This paper studies a dynamic pricing problem in the SS industry. First, the paper formulates the problem as an inventory control model, with random demand (move-ins) and supply (move-outs). In each period, the firm sets the price to control demand, collects revenue from sales, and pays penalty for oversell (or shortage in the newsvendor parlance).
Second, the paper provides theoretical underpinning of the price controller practice. The price controller is a weighted average of performance metrics, including the occupancy change, the vacancy change, and the managers’ incentive. It uses a linear combination of past vacancy levels, demand and supply. The paper shows that the price controller approach can be optimal for four-period cases (since it has three parameters). For longer horizons, the price controller can be adjusted over time, depending on the trends of the recent history. In the stationary environment, because of the updating, the price controller can converges to the optimal. The paper also proposes an improvement of the price controller practice by exploring the similarity between the updating practice and the sub-gradient method.
Third, the paper addresses three managerial questions. Through numerical examples, it shows that the benefit of long-term leasing is limited, that certain myopic pricing (limited to linear form) is inferior, and that the the convergence of the price controller to the optimal can be speeded up by using step length instead of step side.
I read the paper with great interest. The main strength is on the practical side. To my knowledge, it is the first to formalize and validate the practice of the price controller method. As a first order approximation of the optimal solution, the controller can converge to the optimal over time through updating.
The paper is less compelling on the theoretical ground. It is certainly valuable to explicate the link between the practice and the optimal solution. The numerical studies are also important to understand the practice of the self-storage industry. However, without further analytical results, the answers to the three managerial questions are not entirely satisfactory.
I would like to see more analytical results. For example, the paper uses computation to show that the rental lease may not deliver substantial benefits, since it mainly reduces the supply variation. This result can be rigorously established by stochastic comparison. The efforts along this direction will certainly strengthen the conclusions and enhance the contribution.
The exposition can be much improved. For the content it delivers, the paper is way too long. For example, the section 3.1 on the demand function is quite standard, and it should be shortened to a paragraph or two. The formulation in section 3.2 should also be tightened, as it is quite standard in the inventory literature.
In summary, the paper deals with the practice of an interesting operational problem. However, it needs to strengthen the analytical content. I recommend major revision.