  We propose an efficient method of finding an optimal solution for a
multi-item continuous review inventory model in which a bivariate Gaussian
probability distribution represents a correlation between the demands of
different items. By utilizing appropriate normalizations of the demands, we
show that the normalized demands are uncorrelated. Furthermore, the set of
equations coupled with different items can be decoupled in such a way that the
order quantity and reorder point for each item can be evaluated independently
from those of the other. As a result, in contrast to conventional methods, the
solution procedure for the proposed method can be much simpler and more
accurate without any approximation. To demonstrate the advantage of the
proposed method, we present a solution scheme for a multi-item continuous
review inventory model in which the demand of optional components depend on
that of a "vanilla box", representing the customer's stochastic demand, under
stochastic payment and budget constraints. We also perform a sensitivity
analysis to investigate the dependence of order quantities and reorder points
on the correlation coefficient.
