A Lagrangian Column Generation Approach for the Probabilistic Crowdsourced Logistics Planning

In recent years we have increasingly seen the movement for the retail industry to move their operations online. Along the process, it has created brand new patterns for the fulfillment service, and the logistics service providers serving these retailers have no choice but to adapt. The most challenging issues faced by all logistics service providers are the highly fluctuating demands and the shortening response times. All these challenges imply that maintaining a fixed fleet will either be too costly or insufficient. One potential solution is to tap into the crowdsourced workforce. However, existing industry practices of relying on human planners or worker's self-planning have been shown to be inefficient and laborious. In this paper, we introduce a centralized planning model for the crowdsourced logistics delivery paradigm, considering individual worker's spatio-temporal preferences. Considering worker's spatio-temporal preferences is important for the planner as it could significantly improve crowdsourced worker's productivity. Our major contributions are in the formulation of the problem as a mixed-integer program and the proposal of an efficient algorithm that is based on the column generation and the Lagrangian relaxation frameworks. Such a hybrid approach allows us to overcome the difficulty encountered separately by the classical column generation and Lagrangian relaxation approaches. By using a series of real-world-inspired numerical instances, we have demonstrated the effectiveness of our approach against classical column generation and Lagrangian relaxation approaches, and a decentralized, agent-centric greedy approach. Our proposed hybrid approach is scalable to large problem instances, with reasonable solution quality, and achieves better allocation fairness.