Branch-price-and-cut for trucks and drones cooperative delivery

The truck and drone-based cooperative model of delivery can improve the efficiency of last mile delivery, and has thus increasingly attracted attention in academia and from practitioners. In this study, we examine a vehicle routing problem and apply a cooperative form of delivery involving trucks and drones. We propose a mixed-integer programming model and a branch-price-and-cut-based exact algorithm to address this problem. To reduce the computation time, we design several acceleration strategies, including a combination of dynamic programming and calculus-based approximation for the pricing problem, and various effective inequalities for the restricted master problem. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed solution.