Carrier collaboration with the simultaneous presence of transferable and non-transferable utilities

This paper deals with a problem in collaborative logistics which arises when a number of carriers, having both transferable and non-transferable utilities, form a coalition. The main application of the problem is last-mile delivery in urban areas. We propose mathematical models to formulate both cases of cooperation and non-cooperation as multi-objective optimization problems in which carriers seek two objectives, including maximizing profit and increasing customer coverage. To allocate the coalition outcomes to participating carriers in the proposed cooperative game, we develop mathematical conditions to define a generalized core solution concept. In addition, we develop a generalized form of the well-known Shapley value ensued by a detailed discussion on the trust issue in these games. Thereafter, two methods of reaching a compromise among coalition members are proposed. Moreover, a heuristic algorithm and a full-enumeration method are developed to find Pareto-optimal solutions for the bi-objective cooperative game. In order to evaluate the efficacy of the proposed models and algorithms, a set of benchmark instances having up to 225 customers are devised. Computational results indicate that cooperation can lead to profit improvement ranging from 9.07% in small-size instances to 14.7% in large-size instances on average, without worsening the customer coverage.