Winner determination in combinatorial reverse auction using Dantzig-Wolfe decomposition

In this paper, the problem of winner determination in a combinatorial reverse auction mechanism is considered for solving by an exact algorithm. The considered problem is an NP-complete combinatorial optimization problem with a block-diagonal structure in its constraints. So, we propose a Dantzig-Wolfe decomposition method for its solving which includes two problem-specific methods: revised simplex method and column generation method. Since finding feasible solution for the formulated winner determination problem is NP-complete, a genetic algorithm in existing literature is used to find a feasible solution of winner determination problem that is used as an initial basic feasible solution in Dantzig-Wolfe decomposition method. The performance of the proposed Dantzig-Wolfe decomposition method is evaluated by solving several randomly generated instances of problem with different real-world sizes. Computational results show that the proposed method performs well in solving the generated problem instances with respect to solution quality and runtime.