  E-grocery retailing enables ordering products online to be delivered at a
future time slot chosen by the customer. This emerging field of business
provides retailers with large and comprehensive new data sets, yet creates
several challenges for the inventory management process. For example, the risk
of a single item's stock-out leading to a complete cancellation of the shopping
process is higher in e-grocery than in traditional store retailing. As a
consequence, retailers aim at very high service level targets to provide
satisfactory customer service and to ensure long-term business growth. When
determining replenishment order quantities, it is of crucial importance to
precisely account for the full uncertainty in the inventory process. This
requires predictive and prescriptive analytics to (1) estimate suitable
underlying probability distributions to represent the uncertainty caused by
non-stationary customer demand, shelf lives, and supply, and to (2) integrate
those forecasts into a comprehensive multi-period optimisation framework. In
this paper, we model this stochastic dynamic problem by a sequential decision
process that allows us to avoid simplifying assumptions commonly made in the
literature, such as the focus on a single demand period. As the resulting
problem will typically be analytically intractable, we propose a stochastic
lookahead policy incorporating Monte Carlo techniques to fully propagate the
associated uncertainties in order to derive replenishment order quantities.
This policy naturally integrates probabilistic forecasts and allows us to
explicitly derive the value of accounting for probabilistic information
compared to myopic or deterministic approaches in a simulation-based setting.
In addition, we evaluate our policy in a case study based on real-world data
where underlying probability distributions are estimated from historical data
and explanatory variables.
