Optimal inventory policy with limited storage capacity and uncertain demand

High inventory level can certainly increase the meeting of customer demands, but it also leads that the cost is not the lowest one. This means that meeting customer demands and having the lowest cost may not always be consistent. Specially, if storage capacity is limited, the relationship between the two will become more complex to collaborate, and there will be more problems to solve, such as whether to rent warehouses, what size of the rented warehouses (RW) if necessary, and what is the right inventory level, et.c. To solve these problems and get the tradeoff between meeting customer demands and having the lowest cost, the concept of inventory flexibility is introduced into the paper, and an inventory model with uncertain demand is developed and solved through Kuhn-Tucker condition, which is of operation research, and the relationship between marginal cost and average total cost, which is of principles of economics, and then decision makers could get the optimal inventory policy related with the right inventory level and the size of storage space. An example is also introduced for illustration.