Integrated optimization of operations and capacity planning under uncertainty for drayage procurement in container logistics

TL;DR

This work studies integrated drayage procurement by linking strategic capacity planning with operational volume allocation under uncertainty in container inflows/outflows and spot rates. It develops a Markov decision process (MDP) framework for the operational policy and uses sample-average approximation plus a portfolio/option sourcing mechanism; capacity planning uses a quasi-Newton method (L-BFGS-B) to choose reservations. Key results show substantial cost savings (e.g., a 21.2% reduction in a four-period illustrative instance) and strong generalization of the learned capacity plan across out-of-sample scenarios. The findings highlight the value of integrating strategy and operations in drayage procurement and point to scalable approximate methods and future extensions with real data and real-time updates.

Abstract

We present an integrated framework for truckload procurement in container logistics, bridging strategic and operational aspects that are often treated independently in existing research. Drayage, the short-haul trucking of containers, plays a critical role in intermodal container logistics. Using dynamic programming, we identify optimal operational policies for allocating drayage volumes among capacitated carriers under uncertain container flows and spot rates. The computational complexity of optimization under uncertainty is mitigated through sample average approximation. These optimal policies serve as the basis for evaluating specific capacity arrangements. To optimize capacity reservations with strategic and spot carriers, we employ an efficient quasi-Newton method. Numerical experiments demonstrate significant cost-efficiency improvements, including a 21.2% cost reduction in a four-period scenario. Monte Carlo simulations further highlight the strong generalization capabilities of the proposed joint optimization method across out-of-sample scenarios. These findings underscore the importance of integrating strategic and operational decisions to enhance cost efficiency in truckload procurement under uncertainty.

Figures (7)

• Figure 1: An example of intermodal container transportation involves containers being transported by ocean and rail into a system of drayage operations. These containers arrive at rail yards within the system's scope, and from there, they are transported to nearby hubs, where they continue their intermodal journey.
• Figure 2: An elementary drayage system with storage facilities at the entry and exit points.
• Figure 3: The value function for the chosen scenario is evaluated at each period of the planning horizon. The entry state ranges from $0$ to $10$, while the exit state varies between $-10$ and $10$, both defined as integer values. The color bar indicates the negative cumulative cost from the given period up to $t=4$.
• Figure 4: Evolution of the drayage system under the identified optimal volume allocation policy. The left node shows the entry location, and the right node indicates the exit. The top number on each node represents stock levels, while the left of the entry node shows incoming container volume, and the right of the exit node shows outflow. The middle number on the connecting arrow indicates the volume transported between the locations.
• Figure 5: Density of Total Cost (left) and Cost-per-TEU (right) computed by optimizing the value function over $1,000,000$ random examples of the capacity arrangement.