Multi-modal cargo logistics distribution problem: Decomposition of the stochastic risk-averse models

Abstract

This paper aims to develop a solution framework for large size scheduling problems by a novel multi-modal stochastic model in order to help the decision-makers to create a desirable schedule for the Belt & Road (B&R) corridors and North–South corridor, which provide a big trade market for the China–Europe routes. The model incorporates risk measures to resolve the stochastic scheduling problem where the uncertainty of demand, transit time and unloading time are taken into account. The developed model considers the transit cargoes and the various transportation options under time window limitations. In order to select the most effective risk measure, four well-known risk measures are evaluated including Value at Risk (VaR), Conditional Value at Risk (CVaR), Tail Value at Risk (TVaR) and Mean Absolute Deviation (MAD). A two-phase hierarchical algorithm with an integrated novel Golden Search (GS) algorithm is developed to deal with the proposed bi-objective model. In order to cope with the large scale problems, the Sample Average Approximation (SAA) and Scenario Decomposition (SD) methods are further proposed. A Lagrangian Decomposition (LD) algorithm is then developed to estimate the best lower bound of the SD. The efficiency and effectiveness of the proposed model and solution framework has been validated via sets of sensitivity analysis tests. The results of analysis define the optimal flows of the cargoes across the most economic corridor.