Study of
Decentralized Distribution Systems: Part I - A General
Framework
R. Anupindi, Y. Bassok and E. Zemel
*** Abstract ****
We develop a general framework for the analysis of decentralized
distribution systems. Specifically, our distribution system has $N$
retailers who face stochastic demands and hold stocks locally and/or
at one or more central locations. An exogenously specified fraction of
any unsatisfied demand (demand greater than locally available stock)
at a retailer could be satisfied using excess stocks at other
retailers and/or stocks held at a central location. We consider
inventory ordering and allocation decisions. The operational decisions
of inventory and allocation of stocks and the financial decision of
allocation of revenues/costs must be made in a way consistent with the
individual incentives of the various independent retailers. We develop
a ``co-opetitive'' framework for the sequential decisions of
inventory and allocation. We introduce the notion of {\em claims} that
allows us to separate the ownership (with decision rights) and the
location of inventories in the system. For the cooperative shipping
and allocation decision, we use the concept of core and develop
sufficient conditions for the existence of the core. We develop
conditions for the existence of a pure strategy Nash Equilibrium for
the inventory decision. We show that there exists an allocation
mechanism that achieves the first best solution for inventory
deployment and allocation. We develop conditions under which the first
best equilibrium will be unique. Finally, we develop criteria for the
implementability of the solution concepts. The model can be easily
generalized to include complicated ownership structures such as
``super agents'', partnerships, ``inventory speculators'', etc. It
can also be applied to situations involving capacity allocations and
product substitutions.
Study of
Decentralized Distribution Systems: Part II - Applications
R. Anupindi, Y. Bassok and E. Zemel
*** Abstract ****
In Part I we developed a general
framework for the analysis of decentralized distribution
systems. Several key ideas illustrated in that paper include a (i)
``co-opetitive'' framework for the sequential decisions of inventory
and allocation, (ii) the notion of {\em claims} that separate the
ownership (with decision rights) and the location of inventories in
the system, (iii) the existence of allocation mechanisms that achieve
the first best solution, and (iv) meta-core as a criteria for the
implementability of the solution concepts. The purpose of this paper
is to explore, within the context of the general framework, the
strategic role of some simple and intuitive allocation mechanisms in
duopoly and oligopoly models. For the duopoly model, we develop
sufficient conditions for the uniqueness of a pure strategy Nash
Equilibrium and propose some simple allocation rules which exhibit
unique Nash Equilibria. We then develop necessary and sufficient
conditions under which a transfer pricing mechanism achieves first
best. For a symmteric oligopoly model, we develop sufficient
conditions for the existence of a unique Nash Equilibirum. Finally,
for two specific oligopoly models (including the symmetric case) we
show the existence of allocation policies that achieve the first
best.