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Manufacturing companies are using collaborative planning for the coordination of lot-sizing decisions in inter-organisational supply chains. By using collaborative planning, the members of a supply chain try to identify a production plan which results in lower costs compared to individual plans by simultaneously preserving their autonomy. A distributed lot-sizing problem with rivaling agents (DULR) is studied where each item can be produced by more than one member of the coalition (agent). Thereby it occurs that agents compete for the production quotas of items. However, the goal of this contribution is to extend the DULR by considering two types of items. One type can be produced by more than one agent, while the other one can only be produced by a certain agent due to contractual obligations. We denote the former type of items as concurrent item and the latter one as compulsory items. To solve the DULR …