## The customer at a time, but not from

The analysis is based
on forecast demand of 52 weeks for the active codes. We use the forecast
because it triggers the replenishment to the primary hub; thus, it is used to
calculate the net requirements sent to the supplier. Forecast is based on past
demand and future business opportunities. Demand is defined as customer orders
placed to the primary hub. Customer orders are placed either by a secondary hub
of one of DePuy Synthes affiliates or directly by a hospital.

This model highly depends
on the forecast evolution process of the demand behind. As shown by de Treville
et al. (2014a), “choosing a good model
for forecast is crucial, as it will substantially impact the shape of the cost
differential frontier”. Therefore, following de Treville et al. (2014a), we
start by assuming that the forecast process of Flextronics cases follows a
geometric Brownian motion with a constant instantaneous volatility .

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Currently, DePuy
Synthes implements an inventory entitlement model to calculate safety stock,
and the entitled average cycle stock, pipeline stock and maximum stock in an
item level. One of the main inputs for this model is demand. The model assumes
demand is normally distributed for items that have demand in more than 26 weeks,
and assumes a Poisson distribution for items that have demand for less than 26
weeks.

There are two
fundamental issues of using these two distributions used in the entitlement
model. On the one hand, the main problem of assuming normal distribution for
demand is that it accounts for negative demand for higher coefficient of
variations. As shown in Section 4.2, 99% of Flextronics products has a
coefficient of variation of more than 0.9. On the other hand, assuming Poisson
distribution for items that have low demand is appropriate in the case where
customer orders come from one customer at a time, but not from different type
of customers at the same time. In our case, the primary hub could receive
orders from different customers either from a secondary hub or from a hospital.
de Treville et al., (2014a) proposes to use a lognormal distribution to model
demand as it eliminates the problem of negative demand, it models peaks demand
as it has a higher
density in the right tail of distribution and serves as a lower bound for mismatch cost. If the forecast is
being drawn from a lognormal distribution, the volatility parameter increases
with the squared root of time, and demand becomes wider as lead time increases (de
Treville et al., 2014a).

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