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This paper studied a bid generation problem in combinatorial transportation auctions that considered in-vehicle consolidations. The purpose of this paper seeks to establish mixed integer programming to the most profitable transportation task packages.

The authors proposes a mathematical model to identify the most profitable transportation task packages under vehicle capacity, flow balance and in-vehicle consolidation operational constraints, after which a two-phase heuristic algorithm was designed to solve the proposed model. In the first phase, a method was defined to compute bundle synergy, which was then combined with particle swarm optimization (PSO) to determine a satisfactory task package, and in the second phase, the PSO was adopted to program vehicle routings that considered in-vehicle consolidation.

Three numerical examples were given to analyze the effects of the proposed model and method, with the first two small-scale examples coming from the same data base and the third being a larger scale example. The results showed that: (1) the proposed model was able to find a satisfactory solution for the three numerical examples; (2) the computation time was significantly shorter than the accurate algorithm and (3) considering in-vehicle consolidations operations could increase the carrier profits.

The highlights of this paper are summarized as following: (1) it considers in-vehicle consolidation when generating bids to maximize profits; (2) it simultaneously identifies the most valuable lane packages and reconstructs vehicle routes and (3) proposes a simple but effective synergy-based method to solve the model.