Collaborative profit allocation schemes for logistics enterprise coalitions with incomplete information

The issue of collaborative profit allocation in a coalition of enterprises appears important in cooperative games, and arises frequently in the logistics service industry. However, incomplete information usually exists in logistics enterprise coalitions. Therefore, some eminent point-valued solutions of cooperative games appear powerless, such as the Shapley value and the Banzhaf value. They just apply to the cooperative games where all coalitional values could be estimated in advance. This work concerns the issue of profit allocation for collaborative coalitions with incomplete information and develops several profit allocation schemes for logistics enterprise coalitions. First, based on the own profits of the collaborative logistics enterprises and their contributions to the collaborative coalition, a quadratic programming model is developed as a baseline model. Next, the baseline model is extended by taking account of the weights of the collaborative logistics enterprises. Some important properties of the solutions proposed in this paper, such as the efficiency, existence, symmetry, and anonymity, are apparent. One algorithm, if necessary, is described to make them satisfy the property of individual rationality. Through three numerical scenarios and an actual case in the logistics service industry, the advantages of the solutions proposed in this paper are demonstrated.