Probably the most closely related article is by Dada and Hu
(2008), who seminally consider a similar model to our traditional
role model where a bank provides a loan to the retailer, and characterize
the Stackelberg equilibrium. They further suggest a mechanism
to partially coordinate the supply chain. Note that the first
part of our analysis in bank financing (traditional role) is similar
to theirs. Nevertheless, different from their model, we transferred
a bi-level optimal problem into a one-level optimal problem that
is unimodal or monotonic and can be inferred analytically, as
shown in Proposition 1. It is worth noting that the biggest difference
between our model and theirs is that our model allows
financing from the 3PL firm and the supplier. Moreover, none of
the above work has explicitly discussed the impact of different
roles of a 3PL firm in a supply chain.