Introduction
Realizing the competitive advantages of being flexible,
responsive as well as efficient, and enabled by advanced technologies, more and
more manufacturing companies are reengineering their product design and delivery
processes to move toward mass customization (Pine, 1993). This requires
modularizing the production process so that the product can be quickly assembled
from standardized components and modules in different configurations, based on
what customers individually request. As a result, a new kind of
production-inventory system has emerged and is becoming
increasingly
popular. This is the Assemble-To-Order (ATO) system: inventories are kept only
at the component level, and the final products are assembled only after customer
orders are received.
This new system, in turn, presents challenging
operational and system design issues to managers. As each customer order
typically involves several components in different amounts, the stockout of any
component will cause a delay in fulfilling the order. So, the optimal stock
level of one component should be determined in conjunction with those of other
components to ensure their simultaneous availability. Standard single-item
inventory planning tools, while suitable for the mass-production make-to-stock
environment, are no longer applicable. New planning tools are needed to strike
the optimal inventory-service tradeoff in ATO systems. The current paper
presents an effort towards this goal.
More specifically, we consider an ATO system supporting
multiple types of demand, which arrive at the system following compound Poisson
processes. The component inventories are resupplied from outside suppliers after
random replenishment leadtimes. For a given component, the leadtimes are
independent, identically distributed (i.i.d.) random variables. The leadtimes
for different components are also independent but may have different
distributions. Since the form of the optimal inventory-control policy for this
system is unknown, base-stock policies are widely adopted in practice. For this
reason, we assume the inventory of each component is controlled by a base-stock
policy. The system performance measure we focus on is the expected backorder for
each product. Our objective is to minimize a weighted average of backorders over
all product types, subject to a budget constraint on the component inventory.
Through Little's law (Wolff, 1989), this objective relates directly to the
response time performance in fulfilling customer orders.
The optimization problem under study is quite complex.
First, its objective function is nonseparable and non-differentiable. Second,
its evaluation involves joint probabilities, which can be computationally
challenging. To deal with the second difficulty, we develop upper and lower
bounds on the backorders that involve marginal distributions only and use these
bounds and approximations derived from them as surrogate objective functions in
the optimization problem. This approach is similar in spirit to that in Song and
Yao (2002) for the single-product ATO system. However, even with the simpler
surrogate objective functions the first difficulty remains. Moreover, the bounds
for the multiproduct model here are more involved than in the single-product
case and exhibit different structures, so the ideas used to develop the
algorithms in Song and Yao do not apply.