Abstract We address a dynamic decision problem in which decision makers must pay some costs when they change their decisions along the way. We formalize this problem as Dynamic SAT (DynSAT) with decision change costs, whose goal is to ?nd a sequence of models that minimize the aggregation of the costs for changing variables. We provide two solutions to solve a speci?c case of this problem. The ?rst uses a Weighted Partial MaxSAT solver after we encode the entire problem as a Weighted Partial MaxSAT problem. The second solution, which we believe is novel, uses the Lagrangian decomposition technique that divides the entire problem into sub-problems, each of which can be separately solved by an exact Weighted Partial MaxSAT solver, and produces both lower and upper bounds on the optimal in an anytime manner. To compare the performance of these solvers, we experimented on the random problem and the target tracking problem. The experimental results show that a solver based on Lagrangian decomposition performs better for the random problem and competitively for the target tracking problem.