v(n)
b∗ (n, p)
Description
Set of admissible prices
Number of competitors
Holding costs per item and period
Number of items ordered
Fixed order costs
Total order costs for ordering b items
Probability to sell i items within (t, t + h)
Random number of sold items until time t
Random accumulated disc. profit from time t on
Explanatory variables
Price reaction time
Optimal weights for specific training data
Estimated probabilities for a time span h
Maximum inventory capacity
Approximated value function
Starting value for value function VT
Optimal ordering decision
Fig. 9. Dashboard of the HTML-based frontend.
28
R. Schlosser et al. / Repricing and ordering under competition
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E. Adida …
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