Project delays can affect not only the entire program but also result in various losses to subsequent projects. However, in practice, there is no difference between a program and a single project regarding delay claims, and program owners bear these losses. Although some researchers have identified this problem, feasible solutions have yet to be proposed. To solve this problem, this study establishes a project delay-response mechanism by introducing the concept of the free float between any two tasks in the schedule network, known as special free float (SFF), and proposes a hypothesis on risk-cost control for the program based on SFF and synergistic effects. In addition, a risk-cost optimization model for all involved parties is established, and the example is solved using the NSGA-Ⅲ algorithm. The results show that the claims scheme proposed in this study is feasible, adaptable, and can reduce the risk costs for both contractors and owners. This study addresses the interaction between projects within the program, resolving the transition from theoretical soundness to practical feasibility in claim schemes by considering the mutual influence of projects. It also provides valuable references for program owners in establishing claim rules.