Two-echelon collaborative many-to-many pickup and delivery problem for agricultural wholesale markets with workload balance

•A new variant of two-echelon vehicle routing problem, 2E-MPDP-WB, is introduced.•The model is formulated for 2E-MPDP-WB and its decomposition model is proposed.•Some valid inequalities are proposed.•A two-stage iterative algorithm is proposed.•The computational experiments show that the model and proposed algorithm perform well. In the context of cooperation distribution among multiple wholesale markets, each customer can place orders with multiple agricultural wholesale markets, and each agricultural wholesale market can supply different products. To improve their distribution efficiency and avoid traffic congestion, cargoes need to be transshipped among collaborative distribution of different agricultural wholesale markets owing to their product heterogeneity. Each agricultural wholesale market undertakes the cost of completing the task for the reassigned customers of finding a balance among them, respectively. Fairness of allocation is achieved through workload balance and individual rationality constraints instead of monetary transfer payments. Aimed at the collaboration problem, a two-echelon collaborative many-to-many pickup and delivery problem with workload balance (2E-MPDP-WB) is presented in this study. A mixed-integer programming model for 2E-MPDP-WB is established, and a two-stage iterative algorithm combining branch-and-bound algorithm and adaptive large neighborhood search algorithm is proposed according to the problem structure. Some valid inequalities are also proposed. Finally, computational experiments show the correctness of the model and effectiveness of the algorithm, and sensitivity analysis is performed from four aspects, namely, costs before and after collaboration, workload balance, market geographical distribution, and demand mixing degree. The findings provide management insights for the collaborative distribution of multiple wholesale markets.