Solving the collaborative bidirectional multi-period vehicle routing problems under a profit-sharing agreement using a covering model

Abstract

This paper introduces a covering model for collaborative bidirectional multi-period vehicle routing problems under profit-sharing agreements (CB-VRPPA) in bulk transportation (BT) networks involving one control tower and multiple shippers and carriers. The objective is to maximize the total profits of all parties subject to profit allocation constraints among carriers, terminal capability limitations, transport capability limitations and time-window constraints. The proposed method includes three stages: (a) generate all feasible routes of each carrier, (b) eliminate unattractive feasible routes via a proposed screening technique to reduce the initial problem size, and (c) solve the reduced problem using a branch-and-bound algorithm. Computational experiments are performed for real-life, medium-and large-scale instances. The proposed method provides satisfactory results when applied to solve the CB-VRPPA. We also conduct a sensitivity analysis on a critical parameter of the profit-sharing agreement to confirm the effectiveness of the proposed method.