Dynamic allocation and pricing for capacitated stochastic container leasing systems with dynamic arrivals

Container leasing is a flourishing industry characterised by multiple-unit demand, monopolistic supply, and long-standing customer relationships. The constraints imposed by a finite capacity and dynamic customer arrivals mean that leasing companies must address allocation and pricing issues. In this study, we investigate the dynamic rationing and nonlinear pricing problem for a leasing company with high-type and low-type customers (differentiated by per-time valuation for the leasing service) who first arrive randomly at the company and have specific hire duration preferences. We derive the closed-form optimal rationing and pricing policy, and also discuss the effect of capacity constraints and customer dynamic arrivals on the optimal allocation policy. In the setting with the same hire duration preference, the capacity constraint has a greater effect over time for customers with the same entry date and dynamic customer arrivals accelerate the increasing effect of capacity constraints compared with the case of simultaneous entries. In the setting with different hire duration preferences, the effect of the capacity constraint increases for the low-type customers and decreases for the high-type customers. Dynamic arrivals only exacerbate the increasing effect of the capacity constraint for consistent low-type customers.