Analysis of a Decentralized Supply Chain Under Partial Cooperation
by
Nesim Erkip
Bilkent University
In this study, we analyze a decentralized supply chain consisting of a supplier
and two independent retailers. In each order cycle, retailers place their orders
at the supplier to minimize inventory-related expected costs at the end of their
respective response times. There are two types of lead times involved. At the
end of the supplier lead time, retailers are given an opportunity to readjust
their initial orders (without changing the total order size), so that both
retailers can improve their expected costs at the end of respective retailer
lead times (the time it takes for items to be shipped from the supplier to the
retailers). Because of the possibility of cooperation at the end of supplier
lead time, each retailer will consider the other’s order-up-to level in making
the ordering decision. Under mild conditions, we prove the existence of a unique
Nash equilibrium for the retailer order up- to levels, and show that they can be
obtained by solving a set of newsboy-like equations. We also present
computational analysis that provides valuable managerial insight for design and
operation of decentralized systems under the possibility of partial cooperation.
This is a joint work with Refik Güllü, Geert-Jan van Houtum and F. Zeynep Sargut.