Optimizing local pickup and delivery with uncertain loads

The local pickup and delivery problem (LPDP) is an essential operational problem in intermodal industry. While the problem with deterministic settings is already difficult to solve, in reality, there exist a set of loads, called uncertain loads, which are unknown at the beginning of the day. But customers may call in during the day to materialize these loads. In this paper, we call the LPDP considering these uncertain loads as the stochastic LPDP. The problem description and the mathematical modeling of stochastic LPDP are discussed. Then, a simulation-based optimization approach is proposed to solve the problem, which features in a fast solution generation procedure and an intelligent simulation budget allocation framework. The numerical examples show the best strategy to consider the stochastic loads in the planning process and validate the benefits compared to its deterministic counterpart.