Bulk Ship Fleet Renewal and Deployment under Uncertainty: A Multi-Stage Stochastic Programming Approach

We study a maritime fleet renewal and deployment problem under demand and charter cost uncertainty. A decision-maker for an industrial bulk shipping company must determine a suitable fleet size, mix, and deployment strategy to satisfy stochastic demand over a given planning horizon. She may acquire vessels in two ways: time chartering and voyage chartering. Time charter vessels may be acquired for different durations of time and this decision is made before demand and charter costs are known, while voyage charter vessels are chartered for a single voyage from a supply port to a demand port and the decision is made after demand is known. The goal is to determine an optimal fleet size and deployment strategy that minimizes the expected acquisition and transportation costs, while satisfying demand and deployment constraints. To handle the simultaneous fluctuations in demand and charter costs, we introduce a multi-stage stochastic programming look-ahead model that is solved in a rolling horizon fashion and explore the ramifications of using different scenario trees with various recourse options. Computational results indicate that our approach is superior to traditional planning methods that rely on ad hoc heuristics and deterministic optimization models using expected value forecasts of stochastic parameters.