Joint capacity planning and dynamic allocation for container leasing with asymmetric substitution

Abstract

Container leasing companies maintain a flexible container pool to meet short-term requests from committed customers and the spot market. However, capacity planning and container allocation are complicated by stochastic demand, container returns, and asymmetric substitution between container types. This paper investigates the joint planning of type-specific container capacities at a depot and the dynamic allocation of available containers to incoming leasing requests. For a fixed capacity vector, the operational problem is formulated as an infinite-horizon discounted Markov decision process (MDP), and several properties are established to characterize state-dependent acceptance, rejection, and substitution thresholds. A Bayesian optimization and dynamic programming (BO+DP) approach is then developed to determine the capacity vector, supported by queueing-based screening and coarse-to-fine value iteration. Numerical experiments show that the optimal thresholds vary with container availability, customer segment, and directional substitution factors. The screening rule removes about 93.5% of candidate capacity combinations and reduces average computation time from 393.8 s to 47.7 s. The capacity-planning results show that faster container returns can reduce the required capacity even when leasing demand is higher. Under fixed capacities, two-way asymmetric substitution increases expected discounted profit by 7.38% on average relative to one-way substitution and by 9.12% relative to no substitution. Across eight scenarios, BO+DP improves the MDP-based expected discounted profit by 41.78% on average relative to the two-stage stochastic programming benchmark. The results indicate that capacity size should account for both leasing demand and container return rates, while the capacity mix and allocation rules should reflect directional substitution revenues and the effective rejection penalties used to represent implicit service commitments.

The authors' abstract, as published at the source. Transportation Research Part B Methodological, 2026 · DOI ↗