A Branch and Price Algorithm for the Drop-and-Pickup Container Drayage Problem with Empty Container Constraints

Yujian Song, Yuting Zhang, Wanli Wang and Ming Xue ()
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Yujian Song: School of Business Administration, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China
Yuting Zhang: School of Economic and Management, Tongji University, Shanghai 200092, China
Wanli Wang: School of Business Administration, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China
Ming Xue: School of Business Administration, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China

Sustainability, 2023, vol. 15, issue 7, 1-28

Abstract: This paper addresses the drop-and-pickup container drayage problem with empty container constraints. In this problem, a truck is allowed to drop off the container at the customer and then leave. After the container has been packed/unpacked, the truck returns to pick it up. The problem is further complicated by the fact that empty containers at the depot are often limited in number. This container drayage problem is of great practical importance but seldom investigated. In this paper, we first formulate the problem as a directed graph and then mathematically model it as a mixed-integer linear program (MILP) with the objective of minimizing total travel costs. To solve the MILP effectively, we devise a branch and price algorithm that incorporates several performance enhancement strategies, including three versions of the bi-directional label setting algorithm, preprocessing of time windows and a heuristic for high-quality upper bounds. The experimental results indicate that (1) the proposed algorithm significantly outperforms CPLEX in terms of efficiency and effectiveness, (2) an average cost saving of 9.95∼12.25% can be achieved from the drop-and-pickup mode and (3) the benefit of drop-and-pickup mode increases when the customer density and the fixed cost increase.

Keywords: container drayage; drop-and-pickup mode; empty container; branch and price algorithm (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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