Profit distribution in collaborative multiple centers vehicle routing problem

A collaborative multiple-center vehicle routing problem (CMCVRP) is a multi-constraint combinatorial and game optimization issue containing both vehicle routing optimization and profit distribution procedures. The CMCVRP is generally used to study the logistics network structure adjustment from a non-optimal network structure to a collaborative multiple DCs network optimization structure. The optimization of CMCVR can effectively improve vehicle loading rate and reduce the crisscross transportation phenomenon. Designing a reasonable profit distribution mechanism is a critical step of CMCVR optimization. Collaboration can be organized through a negotiation process by a logistics service provider. This paper establishes an integer-programming model that contains transportation costs among distribution centers (DCs) and vehicle routing costs in each DC to minimize the total costs of CMCVRP. A multi-phase hybrid approach with clustering, dynamic programming, and heuristic algorithm is presented to solve the model formulation. The clustering procedure increases the likelihood that the solution will converge to an optimal value, between-route operations (relocate, 2-opt* exchange, and swap move) in the heuristic algorithm will improve the initial solution, and the within-route (dynamic programming) procedure will calculate a good feasible solution for each vehicle route. Both between- and within-route operations are recursively executed to find the best solution. Profit distribution plans are then established using the improved Shapley value model. Optimal sequential coalitions are selected based on strictly monotonic path, cost reduction model, and best strategy of sequential coalition selection in cooperative game theory. An empirical study in Chongqing, China suggests that the proposed approach outperforms other algorithms, and the best sequential coalition can be selected and adjusted to increase the negotiation power for network optimization of logistics distribution.