  This paper investigates a stochastic inventory management problem in which a
cash-constrained small retailer periodically purchases a product from suppliers
and sells it to a market while facing non-stationary demands. In each period,
the retailer's available cash restricts the maximum quantity that can be
ordered. There exists a fixed ordering cost for the retailer when purchasing.
We partially characterize the optimal ordering policy by showing it has an $\bf
s-C$ structure: for each period, when initial inventory is above the $\bf$s
threshold, no product should be ordered no matter how much initial cash it has;
when initial inventory is not large enough to be a $\bf s$ threshold, it is
also better to not order when initial cash is below the threshold $C$. The
values of $C$ may be state-dependent and related to each period's initial
inventory. A heuristic policy $(s, C(x), S)$ is proposed: when initial
inventory $x$ is less than $s$ and initial cash is greater than $C(x)$, order a
quantity that brings inventory as close to $S$ as possible; otherwise, do not
order. We first determine the values of the controlling parameters $s$, $C(x)$
and $S$ based on the results of stochastic dynamic programming and test their
performance via an extensive computational study. The results show that the
$(s, C(x), S)$ policy performs well with a maximum optimality gap of less than
1\% and an average gap of approximately 0.01\%. We then develop a simple and
time-efficient heuristic method for computing policy $(s, C(x), S)$ by solving
a mixed-integer linear programming problem and approximate newsvendor models:
the average gap for this heuristic is approximately 2\% on our test bed.

Optimization and Control