  The growth of e-commerce has resulted in a surge in parcel deliveries,
increasing transportation costs and pollution issues. Alternatives to home
delivery have emerged, such as the delivery to so-called parcel pick-up points
(PUPs), which eliminates delivery failure due to customers not being at home.
Nevertheless, parcels reaching overloaded PUPs may need to be redirected to
alternative PUPs, sometimes far from the chosen ones, which may generate
customer dissatisfaction. Consequently, predicting the PUP load is critical for
a PUP management company to infer the availability of PUPs for future orders
and better balance parcel flows between PUPs.
  This paper proposes a new approach to forecasting the PUP load evolution
using a Markov jump process that models the parcel life cycle. The latest known
status of each parcel is considered to estimate its contribution to the future
load of its target PUP. This approach can account for the variability of
activity, the various parcel preparation delays by sellers, and the diversity
of parcel carriers that may result in different delivery delays. Here, results
are provided for predicting the load associated with parcels ordered from
online retailers by customers (Business-to-Customer, B2C). The proposed
approach is generic and can also be applied to other parcel flows to PUPs, such
as second-hand products (Customer-to-Customer, C2C) sent via a PUP network.
