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A distributed uncapacitated lot-sizing problem with rivaling agents (DULR) is introduced. The DULR considers concurrent items, i.e., items that can be produced by more than one agent. The agents are self-interested and have private information. They coordinate their local plans in order to find a joint global plan which minimizes total cost. The individual plans are coordinated by a collaborative planning approach based on simulated annealing. In addition to some well-known techniques a production responsibility assignment procedure and Shapley compensation payments computed by means of a modified characteristic function are incorporated. The proposed solution approach outperforms a reference value in 206 out of 272 new DULR instances. The approach is more efficient on small instances than on medium sized instances.