  Inventory control typically considers controlling the price and the
production rate. However, such systems have rigidity towards altering the
physical storage capacity -- one can not easily alter the physical size after
the initial design. The paper focuses on this critical aspect, consideration of
which leads to a non-standard control problem. Here, the objective is a
weighted combination of the classical integral term (formed by usual inventory
costs) and an $L^{\infty}$ term (the maximum inventory level in the entire
planning horizon). Our approach is to consider an additional state component to
capture the `instantaneous' $L^{\infty}$ term (maximum inventory level till
that instant) by virtue of which, we could convert the problem to the classical
framework. For the direct ($L^{\infty}$) problem, we first identify a relation
between the optimal price and the production rate policy, thereby reducing the
dimensionality of the problem. By numerically solving a smooth variant of the
converted problem, we obtain an optimal policy that illustrates a significant
reduction in the storage capacity requirement. Interestingly, the loss in the
revenue is negligible (less than $6\%$). As the importance of the $L^{\infty}$
component increases, the variations in the corresponding optimal
inventory-level trajectory reduce. In the scenarios with partial/zero
information about future demand curves, the above observation provides a
guidance -- one should continually tune the policies to maintain instantaneous
inventory-levels as close to zero as possible. With such a policy, the
reduction in revenue is negligible, while having significant improvements for
storage capacity. We theoretically establish certain interesting properties of
the optimal policy, which also support the above guidance.
