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Multistage stochastic optimization for drayage procurement in container logistics using stochastic dual dynamic programming

Georgios Vassos, Richard Lusby, Pierre Pinson

TL;DR

The paper addresses drayage procurement under uncertain cargo flows by modeling it as a multistage stochastic transportation problem and solving it with stochastic dual dynamic programming. It advances- the modeling with a copula-based multivariate Poisson time-series framework to capture interdependencies in cargo flows and uses SDDP to derive operational volume-allocation policies across a realistic horizon. Key findings show that inflow uncertainty dominates cost variability, that spot-market fluctuations have limited impact under contracted-lean procurement, and that the proposed adaptive stopping rule achieves a favorable balance between solution quality and computation time. These results demonstrate the practical viability of scalable, policy-focused optimization for container logistics under deep uncertainty, with implications for capacity contracting and inventory-transport decisions.

Abstract

Truckload procurement plays a vital role in integrated container logistics, particularly under the uncertainties of container flow and market conditions. We formulate the operational volume allocation problem in drayage procurement as a multistage stochastic transportation problem and solve it using stochastic dual dynamic programming (SDDP). We employ a multivariate count time series approach from the literature to model cargo flow dynamics, relaxing independence assumptions and capturing complex correlations. Our numerical experiments demonstrate the scalability of SDDP and its effectiveness in approximating high-quality policies across realistic problem instances. Sensitivity analyses highlight the significant impact of inflow uncertainties on costs, while spot market variability has a comparatively minor effect. Additionally, we propose an alternative stopping rule for SDDP iterations, balancing computational efficiency and solution fidelity.

Multistage stochastic optimization for drayage procurement in container logistics using stochastic dual dynamic programming

TL;DR

The paper addresses drayage procurement under uncertain cargo flows by modeling it as a multistage stochastic transportation problem and solving it with stochastic dual dynamic programming. It advances- the modeling with a copula-based multivariate Poisson time-series framework to capture interdependencies in cargo flows and uses SDDP to derive operational volume-allocation policies across a realistic horizon. Key findings show that inflow uncertainty dominates cost variability, that spot-market fluctuations have limited impact under contracted-lean procurement, and that the proposed adaptive stopping rule achieves a favorable balance between solution quality and computation time. These results demonstrate the practical viability of scalable, policy-focused optimization for container logistics under deep uncertainty, with implications for capacity contracting and inventory-transport decisions.

Abstract

Truckload procurement plays a vital role in integrated container logistics, particularly under the uncertainties of container flow and market conditions. We formulate the operational volume allocation problem in drayage procurement as a multistage stochastic transportation problem and solve it using stochastic dual dynamic programming (SDDP). We employ a multivariate count time series approach from the literature to model cargo flow dynamics, relaxing independence assumptions and capturing complex correlations. Our numerical experiments demonstrate the scalability of SDDP and its effectiveness in approximating high-quality policies across realistic problem instances. Sensitivity analyses highlight the significant impact of inflow uncertainties on costs, while spot market variability has a comparatively minor effect. Additionally, we propose an alternative stopping rule for SDDP iterations, balancing computational efficiency and solution fidelity.
Paper Structure (11 sections, 18 equations, 4 figures, 1 table)

This paper contains 11 sections, 18 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature review
  3. Mathematical model
  4. Stochastic Dual Dynamic Programming
  5. General multivariate uncertainty model
  6. Numerical analysis
  7. Optimal volume allocation policy
  8. Practical instance specifications
  9. Sensitivity analysis
  10. Computational performance of the SDDP
  11. Discussion

Figures (4)

  • Figure 4.1: Optimal drayage operations in a system with 2 entry hubs and 2 exit hubs over 12 time stages, illustrating stock levels, inflows, outflows, and volume allocations between hubs.
  • Figure 4.2: Optimal volume allocation between carriers and lanes.
  • Figure 4.3: Distribution of the objective function across 1000 examples of inflow and spot rates for 100 instances of the 12-stage drayage problem, featuring 6 entry hubs, 6 exit hubs, and 20 carriers operating in both contract and spot markets.
  • Figure 4.4: Distribution of regret recorded from 1,000 out-of-bag inflow/outflow scenarios simulated for 100 instances of the 12-stage stochastic transportation problem with 6 entry hubs, 6 exit hubs, and 20 carriers.