2 DEMAND ESTIMATION
One of the ecommerce business key performance
indices is to maximize sales conversion rate of
merchandise on site. The conversion rate can be
measured by the quantity sold divided by total
quantity available for a SKU during a sales event. It
can be affected by many business processes, from
product selection to its ranked display on site, and to
the timely delivery to customers. All else being equal,
how can we improve overall sales conversion rate by
improving regional merchandise distribution
planning? Specifically, given some quantity of a SKU
that we may have limited past sales knowledge, we
need to determine the quantity allocation ratio for pre-
distribution of the merchandise to each regional
warehouse.
Although flash sale is unique in its business
operation, merchandise sell-or-not is inherently
determined by the quality of a product and demand
and display ranking factors such as brand recognition,
fashion, price discount, seasonality, color, size
preference by region, etc. To determine regional
quantity allocation ratio based on the demand
estimation of sales of merchandise, we built ML
models to predict the regional demand for a SKU.
There has been a large literature on multi-echelon
distribution systems and inventory allocation (
Ghiani
et al., 2004). In our distribution configuration, we
assume overall supply is given and must be pre-
distributed to customer-facing regional warehouses
(fulfilment centers) before a flash sale event starts.
Due to the short period of a flash sale and business
policy, transferring merchandises between regional
distribution warehouses, or warehouse serving
customers in a different region, is typically not
allowed.
2.1 Newsvendor Model
Newsvendor, or newsboy or single-period
(Stevenson, 2009) or perishable (Malakooti, 2013),
model can be traced back to a paper (Edgeworth,
1888) where Edgeworth used central limit theorem to
estimate the optimal cash reserves to satisfy random
withdrawals from depositors.
In the Newsvendor model (Arrow et al., 1951) of
inventory optimization, it concerns how many copies
of the day's paper to stock in the face of uncertain
demand and knowing that unsold copies will be
worthless at the end of the day. The optimal solution
is to statistically balance the cost of being
understocked (a loss of sale) with inventory cost of
being overstocked. By and large, this simple model is
applicable to retail inventory management (Gallego et
al., 1993). We can develop business specific supply
and demand estimation to plug into the model.
Figure 1 shows that the uncertainty around the
minimum cost in the Newsvendor model is greatly
affected by the variance of the underlying demand
and supply estimation. The decreasing linear dotted
line at left represents the cost of sales loss due to
understock when demand is greater than supply, the
increasing linear dotted line at right represents
inventory cost due to overstock when demand is less
than supply. When demand equals supply, there is no
sales loss or leftovers and the cost is zero. These are
the cases when the demand and supply are estimated
accurately without uncertainty. The three curves
show the minimum costs under uncertainty due to the
fluctuation of demand and supply. The lowest curve
is when the demand and supply fluctuation variance
is low, and the top curve is when variance is high. We
see as demand and supply variance gets higher, both
the expected minimum cost and the “safety” stock
level increase, and the cost function becomes much
more flat. In other words, the impact of the optimal
solution to business diminishes fast if the demand and
supply estimation has large statistical variance.
Figure 1: Cost under uncertain demand (D) and supply (S).
In flash sale, it usually acquires fixed quantity of each
SKU for a short-term sales event. It boils down to
stochastic demand estimation at each regional
warehouse based on historical sales and viewing
records if exist, and from aggregated statistics of sales
of similar merchandise or product category,
seasonality, regional discriminative factors such as
size, color, fashion, etc.
Among many choices, we choose to train non-
linear, non-parameterized machine learning models
using gradient boosted decision trees (GBDT)
(Friedman, 1999) to predict demand and regional
warehouse merchandise allocation ratio based on past
sales and sales proportion ratio in the regions. Our
training datasets are typically in the size of millions
with features extracted from brand, product and