  Local delivery platforms are collaborative undertakings where local stores
offer instant-delivery to local customers ordering their products online.
Offering such delivery services both cost-efficiently and reliably is one of
the main challenges for local delivery platforms, as they face a complex,
dynamic, stochastic dynamic pickup-and-delivery problem. Orders need to be
consolidated to increase the efficiency of the delivery operations and thereby
enable a high service guarantee towards the customer and stores. But, waiting
for consolidation opportunities may jeopardize delivery service reliability in
the future, and thus requires anticipating future demand. This paper introduces
a generic approach to balance the consolidation potential and delivery urgency
of orders. Specifically, it presents a newly developed parameterized
Cost-Function Approximation (CFA) approach that modifies a set-packing
formulation with two parameters. This CFA approach not only anticipates future
demand but also utilizes column generation to search the large decision space
related to pickup-and-delivery problems fast. Inspired by a motivating
application in the city of Groningen, the Netherlands, numerical experiments
show that our CFA approach strongly increases perceived customer satisfaction
while lowering the total travel time of the vehicles compared to various
benchmark policies. Furthermore, our CFA also reduces the percentage of late
deliveries, and their lateness, to a minimum. Finally, our approach may assist
managers in practice to manage the non-trivial balance between consolidation
opportunity and delivery urgency.
