The Job Shop Scheduling Problem with Power Requirements (JSPPR) extends the classical job shop scheduling problem by imposing time-varying limits on instantaneous power consumption. Previous studies have used a mixed-integer linear programming formulation and the GRASP x ELS metaheuristic, but no SAT-based exact approach or constraint programming model has been reported. This paper develops the first exact SAT and constraint programming (CP) formulations for the JSPPR. On the 35 published benchmark instances, both SAT and CP prove global optimality for all instances and obtain identical optimal makespans, substantially improving upon the best previously reported results. They also establish four improved makespan values over the GRASP x ELS results reported in the original study. CP proves optimality faster than SAT, while both exact approaches substantially improve the optimality coverage of the MILP formulations, which prove optimality on only 6 and 10 instances using CPLEX and Gurobi, respectively. The certified optimal solutions also reveal inconsistencies in several previously reported benchmark results, including makespans below the proven optimum. We provide corrected optimal makespans and a complete set of certified optimal results for the JSPPR benchmark, establishing a reliable reference for future studies.

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