Reformulation of the set partitioning problem as a pure network with special order set constraints

In this paper, the set partitioning problem is reformulated as a network flow problem with special order sets. The reformulation is based on identifying network structure that is hidden in the element-set incidence matrix. The special order sets and the revealed network in the reformulation together define an effective structure for solution by enumeration. The resulting enumeration procedure for the solution of the set partitioning problem is computationally advantageous since it uses a pure network relaxation that is solved using reoptimization, allows a large number of variables to be fixed in a subproblem, and is defined over a relatively small enumeration tree. Computational experience is included.