An extended robust approach for a cooperative inventory routing problem

The impact of the horizontal collaboration of logistic providers as upstream supply chain elements is studied in this paper. The logistic providers can be considered as different players and, in order to analyze different types of coalitions by computing the synergy between the players in each cooperative structure, we developed a mixed integer programming (MIP) formulation for a cooperative inventory routing problem (Co-IRP). In this paper, each player has one depot and some retailers, which are considered as its available market. The model will have a many-to-many network structure once a coalition is formed, where a single product from different depots will be delivered to different retailers. We establish a robust version of Co-IRP, which is called Co-RIRP, considering uncertainty in the network. We developed a few metaheuristic algorithms to promote the gained results once MIP is solved. Finally, in order to share the possible cost saving between players and compare the assignments, we applied a few payoff distribution methods. In addition, a comprehensive analysis of example results and some important managerial insights are presented.