Williams [8] develops a dynamic programming
algorithm for simultaneously determining the production
and distribution batch sizes at each node
within a supply chain network. As in Williams [7],
it is assumed that the production process is an
assembly process. The objective of the heuristic is
to minimize the average cost per period over an
inÞnite horizon, where the average cost is a function
of processing costs and inventory holding costs
for each node in the network.
Ishii et al. [9] develop a deterministic model for
determining the base stock levels and lead times
associated with the lowest cost solution for an
integrated supply chain on a Þnite horizon. The
stock levels and lead times are determined in such
a way as to prevent stockout, and to minimize the
amount of obsolete (ªdeadº) inventory at each
stock point. Their model utilizes a pull-type ordering
system which is driven by, in this case, linear
(and known) demand processes.