This paper introduces a generalized algorithm that leverages constraint programming (CP) to solve shop scheduling problems, including the flow shop (FSSP) and job shop (JSSP). The method combines a decomposition strategy that prioritizes resources by aggregated processing time with a warm-start mechanism that transfers partial solutions between subproblems. For each selected resource, a CP subproblem is solved within an adaptive time allocation, producing progressively tighter lower bounds and high-quality feasible solutions; the best solution at termination yields a valid upper bound for the original instance. Preliminary experiments on ten Taillard FSSP benchmarks, solved with CP Optimizer, show that the decomposition approach improves the average optimality gap and relative percentage deviation relative to a direct (decomposition-less) CP baseline and produces several new best lower and upper bounds. Results highlight the promise of combining structured decomposition and warm restarting to strengthen bounds and accelerate convergence in large-scale shop scheduling with CP.