Abstract: This paper deals with a periodic-review substitutable
inventory system for a finite and an infinite number of periods. Here
an upward substitution structure, a substitution of a more costly item
by a less costly one, is assumed, with two products. At the beginning
of each period, a stochastic demand comes for the first item only,
which is quality-wise better and hence costlier. Whenever an arriving
demand finds zero inventory of this product, a fraction of unsatisfied
customers goes for its substitutable second item. An optimal ordering
policy has been derived for each period. The results are illustrated
with numerical examples. A sensitivity analysis has been done to
examine how sensitive the optimal solution and the maximum profit
are to the values of the discount factor, when there is a large number
of periods.