Markdown management
Lecture 5
„Waiting for the sale“ is a timehonored strategy for savvy shoppers
• The fashion-conscious may splurge on spring fashions
shortly after they arrive
• But budget-minded know they can save by waiting
• Many items will be marked down by 70% or more by the
end of the season
• This strategy, however, is not without risk – as the item
might be sold out eventually
• Nonetheless, an increasing number of people are willing to
take the risk in order to realize the savings
• In many categories retail list price is becoming a ceiling,
with most sales taking place at a discount
• More and more customers won’t buy an item if it isn’t on
sale
Markdowns and promotions
• The point of mark-down management is to
find the timing and magnitude of price
reductions that move the inventory while
maximizing revenue
• For many years, retailers relied on their
judgment or simple rules of thumb to
determine markdowns
Nobody but a fungoid creature from
another galaxy with no familiarity with
earthly ways would ever pay list price
for anything. —Dave Barry
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Valentine’s Day
Black Friday*
Cyber Monday
Christmas
Kohl’s, Macy’s, Saks
State of the art
• Software offered by companies such as
– Manugistics
– ProfitLogic – acquired by Oracle
• Situation is reminiscent of the early days of
revenue management in the airline, hotel and
rental car industries – the leaders are applying
• Early adopters have reported 10%-15%
revenue increases – see game theory with
respect to that
• For certain goods and services markdown
segments the market and provides a simple
method for profiting from price discrimination
• In the early days sales were associated with price wars
during holidays such as Christmas and Thanksgiving
between rivals such as Macy’s and Gimbels in Manhattan
• In 1950, managers at The Emporium, leading San Francisco
department store were given a memo stating
– High markdowns benefit no one. Not the store. Not the
manufacturer. Not the customer. The store loses in value of
assets or inventory. The manufacturer loses in future sales and
by loss of prestige of his product. The customer is getting
merchandise that is not up to standard, at a low price it is true,
but, remember—she would rather have fresh, new merchandise
that she can be proud of and with real value at regular price
than pay less for questionable merchandise.
• These were considered as mistakes in purchasing, pricing
and marketing
Average discount from list price –
department and specialty store. Stores
with sales over $1 million before 1982
and $5 million thereafter
• On the other hand, as early as 1915, a
retailing textbook also tied markdowns to
many of its pros
• Sometime in the 1970s, purchasing goods at a
discount went from being an exception to
being the rule
• (National Retail Federation, 1998) states that
72% of all fashion items sold in 1998 were sold
at a discount
Reasons
• Increased customer mobility
• The rise of discount chains and outlets, many
with „everyday low pricing“
• A self-reinforcing „vicious cycle“
• An increasing interest in nonstandard items – that
have shorter shelf lives. Patterned and colored
sheets have their market share go up from 12% in
1970 to 60% in 1990 against white sheets
• The use of markdown money, moving some of
the risk of unsold inventory from retailers to
manufacturers
• Discounting is still relatively rare in prescription
drugs, movie tickets and various staple food and
home items
• Thus for those goods, even small price decreases
can have a big impact on sales
• Consensus is that retail discounting is likely to
continue and increase – in this notoriously thinmargin business this can make a difference
• The „everyday low price“ retailers, such as WalMart, discount rarely
• Clothing items will at first be discounted, and
in the end sent to an outlet store or to a
jobber – for 20% or less of its original price
• For the TV sets, which were depicted on a
graph as promotions, they also have to be
marked down occasionally – when a new
model comes out
The main characteristics for
seller/buyer
• Inventory is fixed (seller)
• The inventory must be sold by a certain out date – or
its value drops precipitously (seller)
• Time of use – winter overcoat in September and in
April
• Fashionability – clothes, consumer electronics, video
games
• Deterioration – day old bread
• Obsolescence – the new version comes soon –
automobiles, consumer electronics, computer
equipment
Customer segmentation and price
discrimination
• Time of use – those who need it now/who are
willing to wait
• Fashionability – fashionistas/ones who are
willing to wait
• Deterioration – who are ok with the inferior
product at a lower price
• As we have seen, segmentation and
discrimination are powerful ways of increasing
revenue
Lazear, 1986
• Linear price-response
curve d(p)=1000-100p
• Population of 1000
buyers
• Willingness to pay is
distributed uniformly
$0..$10
• Marginal cost is 0
• P*=$5; sales 500; total
contribution $2500
Lazear, 1986
• If he sells at $5 and
$2.5, his total revenue
will be $3125 – 24%
increase
• Selling at $6.67 at first,
and then at $3.33, he
can get $3333 – 33%
increase!
This customer segmentation…
• assumes global linearity of price-response curve and no
anticipation of markdowns and also the fact that some
customers would not have a lower wtp later on
• there are two such cases that are commonly practiced,
however: baked goods and broadway tickets (afterwards
sold through a TKTS outlet at Times Square)*
• used time of purchase and decreasing prices as a way of
segmenting customers between those with a high
willingness to pay and those with a low wtp.
• Furthermore, TKTS tickets require waiting in line and no
guarantee, that the product will be available … and bakery
goods are just not as good
• Lower willingness to pay, later on
• Anticipation of markdowns
– Cannibalization fraction – 0%..100%
The role of demand uncertainty
• A merchant, selling a sweater, does not know,
whether it will be a top seller during the
upcoming season
• As not a top seller, the market price will be
$59
• As a top seller, it will all be sold at $79
• Thus the optimal decision is to sell for $79 at
the first period and then lower the price to
$59
Another example, the Dutch flower
auction
• 4 billion flowers sold in Aalsmeer annualy
• Set the maximum and the minimum price
• In five minutes, price drops steadily from
maximum to minimum
• Each potential buyer has a PURCHASE button, he
can press
• Both for selling sweaters and flower sellers seek
to extract the highest price for their constrained
and perishable supply in the face of demand
uncertainty
Markdown management businesses
• Holiday items – Christmas trees, fireworks
• Tours – only 10% of leisure travel in the US, a major
proportion of vacation travel in Europe and Asia*
• Automobiles – seasons begin in September, these
markdowns are realized through various promotional
vehicles, not through reduced list price
• Clearances and discontinuations – e.g. a new model of
a washing machine is announced in three months and
retailers and wholesalers have to react; most accute,
when the life-cycle is short, as therein some portion of
total inventory is marked down every day
Assumptions for markdown
optimization
• A seller has a fixed inventory and cannot reorder
• There is an out date after which the salvage value is small
• There is an initial list price, which can be reduced a number
of times
• Only price reductions are allowed
• The objective is to maximize the total revenue, including
salvage value
• Marginal costs are zero – costs are sunk
---------------• The marked-down good being sold is inferior, as it might no
longer be fashionable, or simply not be available
A deterministic model
Results
When the sales deviate from
expectations – a deterministic
markdown algorithm
• Solve for p1, p2 .. pt – to determine p1
• Observe sales and set starting inventory x2
• Solve with remaining projected demands to
determine p2
• Etc…
Example
• Demand will be 70, instead of the anticipated
56
• Inventory for period 2 is 90
• Use d2(p2), d3(p3) and d4(p4) to recalculate
prices for months 2, 3, 4: p2=$34, p3=$30.67,
p4=$16.50
• Set p2 = $34
• Etc…
A study of a similar deterministic
algorithm: Heching, Gallego, and van
Ryzin, 2002
• 60 fashion goods at a women’s specialty
apparel retail in the US
• Constraints:
– discount had to be at least 20%
– Initial discount not sooner than after 4 weeks
• Increased total revenue – 4.8% – relative to
standard store practice
• Most common – small markdowns sooner
than the usual store policy
A simple approach to including
uncertainty
• The current markdown opportunity is the last
• Salvage price r (may be zero) = $5
• D(p) is a random variable, whose distribution
depends on p
• D(p) – uniform distribution between 0 and abp, a=200, b=10
• Inventory x=60
Simple probabilistic markdown pricing
algorithm – dynamic programming
• We estimate demand as if we are going to hold the
price constant for all remaining periods
• E.g. D1($5) – normal distribution mean 50, variance 25;
D2($5) – normal distribution mean 30, variance 10
• Thus D^($5) – mean 80, variance 35
• We calculate the price for the upcoming period as if it
were the final markdown period
• After setting price for period 1, do the same
calculations with D2 only and again set prices, if there
were more time periods, repeat; finally sell for salvage
value
Results: Bitran, Caldentey, and
Mondschein, 1998
• Was tested for six items in eight stores of the
Chilean fashion retail chain Falabella and
compared against sales for the 1995 autumnwinter
• 12% improvement
• Cannot directly compare to the 4.8% of the
deterministic model, as bases might be
different as well as the environment
Estimating markdown sensitivity
(increased sales due to additional
discount) Levy and Woo, 1999
• Techniques for measuring price sensitivity –
such as price testing
• Systems that allow tracking historic sales and
discounts by item and category
• Calculate baseline product life cycle forecast
– Aggregating sales of fashion goods for periods in
which no markdowns have been taken
• Attribute all sales in excess of the baseline
product life cycle to the markdowns
– Fit an appropriate price-response curve
• Weeks 32-39 – the 30% markdown at week
32; 40-47 – the 50% markdown; 48-52 – the
70% markdown
Establishing a price response curve
• 0% markdown 1219 sales and 30% markdown
4253 – two points through which we can fit
the price response curve
Markdown elasticity
• (4253-1219)/1219=249% increase in sales
from a 30% decrease in price – the markdown
elasticity is 249/30=8.3
• We may expect such high levels, not found in
elasticity regarding the list price
Markdown management did not get
off the ground before the mid 1990s
• Prior to 1990, the required Enterprise
Resource Planning (ERP) and Customer
Relationship Management (CRM) software
was not in place
• Most retailers managed markdown using
promotions budget – $100M inventory and
$15M promotions budget
• In a decentralized fashion, buyers were in
charge of the lifecycle of fashion merchandise
A more general cycle
• By mid 2000s, the retail expansion of mid-nineties was
over, and not that many new stores were opened
• The 800-pound gorilla of retailing: Wal-Mart had
arrived
• The first widely published success was at ShopKo – 141
discount stores under ShopKo and 229 smaller Pamida
stores, applying Spotlight Solutions system
• 300 programs showed a 14% increase, according to
Wall Street Journal
• Followers include The Gap, JC Penney, Home Depot,
Bloomingdale’s, Sears, Circuit City
• One basic conclusion from optimal markdowns, is to
take earlier, smaller discounts, than before was
considered feasible
• The effect of optimization has additionally been the
tailored markdown schedules – e.g. earlier the same
discount was given to a specific sweater both in Boston
and in LA
• E.g. Canadian Northern Group Retail, using Profitlogic
„regional needs, weather patterns and other trends“,
e.g. nationwide swimsuit discount in September – ok
for Boston, Chicago and NY, whereas tourist season was
just beginning in Orlando and Miami
Cumbersome business rules
• First markdown after 4 weeks, and at least 15%
• All Liz Claiborne sweaters, must be marked down by
the same % @ same time
• One item – max 4 markdowns
• Every markdown must discount by at least 10% more
than previous
• 5% units, e.g. 13% and 22% not allowed
• Final price at least 25% of the original
• One week span minimum
• All stores in one region must have the same strategy
• Outlet stores must also have enough to sell, as a result
Business rules
• Are constraints on the basic optimization
problem
• Many are INT constraints, that are hard to
implement
• Constraints can make our methods too
complex to be solved by standard methods
• Thus the need to use custom algorithms like
simulated annealing and genetic algorithms